Time bar (total: 13.7s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 0 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 1 |
| 0% | 0% | 50% | 0.1% | 0% | 50% | 0% | 2 |
| 0% | 0% | 50% | 0.1% | 0% | 50% | 0% | 3 |
| 0% | 0% | 50% | 0.1% | 0% | 50% | 0% | 4 |
| 25% | 12.5% | 37.5% | 0.1% | 0% | 50% | 0% | 5 |
| 26.7% | 12.5% | 34.3% | 0.1% | 0% | 53.1% | 0% | 6 |
| 37% | 15.6% | 26.5% | 0.1% | 1.6% | 54.6% | 1.6% | 7 |
| 40.8% | 15.6% | 22.6% | 0.1% | 2.3% | 57% | 2.3% | 8 |
| 49.4% | 17.2% | 17.6% | 0.1% | 3.5% | 58.1% | 3.5% | 9 |
| 53.3% | 17.2% | 15% | 0.1% | 4.1% | 59.5% | 4.1% | 10 |
| 59.5% | 18% | 12.2% | 0.1% | 4.8% | 60.2% | 4.8% | 11 |
| 62.5% | 18% | 10.8% | 0.1% | 5.1% | 60.9% | 5.1% | 12 |
Compiled 19 to 16 computations (15.8% saved)
| 1.5s | 8256× | body | 256 | valid |
| 953.0ms | 1373× | body | 1024 | invalid |
| 203.0ms | 667× | body | 512 | invalid |
| 194.0ms | 1558× | body | 256 | invalid |
| 88.0ms | 515× | body | 256 | infinite |
| 60.0ms | 258× | body | 256 | unsamplable |
| 2× | egg-herbie |
| 1178× | rational_best_oopsla_all_46_json_45_simplify-49 |
| 1140× | rational_best_oopsla_all_46_json_45_simplify-23 |
| 942× | rational_best_oopsla_all_46_json_45_simplify-10 |
| 908× | rational_best_oopsla_all_46_json_45_simplify-7 |
| 904× | rational_best_oopsla_all_46_json_45_simplify-30 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 98 |
| 1 | 48 | 98 |
| 2 | 151 | 98 |
| 3 | 566 | 98 |
| 4 | 2732 | 98 |
| 5 | 6455 | 98 |
| 0 | 2 | 2 |
| 1× | saturated |
| 1× | node limit |
| Inputs |
|---|
0 |
1 |
| Outputs |
|---|
0 |
1 |
| Inputs |
|---|
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2))) |
| Outputs |
|---|
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2))) |
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 k (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 n) 2))) |
Compiled 20 to 17 computations (15% saved)
| 1× | egg-herbie |
| 1534× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 1242× | rational_best_oopsla_all_46_json_45_simplify-74 |
| 1000× | rational_best_oopsla_all_46_json_45_simplify-24 |
| 884× | rational_best_oopsla_all_46_json_45_simplify-23 |
| 648× | rational_best_oopsla_all_46_json_45_simplify-49 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 49 |
| 1 | 32 | 49 |
| 2 | 92 | 49 |
| 3 | 337 | 49 |
| 4 | 1622 | 49 |
| 5 | 6024 | 49 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| Outputs |
|---|
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) |
Compiled 50 to 37 computations (26% saved)
2 alts after pruning (2 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 2 | 1 | 3 |
| Fresh | 0 | 1 | 1 |
| Picked | 0 | 0 | 0 |
| Done | 0 | 0 | 0 |
| Total | 2 | 2 | 4 |
| Status | Error | Program |
|---|---|---|
| ▶ | 0.5b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
Compiled 18 to 15 computations (16.7% saved)
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.3b | (/.f64 1 (sqrt.f64 k)) |
| ✓ | 0.3b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| ✓ | 0.3b | (*.f64 (*.f64 2 (PI.f64)) n) |
| ✓ | 0.3b | (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) |
Compiled 56 to 38 computations (32.1% saved)
18 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 24.0ms | n | @ | 0 | (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) |
| 19.0ms | n | @ | -inf | (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) |
| 7.0ms | n | @ | inf | (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) |
| 2.0ms | k | @ | 0 | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| 1.0ms | k | @ | -inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| 1× | batch-egg-rewrite |
| 954× | rational_best_oopsla_all_46_json_45_simplify-35 |
| 674× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 662× | rational_best_oopsla_all_46_json_45_simplify-23 |
| 602× | rational_best_oopsla_all_46_json-2 |
| 602× | rational_best_oopsla_all_46_json-1 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 108 |
| 1 | 98 | 108 |
| 2 | 288 | 108 |
| 3 | 1284 | 108 |
| 4 | 5914 | 108 |
| 1× | node limit |
| Inputs |
|---|
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) |
(*.f64 (*.f64 2 (PI.f64)) n) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
(/.f64 1 (sqrt.f64 k)) |
| Outputs |
|---|
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| 1× | egg-herbie |
| 1418× | rational_best_oopsla_all_46_json_45_simplify-72 |
| 1184× | rational_best_oopsla_all_46_json_45_simplify-7 |
| 966× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 800× | rational_best_oopsla_all_46_json_45_simplify-24 |
| 738× | rational_best_oopsla_all_46_json_45_simplify-74 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 296 | 7414 |
| 1 | 1050 | 7368 |
| 2 | 4745 | 7336 |
| 1× | node limit |
| Inputs |
|---|
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
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(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
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(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(+.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) 0) |
(+.f64 0 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) |
(-.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) 0) |
(-.f64 0 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)))) |
(*.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) 1) |
(*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))))) |
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(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)))))) |
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)))))) |
(*.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) -1) |
(*.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) (neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))))) |
(*.f64 -1 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)))) |
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(*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) -1) |
(*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) |
(*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (*.f64 (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) |
(*.f64 -1 (neg.f64 (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (neg.f64 (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (sqrt.f64 k))) |
(neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) |
| Outputs |
|---|
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k)))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 1/8 (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1/8)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 1/8 (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (*.f64 -1/48 (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1/8))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 1/2 (+.f64 1 (neg.f64 k))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 1/2 (+.f64 1 (neg.f64 k))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 1/2 (+.f64 1 (neg.f64 k))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 1/2 (+.f64 1 (neg.f64 k))))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (/.f64 1 k))) |
(*.f64 (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (/.f64 1 k))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (/.f64 1 k))) |
(*.f64 (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (/.f64 1 k))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (/.f64 1 k))) |
(*.f64 (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (/.f64 1 k))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (/.f64 1 k))) |
(*.f64 (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (/.f64 1 k))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) (sqrt.f64 (/.f64 1 k))) |
(*.f64 (exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k)))) (sqrt.f64 (/.f64 1 k))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) (sqrt.f64 (/.f64 1 k))) |
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(/.f64 1 (sqrt.f64 k)) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 1 (sqrt.f64 k)) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 1 (sqrt.f64 k)) |
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k))) |
(/.f64 1 (sqrt.f64 k)) |
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 1 (sqrt.f64 k)) |
(*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) -1) |
(/.f64 1 (sqrt.f64 k)) |
(*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 1 (sqrt.f64 k)) |
(*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (*.f64 (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 1 (sqrt.f64 k)) |
(*.f64 -1 (neg.f64 (/.f64 1 (sqrt.f64 k)))) |
(/.f64 1 (sqrt.f64 k)) |
(*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (sqrt.f64 k))) |
(/.f64 1 (sqrt.f64 k)) |
(*.f64 (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (neg.f64 (/.f64 1 (sqrt.f64 k)))) |
(/.f64 1 (sqrt.f64 k)) |
(*.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (sqrt.f64 k))) |
(/.f64 1 (sqrt.f64 k)) |
(neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) |
(/.f64 1 (sqrt.f64 k)) |
Compiled 5656 to 3243 computations (42.7% saved)
9 alts after pruning (8 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 170 | 8 | 178 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 170 | 9 | 179 |
| Status | Error | Program |
|---|---|---|
| ▶ | 0.5b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2))) |
| ✓ | 0.5b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| ▶ | 22.0b | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))) |
| ▶ | 21.7b | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))) |
| 21.9b | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))))) | |
| 21.1b | (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)))))) | |
| ▶ | 22.2b | (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
| 3.3b | (*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) | |
| ▶ | 3.7b | (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))) |
Compiled 606 to 439 computations (27.6% saved)
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.3b | (/.f64 1 (sqrt.f64 k)) | |
| ✓ | 0.3b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2))) |
| ✓ | 0.3b | (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) |
| ✓ | 0.3b | (pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2)) |
Compiled 112 to 78 computations (30.4% saved)
15 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | k | @ | 0 | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2))) |
| 0.0ms | k | @ | -inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2))) |
| 0.0ms | k | @ | inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2))) |
| 0.0ms | k | @ | 0 | (pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2)) |
| 0.0ms | n | @ | 0 | (pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2)) |
| 1× | batch-egg-rewrite |
| 1154× | rational_best_oopsla_all_46_json_45_simplify-23 |
| 1138× | rational_best_oopsla_all_46_json_45_simplify-13 |
| 1120× | rational_best_oopsla_all_46_json_45_simplify-37 |
| 1016× | rational_best_oopsla_all_46_json-2 |
| 1016× | rational_best_oopsla_all_46_json-1 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 23 | 193 |
| 1 | 144 | 193 |
| 2 | 466 | 163 |
| 3 | 2421 | 145 |
| 1× | node limit |
| Inputs |
|---|
(pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2)) |
(*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2))) |
| Outputs |
|---|
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| 1× | egg-herbie |
| 1338× | rational_best_oopsla_all_46_json_45_simplify-49 |
| 1124× | rational_best_oopsla_all_46_json_45_simplify-37 |
| 1000× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 920× | rational_best_oopsla_all_46_json_45_simplify-7 |
| 880× | rational_best_oopsla_all_46_json_45_simplify-24 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 351 | 11315 |
| 1 | 1260 | 11229 |
| 2 | 4686 | 11229 |
| 1× | node limit |
| Inputs |
|---|
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
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(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
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(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(+.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) 0) |
(+.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))) 0)) |
(+.f64 0 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))) |
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(-.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) 0) |
(-.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))) 0)) |
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(-.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))) -1) 0) |
(*.f64 1 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))) |
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(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))) (neg.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))))) |
| Outputs |
|---|
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))) (*.f64 1/8 (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))))) |
(+.f64 (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))) (*.f64 1/8 (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3))) (*.f64 -1/48 (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))) (*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))) (*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (neg.f64 k))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (neg.f64 k))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (neg.f64 k))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (neg.f64 k))))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 n (*.f64 2 (PI.f64))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
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(/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))) (neg.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))))) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))))) |
(*.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.3b | (/.f64 1 (sqrt.f64 k)) | |
| ✓ | 0.3b | (*.f64 n (PI.f64)) |
| ✓ | 0.4b | (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
| ✓ | 0.5b | (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
Compiled 41 to 21 computations (48.8% saved)
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | n | @ | 0 | (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
| 1.0ms | k | @ | -inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
| 1.0ms | k | @ | 0 | (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
| 1.0ms | n | @ | -inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
| 1.0ms | n | @ | 0 | (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
| 1× | batch-egg-rewrite |
| 944× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 788× | rational_best_oopsla_all_46_json_45_simplify-23 |
| 754× | rational_best_oopsla_all_46_json_45_simplify-37 |
| 746× | rational_best_oopsla_all_46_json_45_simplify-87 |
| 746× | rational_best_oopsla_all_46_json_45_simplify-13 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 71 |
| 1 | 98 | 71 |
| 2 | 328 | 71 |
| 3 | 1597 | 71 |
| 4 | 7360 | 71 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 n (PI.f64)) |
| Outputs |
|---|
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| 1× | egg-herbie |
| 1730× | rational_best_oopsla_all_46_json_45_simplify-10 |
| 896× | rational_best_oopsla_all_46_json_45_simplify-72 |
| 870× | rational_best_oopsla_all_46_json_45_simplify-23 |
| 720× | rational_best_oopsla_all_46_json_45_simplify-30 |
| 664× | rational_best_oopsla_all_46_json_45_simplify-77 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 260 | 5426 |
| 1 | 859 | 5426 |
| 2 | 3009 | 5388 |
| 3 | 7748 | 5388 |
| 1× | node limit |
| Inputs |
|---|
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(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) 0) |
(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 1 (sqrt.f64 k)))) 0)) |
(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) 0)) |
(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0)) |
(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) 0)) |
(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))))) 0)) |
(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) 0)) |
(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) 0)) |
(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) 0)) |
(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (/.f64 1 (sqrt.f64 k)))) 0)) |
(-.f64 0 (*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (/.f64 1 (sqrt.f64 k))))) |
(-.f64 0 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (/.f64 1 (sqrt.f64 k)))))) |
(-.f64 0 (*.f64 1 (*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (/.f64 1 (sqrt.f64 k)))))) |
(-.f64 0 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (/.f64 1 (sqrt.f64 k)))))) |
(-.f64 0 (*.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))))) |
(-.f64 0 (*.f64 -1 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))))) |
(-.f64 0 (*.f64 (neg.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 0 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (/.f64 1 (sqrt.f64 k)))) (sqrt.f64 2))) |
(-.f64 (*.f64 0 (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))))) (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))))) (*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (/.f64 1 (sqrt.f64 k)))))) |
(-.f64 (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) 1) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(neg.f64 (*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (/.f64 1 (sqrt.f64 k))))) |
(neg.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (/.f64 1 (sqrt.f64 k)))))) |
(neg.f64 (*.f64 1 (*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (/.f64 1 (sqrt.f64 k)))))) |
(neg.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (/.f64 1 (sqrt.f64 k)))))) |
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))))) |
(neg.f64 (*.f64 -1 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))))) |
(neg.f64 (*.f64 (neg.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (/.f64 1 (sqrt.f64 k)))) |
(neg.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (/.f64 1 (sqrt.f64 k)))) (sqrt.f64 2))) |
(+.f64 (*.f64 n (PI.f64)) 0) |
(+.f64 (*.f64 n (PI.f64)) (*.f64 (*.f64 n (/.f64 (PI.f64) (PI.f64))) 0)) |
(+.f64 (*.f64 n (PI.f64)) (*.f64 (*.f64 n (PI.f64)) 0)) |
(+.f64 (*.f64 n (PI.f64)) (*.f64 (*.f64 n (/.f64 (PI.f64) n)) 0)) |
(+.f64 (*.f64 n (PI.f64)) (*.f64 (*.f64 (/.f64 n n) (*.f64 (PI.f64) (/.f64 n n))) 0)) |
(+.f64 (*.f64 n (PI.f64)) (*.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))) 0)) |
(+.f64 (*.f64 n (PI.f64)) (*.f64 (neg.f64 (*.f64 (PI.f64) (/.f64 n n))) 0)) |
(+.f64 0 (*.f64 n (PI.f64))) |
(+.f64 (*.f64 0 (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))) (*.f64 n (PI.f64))) |
(+.f64 (*.f64 0 (*.f64 n (/.f64 (PI.f64) n))) (*.f64 n (PI.f64))) |
(+.f64 (*.f64 0 (*.f64 (/.f64 n n) (*.f64 (PI.f64) (/.f64 n n)))) (*.f64 n (PI.f64))) |
(+.f64 (*.f64 0 (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (*.f64 n (PI.f64))) |
(-.f64 (*.f64 n (PI.f64)) 0) |
(-.f64 (*.f64 n (PI.f64)) (*.f64 (*.f64 n (/.f64 (PI.f64) (PI.f64))) 0)) |
(-.f64 (*.f64 n (PI.f64)) (*.f64 (*.f64 n (PI.f64)) 0)) |
(-.f64 (*.f64 n (PI.f64)) (*.f64 (*.f64 n (/.f64 (PI.f64) n)) 0)) |
(-.f64 (*.f64 n (PI.f64)) (*.f64 (*.f64 (/.f64 n n) (*.f64 (PI.f64) (/.f64 n n))) 0)) |
(-.f64 (*.f64 n (PI.f64)) (*.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))) 0)) |
(-.f64 (*.f64 n (PI.f64)) (*.f64 (neg.f64 (*.f64 (PI.f64) (/.f64 n n))) 0)) |
(-.f64 0 (*.f64 n (neg.f64 (PI.f64)))) |
(-.f64 0 (*.f64 1 (*.f64 n (neg.f64 (PI.f64))))) |
(-.f64 0 (*.f64 (/.f64 n n) (*.f64 n (neg.f64 (PI.f64))))) |
(-.f64 0 (*.f64 -1 (*.f64 n (PI.f64)))) |
(-.f64 0 (*.f64 (neg.f64 (*.f64 (PI.f64) (/.f64 n n))) n)) |
(-.f64 (*.f64 0 (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))) (*.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))) (*.f64 n (neg.f64 (PI.f64))))) |
(/.f64 (*.f64 n (PI.f64)) 1) |
(/.f64 (*.f64 n (PI.f64)) (/.f64 n n)) |
(/.f64 (*.f64 n (PI.f64)) (/.f64 (PI.f64) (PI.f64))) |
(/.f64 (*.f64 n (PI.f64)) (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))) |
(/.f64 (*.f64 n (PI.f64)) (/.f64 (/.f64 n n) (/.f64 n n))) |
(/.f64 (*.f64 n (PI.f64)) (/.f64 (*.f64 (PI.f64) (/.f64 n n)) (*.f64 (PI.f64) (/.f64 n n)))) |
(/.f64 (*.f64 n (PI.f64)) (/.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))) (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))))) |
(/.f64 (*.f64 n (PI.f64)) (/.f64 (*.f64 n (/.f64 (PI.f64) (PI.f64))) (*.f64 n (/.f64 (PI.f64) (PI.f64))))) |
(/.f64 (*.f64 n (PI.f64)) (/.f64 (*.f64 n (/.f64 (PI.f64) n)) (*.f64 n (/.f64 (PI.f64) n)))) |
(/.f64 (*.f64 n (PI.f64)) (/.f64 (*.f64 (/.f64 n n) (*.f64 (PI.f64) (/.f64 n n))) (*.f64 (/.f64 n n) (*.f64 (PI.f64) (/.f64 n n))))) |
(neg.f64 (*.f64 n (neg.f64 (PI.f64)))) |
(neg.f64 (*.f64 1 (*.f64 n (neg.f64 (PI.f64))))) |
(neg.f64 (*.f64 (/.f64 n n) (*.f64 n (neg.f64 (PI.f64))))) |
(neg.f64 (*.f64 -1 (*.f64 n (PI.f64)))) |
(neg.f64 (*.f64 (neg.f64 (*.f64 (PI.f64) (/.f64 n n))) n)) |
| Outputs |
|---|
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) 0) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0)) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) 0)) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2))) 0)) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0)) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 0 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 0 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(-.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) 0) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(-.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0)) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(-.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) 0)) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(-.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2))) 0)) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(-.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0)) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(-.f64 0 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2)))) |
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2)))) |
(*.f64 1 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
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(*.f64 n (PI.f64)) |
(/.f64 (*.f64 n (PI.f64)) (/.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))) (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))))) |
(/.f64 (*.f64 n (PI.f64)) (/.f64 (*.f64 n (/.f64 (PI.f64) (PI.f64))) (*.f64 n (/.f64 (PI.f64) (PI.f64))))) |
(/.f64 (*.f64 n (PI.f64)) (/.f64 (*.f64 n (/.f64 (PI.f64) n)) (*.f64 n (/.f64 (PI.f64) n)))) |
(/.f64 (*.f64 n (PI.f64)) (/.f64 (*.f64 (/.f64 n n) (*.f64 (PI.f64) (/.f64 n n))) (*.f64 (/.f64 n n) (*.f64 (PI.f64) (/.f64 n n))))) |
(/.f64 (*.f64 n (PI.f64)) (/.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n n) (/.f64 n n))) (*.f64 (PI.f64) (*.f64 (/.f64 n n) (/.f64 n n))))) |
(neg.f64 (*.f64 n (neg.f64 (PI.f64)))) |
(*.f64 n (PI.f64)) |
(neg.f64 (*.f64 1 (*.f64 n (neg.f64 (PI.f64))))) |
(*.f64 n (PI.f64)) |
(neg.f64 (*.f64 (/.f64 n n) (*.f64 n (neg.f64 (PI.f64))))) |
(*.f64 n (PI.f64)) |
(neg.f64 (*.f64 -1 (*.f64 n (PI.f64)))) |
(*.f64 n (PI.f64)) |
(neg.f64 (*.f64 (neg.f64 (*.f64 (PI.f64) (/.f64 n n))) n)) |
(*.f64 n (PI.f64)) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.3b | (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))) |
| ✓ | 0.4b | (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
| ✓ | 1.0b | (log.f64 (*.f64 2 (PI.f64))) |
| ✓ | 3.3b | (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
Compiled 85 to 60 computations (29.4% saved)
15 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 86.0ms | n | @ | -inf | (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
| 60.0ms | n | @ | inf | (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
| 16.0ms | n | @ | 0 | (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
| 2.0ms | k | @ | 0 | (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))) |
| 1.0ms | k | @ | -inf | (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))) |
| 1× | batch-egg-rewrite |
| 968× | rational_best_oopsla_all_46_json_45_simplify-13 |
| 968× | rational_best_oopsla_all_46_json_45_simplify-37 |
| 944× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 828× | rational_best_oopsla_all_46_json-2 |
| 828× | rational_best_oopsla_all_46_json-1 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 142 |
| 1 | 130 | 142 |
| 2 | 393 | 142 |
| 3 | 1781 | 142 |
| 1× | node limit |
| Inputs |
|---|
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
(log.f64 (*.f64 2 (PI.f64))) |
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))) |
| Outputs |
|---|
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| 1× | egg-herbie |
| 1016× | rational_best_oopsla_all_46_json_45_simplify-72 |
| 908× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 760× | rational_best_oopsla_all_46_json_45_simplify-24 |
| 722× | rational_best_oopsla_all_46_json_45_simplify-74 |
| 564× | rational_best_oopsla_all_46_json_45_simplify-82 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 277 | 8294 |
| 1 | 1032 | 8238 |
| 2 | 4101 | 8230 |
| 1× | node limit |
| Inputs |
|---|
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
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(exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
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(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))) (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k)))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k)))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))))) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k)))) (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k)))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k)))) (/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k)))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))))) (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))))))) |
| Outputs |
|---|
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 n)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 n)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 n)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 n)))))))) |
(exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) |
(+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 -1/2 (*.f64 k (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))) |
(+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 k (*.f64 -1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))))) |
(+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 -1/2 (*.f64 k (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))))) |
(+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 2)))) (*.f64 -1/2 (*.f64 k (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))) |
(+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (*.f64 k (*.f64 -1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))) (*.f64 1/8 (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 (pow.f64 k 2) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 2)))))) |
(+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (*.f64 -1/2 (*.f64 k (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))) (*.f64 1/8 (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 (pow.f64 k 2) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 2)))))) |
(+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 3)))) (+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 2)))) (*.f64 -1/2 (*.f64 k (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))))) |
(+.f64 (+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (*.f64 k (*.f64 -1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))) (*.f64 1/8 (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 (pow.f64 k 2) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 2)))))) (*.f64 -1/48 (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 (pow.f64 k 3) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 3))))) |
(+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (*.f64 -1/2 (*.f64 k (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))) (+.f64 (*.f64 -1/48 (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 (pow.f64 k 3) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 3)))) (*.f64 1/8 (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 (pow.f64 k 2) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 2))))))) |
(+.f64 (*.f64 1/8 (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 (pow.f64 k 2) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 2)))) (+.f64 (*.f64 k (*.f64 -1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))) (+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 -1/48 (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 (pow.f64 k 3) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 3))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (+.f64 1 (*.f64 -1 k))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1 (neg.f64 k))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (+.f64 1 (*.f64 -1 k))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1 (neg.f64 k))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (+.f64 1 (*.f64 -1 k))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1 (neg.f64 k))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (+.f64 1 (*.f64 -1 k))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1 (neg.f64 k))))) |
(+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) |
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
(+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) |
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) |
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(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))))) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))))))) |
(/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))) (/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))) (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))) (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k)))) (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k)))))) |
(/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k)))) (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k)))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k)))) (/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k)))))) |
(/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))) (/.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))) (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))) (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))))) (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.3b | (*.f64 n (*.f64 2 (PI.f64))) |
| 0.5b | (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) | |
| ✓ | 0.5b | (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) |
| ✓ | 4.1b | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))) |
Compiled 145 to 86 computations (40.7% saved)
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | n | @ | -inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))) |
| 2.0ms | k | @ | inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))) |
| 2.0ms | n | @ | inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))) |
| 2.0ms | n | @ | 0 | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))) |
| 1.0ms | k | @ | -inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))) |
| 1× | batch-egg-rewrite |
| 1836× | rational_best_oopsla_all_46_json-2 |
| 1836× | rational_best_oopsla_all_46_json-1 |
| 1836× | rational_best_oopsla_all_46_json-4 |
| 1836× | rational_best_oopsla_all_46_json-3 |
| 924× | rational_best_oopsla_all_46_json_45_simplify-7 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 147 |
| 1 | 175 | 129 |
| 2 | 693 | 129 |
| 3 | 3969 | 129 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))) |
(*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) |
(*.f64 n (*.f64 2 (PI.f64))) |
| Outputs |
|---|
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(*.f64 2 (PI.f64)))))))))))))))) |
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 0 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 0 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 0 (neg.f64 (sqrt.f64 2))) (*.f64 (neg.f64 (sqrt.f64 2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 0 (neg.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (neg.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))))))) |
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 n (*.f64 2 (PI.f64))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 0 (*.f64 2 (*.f64 (PI.f64) (/.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 n (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 0 (*.f64 2 (*.f64 (PI.f64) (/.f64 n n)))) (*.f64 n (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (*.f64 2 (PI.f64))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (*.f64 -2 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 0 (neg.f64 n)) (*.f64 (neg.f64 n) (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 0 (*.f64 -2 (PI.f64))) (*.f64 (*.f64 -2 (PI.f64)) n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 2 (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 n n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 2 (PI.f64)) (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (PI.f64) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 n (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n n))) (*.f64 2 (*.f64 (PI.f64) (/.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))) |
| 1× | egg-herbie |
| 1024× | rational_best_oopsla_all_46_json_45_simplify-10 |
| 996× | rational_best_oopsla_all_46_json_45_simplify-30 |
| 954× | rational_best_oopsla_all_46_json_45_simplify-77 |
| 836× | rational_best_oopsla_all_46_json_45_simplify-13 |
| 714× | rational_best_oopsla_all_46_json_45_simplify-35 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 132 | 2922 |
| 1 | 461 | 2906 |
| 2 | 2030 | 2906 |
| 3 | 5043 | 2906 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) |
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) |
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) |
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) |
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))) |
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))) |
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))) |
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))) |
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))) |
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))) |
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))) |
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) 0) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (*.f64 0 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))))) |
(+.f64 0 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))) |
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))) |
(-.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) 0) |
(-.f64 (*.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))) |
(-.f64 (*.f64 0 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (/.f64 1 (sqrt.f64 k)))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) 1) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 0) |
(+.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 0 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) |
(+.f64 0 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) |
(+.f64 (*.f64 0 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) |
(-.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 0) |
(-.f64 (*.f64 0 (neg.f64 (sqrt.f64 2))) (*.f64 (neg.f64 (sqrt.f64 2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) |
(-.f64 (*.f64 0 (neg.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (neg.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 2))) |
(/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 1) |
(/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) |
(/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) |
(/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) |
(+.f64 (*.f64 n (*.f64 2 (PI.f64))) 0) |
(+.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 0 (*.f64 2 (*.f64 (PI.f64) (/.f64 n n))))) |
(+.f64 0 (*.f64 n (*.f64 2 (PI.f64)))) |
(+.f64 (*.f64 0 (*.f64 2 (*.f64 (PI.f64) (/.f64 n n)))) (*.f64 n (*.f64 2 (PI.f64)))) |
(-.f64 (*.f64 n (*.f64 2 (PI.f64))) 0) |
(-.f64 0 (*.f64 -2 (*.f64 n (PI.f64)))) |
(-.f64 (*.f64 0 (neg.f64 n)) (*.f64 (neg.f64 n) (*.f64 2 (PI.f64)))) |
(-.f64 (*.f64 0 (*.f64 -2 (PI.f64))) (*.f64 (*.f64 -2 (PI.f64)) n)) |
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) 1) |
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 n n)) |
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 2 (PI.f64)) (*.f64 2 (PI.f64)))) |
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (PI.f64) (PI.f64))) |
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))) |
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 n (*.f64 2 (PI.f64))))) |
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n n))) (*.f64 2 (*.f64 (PI.f64) (/.f64 n n))))) |
(neg.f64 (*.f64 -2 (*.f64 n (PI.f64)))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) |
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) |
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) |
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) |
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))) |
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))) |
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) |
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))) |
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))) |
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) |
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))) |
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))) |
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) |
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))) |
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))) |
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))) |
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))) |
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))) |
(*.f64 (sqrt.f64 2) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))) |
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))) |
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))) |
(*.f64 (sqrt.f64 2) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))) |
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(/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) |
(/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) |
(*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) |
(+.f64 (*.f64 n (*.f64 2 (PI.f64))) 0) |
(*.f64 2 (*.f64 (PI.f64) n)) |
(+.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 0 (*.f64 2 (*.f64 (PI.f64) (/.f64 n n))))) |
(*.f64 2 (*.f64 (PI.f64) n)) |
(+.f64 0 (*.f64 n (*.f64 2 (PI.f64)))) |
(*.f64 2 (*.f64 (PI.f64) n)) |
(+.f64 (*.f64 0 (*.f64 2 (*.f64 (PI.f64) (/.f64 n n)))) (*.f64 n (*.f64 2 (PI.f64)))) |
(*.f64 2 (*.f64 (PI.f64) n)) |
(-.f64 (*.f64 n (*.f64 2 (PI.f64))) 0) |
(*.f64 2 (*.f64 (PI.f64) n)) |
(-.f64 0 (*.f64 -2 (*.f64 n (PI.f64)))) |
(neg.f64 (*.f64 n (*.f64 (PI.f64) -2))) |
(*.f64 (*.f64 (PI.f64) -2) (neg.f64 n)) |
(-.f64 (*.f64 0 (neg.f64 n)) (*.f64 (neg.f64 n) (*.f64 2 (PI.f64)))) |
(*.f64 2 (*.f64 (PI.f64) n)) |
(-.f64 (*.f64 0 (*.f64 -2 (PI.f64))) (*.f64 (*.f64 -2 (PI.f64)) n)) |
(neg.f64 (*.f64 n (*.f64 (PI.f64) -2))) |
(*.f64 (*.f64 (PI.f64) -2) (neg.f64 n)) |
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) 1) |
(*.f64 2 (*.f64 (PI.f64) n)) |
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 n n)) |
(*.f64 2 (*.f64 (PI.f64) n)) |
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 2 (PI.f64)) (*.f64 2 (PI.f64)))) |
(*.f64 2 (*.f64 (PI.f64) n)) |
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (PI.f64) (PI.f64))) |
(*.f64 2 (*.f64 (PI.f64) n)) |
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))) |
(*.f64 2 (*.f64 (PI.f64) n)) |
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 n (*.f64 2 (PI.f64))))) |
(*.f64 2 (*.f64 (PI.f64) n)) |
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n n))) (*.f64 2 (*.f64 (PI.f64) (/.f64 n n))))) |
(*.f64 2 (*.f64 (PI.f64) n)) |
(neg.f64 (*.f64 -2 (*.f64 n (PI.f64)))) |
(neg.f64 (*.f64 n (*.f64 (PI.f64) -2))) |
(*.f64 (*.f64 (PI.f64) -2) (neg.f64 n)) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 1.4b | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))) |
| ✓ | 1.5b | (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))) |
| ✓ | 2.1b | (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
| ✓ | 12.0b | (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))) |
Compiled 504 to 310 computations (38.5% saved)
24 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 11.0ms | k | @ | 0 | (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
| 7.0ms | k | @ | 0 | (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))) |
| 4.0ms | n | @ | inf | (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))) |
| 4.0ms | n | @ | -inf | (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))) |
| 4.0ms | n | @ | -inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))) |
| 1× | batch-egg-rewrite |
| 894× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 826× | rational_best_oopsla_all_46_json_45_simplify-35 |
| 802× | rational_best_oopsla_all_46_json_45_simplify-74 |
| 744× | rational_best_oopsla_all_46_json_45_simplify-37 |
| 672× | rational_best_oopsla_all_46_json-2 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 41 | 532 |
| 1 | 295 | 532 |
| 2 | 1175 | 514 |
| 3 | 5905 | 514 |
| 1× | node limit |
| Inputs |
|---|
(+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n 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(sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 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| 1× | egg-herbie |
| 1292× | rational_best_oopsla_all_46_json_45_simplify-37 |
| 846× | rational_best_oopsla_all_46_json_45_simplify-72 |
| 694× | rational_best_oopsla_all_46_json_45_simplify-49 |
| 682× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 578× | rational_best_oopsla_all_46_json_45_simplify-7 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 195 | 12439 |
| 1 | 702 | 11935 |
| 2 | 3271 | 11935 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
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(*.f64 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))) |
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(*.f64 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))) |
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(*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))) (*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))) (/.f64 1 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) |
(*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))) (*.f64 (/.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))) (/.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) |
(*.f64 1 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))) |
(*.f64 (/.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))) |
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(+.f64 (*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))) (/.f64 1 (sqrt.f64 k))) (+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))))) |
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))))) |
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 1 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))) (*.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 0 (*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))))) |
(+.f64 (+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))) (*.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) 0) |
(-.f64 (*.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))))) |
(-.f64 (*.f64 0 (neg.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))))) (*.f64 (neg.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (/.f64 1 (sqrt.f64 k)))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) 1) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (/.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (/.f64 (*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) |
| Outputs |
|---|
(*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) |
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(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (/.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (*.f64 1/8 (pow.f64 k 2))))))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2))))))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (*.f64 1/8 (pow.f64 k 2))))))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (*.f64 1/8 (pow.f64 k 2))))))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (*.f64 1/8 (pow.f64 k 2))))))))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2))))))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2))))))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2))))))))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (/.f64 (*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (*.f64 1/8 (pow.f64 k 2))))))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2))))))))) |
Compiled 37850 to 23109 computations (38.9% saved)
16 alts after pruning (12 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 804 | 11 | 815 |
| Fresh | 2 | 1 | 3 |
| Picked | 1 | 0 | 1 |
| Done | 1 | 4 | 5 |
| Total | 808 | 16 | 824 |
| Status | Error | Program |
|---|---|---|
| 22.2b | (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) 1) | |
| 21.7b | (+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) | |
| 0.5b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 0 (*.f64 (*.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n (*.f64 2 (PI.f64)))) (/.f64 (*.f64 2 (PI.f64)) (*.f64 (*.f64 2 (PI.f64)) (/.f64 n (*.f64 2 (PI.f64)))))) (*.f64 -2 (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2))) | |
| ▶ | 0.5b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2))) |
| ✓ | 0.5b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| ▶ | 0.5b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2))) |
| 21.7b | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (*.f64 1/8 (pow.f64 k 2))))))))) | |
| 21.9b | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))))))) | |
| ✓ | 22.0b | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))) |
| 21.1b | (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)))))) | |
| ✓ | 22.2b | (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
| ▶ | 3.3b | (*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) |
| ▶ | 21.9b | (*.f64 (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) |
| ✓ | 3.7b | (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))) |
| 25.2b | (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) | |
| ▶ | 22.2b | (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
Compiled 1020 to 735 computations (27.9% saved)
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.3b | (/.f64 1 (sqrt.f64 k)) | |
| ✓ | 0.3b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2))) |
| ✓ | 0.3b | (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) |
| ✓ | 0.5b | (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) |
Compiled 88 to 59 computations (33% saved)
15 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | k | @ | 0 | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2))) |
| 0.0ms | k | @ | -inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2))) |
| 0.0ms | k | @ | inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2))) |
| 0.0ms | k | @ | 0 | (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) |
| 0.0ms | n | @ | inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2))) |
| 1× | batch-egg-rewrite |
| 1082× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 950× | rational_best_oopsla_all_46_json_45_simplify-23 |
| 902× | rational_best_oopsla_all_46_json_45_simplify-13 |
| 886× | rational_best_oopsla_all_46_json_45_simplify-87 |
| 880× | rational_best_oopsla_all_46_json_45_simplify-37 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 163 |
| 1 | 129 | 163 |
| 2 | 415 | 163 |
| 3 | 1935 | 163 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) |
(pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2))) |
| Outputs |
|---|
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(PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))))))))) |
| 1× | egg-herbie |
| 1520× | rational_best_oopsla_all_46_json_45_simplify-37 |
| 1336× | rational_best_oopsla_all_46_json_45_simplify-13 |
| 952× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 912× | rational_best_oopsla_all_46_json_45_simplify-7 |
| 824× | rational_best_oopsla_all_46_json_45_simplify-24 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 337 | 11798 |
| 1 | 1191 | 11750 |
| 2 | 4577 | 11738 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 2 (*.f64 n (PI.f64))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))) |
(+.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) 0) |
(+.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) 0)) |
(+.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (*.f64 (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))) 0)) |
(+.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (*.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) 4)) (/.f64 n (*.f64 2 (PI.f64))))) 0)) |
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(+.f64 (*.f64 0 (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64))))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4)))) |
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(-.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) 0) |
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(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)))) (neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))))) |
| Outputs |
|---|
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 2 n)) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 2 n)) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 2 n)) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 2 n)) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 2 n)) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 2 n)) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 2 n)) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 2 n)) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 2 n)) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 2 n)) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 2 n)) |
(*.f64 2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 2 n)) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2)))))) |
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k)))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 1/8 (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 1/8 (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (*.f64 -1/48 (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))) (*.f64 -1/48 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (neg.f64 k))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) (+.f64 1 (neg.f64 k))))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
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(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)))) (neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)))))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (-.f64 (/.f64 1 (sqrt.f64 k)) 0) (-.f64 (/.f64 1 (sqrt.f64 k)) 0))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (neg.f64 (/.f64 1 (sqrt.f64 k))))) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.3b | (/.f64 1 (sqrt.f64 k)) | |
| 0.3b | (*.f64 n (PI.f64)) | |
| ✓ | 0.4b | (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
| ✓ | 0.5b | (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
Compiled 41 to 23 computations (43.9% saved)
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | k | @ | -inf | (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
| 0.0ms | k | @ | 0 | (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
| 0.0ms | k | @ | inf | (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
| 0.0ms | k | @ | -inf | (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
| 0.0ms | n | @ | -inf | (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
| 1× | batch-egg-rewrite |
| 936× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 788× | rational_best_oopsla_all_46_json_45_simplify-23 |
| 754× | rational_best_oopsla_all_46_json_45_simplify-37 |
| 752× | rational_best_oopsla_all_46_json_45_simplify-87 |
| 746× | rational_best_oopsla_all_46_json_45_simplify-13 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 60 |
| 1 | 98 | 60 |
| 2 | 328 | 60 |
| 3 | 1606 | 60 |
| 4 | 7367 | 60 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
| Outputs |
|---|
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| 1× | egg-herbie |
| 1236× | rational_best_oopsla_all_46_json_45_simplify-10 |
| 1216× | rational_best_oopsla_all_46_json_45_simplify-30 |
| 814× | rational_best_oopsla_all_46_json_45_simplify-37 |
| 658× | rational_best_oopsla_all_46_json_45_simplify-72 |
| 634× | rational_best_oopsla_all_46_json_45_simplify-23 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 188 | 4476 |
| 1 | 614 | 4476 |
| 2 | 2169 | 4468 |
| 3 | 5586 | 4468 |
| 1× | node limit |
| Inputs |
|---|
(+.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) 0) |
(+.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0)) |
(+.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) 0)) |
(+.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2))) 0)) |
(+.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0)) |
(+.f64 0 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 0 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) 0) |
(-.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0)) |
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(-.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2))) 0)) |
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(-.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2)))) |
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(-.f64 0 (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2))))) |
(-.f64 0 (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (sqrt.f64 2))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) 1) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2))) -1) |
(neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2)))) |
(neg.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2))))) |
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(neg.f64 (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (sqrt.f64 2))) |
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(+.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) 0)) |
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(+.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0)) |
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(+.f64 (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
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(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) 0) |
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(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) 0)) |
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(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) 1) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) |
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(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))) |
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(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))) |
(neg.f64 (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))) |
(neg.f64 (*.f64 (sqrt.f64 2) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(neg.f64 (*.f64 1 (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))) |
(neg.f64 (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))) |
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(neg.f64 (*.f64 -1 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(neg.f64 (*.f64 (neg.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) |
(neg.f64 (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (sqrt.f64 2))) |
| Outputs |
|---|
(+.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) 0) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(+.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0)) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(+.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) 0)) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(+.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2))) 0)) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(+.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0)) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(+.f64 0 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(+.f64 (*.f64 0 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(-.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) 0) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(-.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0)) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(-.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) 0)) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(-.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2))) 0)) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(-.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0)) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(-.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2)))) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(-.f64 0 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2))))) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(-.f64 0 (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2))))) |
(neg.f64 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))))) |
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (sqrt.f64 k))))) |
(neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))))) |
(-.f64 0 (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (sqrt.f64 2))) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) 1) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2))) -1) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2)))) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(neg.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2))))) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(neg.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2))))) |
(neg.f64 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))))) |
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (sqrt.f64 k))))) |
(neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))))) |
(neg.f64 (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (sqrt.f64 2))) |
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) |
(+.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) 0) |
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) 0)) |
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) 0)) |
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) 0)) |
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) 0)) |
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0)) |
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (*.f64 n (PI.f64))))) 0)) |
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) 0)) |
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) 0)) |
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) 0)) |
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 0 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 0 (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
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(neg.f64 (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (sqrt.f64 2))) |
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.3b | (/.f64 1 (sqrt.f64 k)) | |
| ✓ | 0.3b | (*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) |
| 0.3b | (*.f64 n (*.f64 2 (PI.f64))) | |
| ✓ | 3.3b | (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
Compiled 82 to 58 computations (29.3% saved)
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | k | @ | 0 | (*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) |
| 1.0ms | n | @ | -inf | (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
| 1.0ms | n | @ | 0 | (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
| 1.0ms | k | @ | -inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) |
| 0.0ms | n | @ | inf | (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
| 1× | batch-egg-rewrite |
| 1036× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 1008× | rational_best_oopsla_all_46_json_45_simplify-13 |
| 880× | rational_best_oopsla_all_46_json_45_simplify-23 |
| 866× | rational_best_oopsla_all_46_json_45_simplify-87 |
| 864× | rational_best_oopsla_all_46_json-2 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 20 | 98 |
| 1 | 124 | 98 |
| 2 | 404 | 98 |
| 3 | 1886 | 98 |
| 1× | node limit |
| Inputs |
|---|
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) |
| Outputs |
|---|
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| 1× | egg-herbie |
| 1480× | rational_best_oopsla_all_46_json_45_simplify-37 |
| 1286× | rational_best_oopsla_all_46_json_45_simplify-13 |
| 828× | rational_best_oopsla_all_46_json_45_simplify-49 |
| 728× | rational_best_oopsla_all_46_json_45_simplify-72 |
| 626× | rational_best_oopsla_all_46_json_45_simplify-89 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 216 | 6787 |
| 1 | 756 | 6743 |
| 2 | 2968 | 6731 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
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(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
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(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
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(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))) |
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(-.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) 0)) |
(-.f64 0 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (neg.f64 (/.f64 1 (sqrt.f64 k))))) |
(-.f64 0 (*.f64 1 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (neg.f64 (/.f64 1 (sqrt.f64 k)))))) |
(-.f64 0 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (neg.f64 (/.f64 1 (sqrt.f64 k)))))) |
(-.f64 0 (*.f64 -1 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))))) |
(-.f64 0 (*.f64 (neg.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 0 (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (neg.f64 (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) 1) |
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) |
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (neg.f64 (neg.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1/8)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))) (*.f64 -1/48 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))) (*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (+.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1/8)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/48))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 1/2 (+.f64 1 (neg.f64 k))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (neg.f64 k) 1/2) 1/2))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 1/2 (+.f64 1 (neg.f64 k))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (neg.f64 k) 1/2) 1/2))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 1/2 (+.f64 1 (neg.f64 k))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (neg.f64 k) 1/2) 1/2))) |
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 1/2 (+.f64 1 (neg.f64 k))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (neg.f64 k) 1/2) 1/2))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (*.f64 1/2 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
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(/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))) |
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (neg.f64 (neg.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))) |
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (-.f64 (/.f64 1 (sqrt.f64 k)) 0) (-.f64 (/.f64 1 (sqrt.f64 k)) 0))) |
(/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (neg.f64 (/.f64 1 (sqrt.f64 k))))) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.3b | (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) |
| ✓ | 0.3b | (*.f64 (PI.f64) n) |
| ✓ | 0.4b | (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k))) |
| ✓ | 0.7b | (*.f64 (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) |
Compiled 111 to 66 computations (40.5% saved)
21 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 15.0ms | k | @ | 0 | (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k))) |
| 1.0ms | n | @ | -inf | (*.f64 (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) |
| 1.0ms | k | @ | -inf | (*.f64 (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) |
| 1.0ms | n | @ | 0 | (*.f64 (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) |
| 1.0ms | n | @ | inf | (*.f64 (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) |
| 1× | batch-egg-rewrite |
| 1748× | rational_best_oopsla_all_46_json_45_simplify-23 |
| 1482× | rational_best_oopsla_all_46_json-2 |
| 1482× | rational_best_oopsla_all_46_json-1 |
| 1482× | rational_best_oopsla_all_46_json-4 |
| 1482× | rational_best_oopsla_all_46_json-3 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 23 | 164 |
| 1 | 154 | 160 |
| 2 | 579 | 160 |
| 3 | 3169 | 160 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k))) |
(*.f64 (PI.f64) n) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) |
| Outputs |
|---|
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| 1× | egg-herbie |
| 1392× | rational_best_oopsla_all_46_json_45_simplify-10 |
| 998× | rational_best_oopsla_all_46_json_45_simplify-23 |
| 876× | rational_best_oopsla_all_46_json_45_simplify-72 |
| 658× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 566× | rational_best_oopsla_all_46_json_45_simplify-30 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 185 | 4860 |
| 1 | 675 | 4844 |
| 2 | 3078 | 4840 |
| 3 | 7958 | 4840 |
| 1× | node limit |
| Inputs |
|---|
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(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
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(*.f64 n (PI.f64)) |
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(+.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)))) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k)))) (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)))))) |
(+.f64 (*.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1))))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)))) (sqrt.f64 2))) |
(+.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)))) (sqrt.f64 2)) (*.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)))))) |
(+.f64 (*.f64 0 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1))) |
(-.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) 0) |
(-.f64 (*.f64 0 (neg.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))) |
(-.f64 (*.f64 0 (neg.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) 1) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (/.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (/.f64 (*.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)))))) |
(+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) 0) |
(+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (*.f64 0 (*.f64 (sqrt.f64 2) (*.f64 -1/2 k)))) |
(+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (*.f64 0 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))) |
(+.f64 0 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k)))) |
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k)))) |
(+.f64 (*.f64 0 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k)))) |
(-.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) 0) |
(-.f64 (*.f64 0 (neg.f64 (sqrt.f64 2))) (*.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) |
(-.f64 (*.f64 0 (neg.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (neg.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k))) (sqrt.f64 2))) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) 1) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 k k)) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k)) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k)))) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k))) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k))))) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/2 k)) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k)))) |
(+.f64 (*.f64 (PI.f64) n) 0) |
(+.f64 (*.f64 (PI.f64) n) (*.f64 0 (*.f64 n (/.f64 (PI.f64) (PI.f64))))) |
(+.f64 0 (*.f64 (PI.f64) n)) |
(+.f64 (*.f64 0 (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (*.f64 (PI.f64) n)) |
(-.f64 (*.f64 (PI.f64) n) 0) |
(-.f64 (*.f64 0 (neg.f64 (PI.f64))) (*.f64 (neg.f64 (PI.f64)) n)) |
(-.f64 (*.f64 0 (neg.f64 n)) (*.f64 (neg.f64 n) (PI.f64))) |
(/.f64 (*.f64 (PI.f64) n) 1) |
(/.f64 (*.f64 (PI.f64) n) (/.f64 (PI.f64) (PI.f64))) |
(/.f64 (*.f64 (PI.f64) n) (/.f64 n n)) |
(/.f64 (*.f64 (PI.f64) n) (/.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) |
(/.f64 (*.f64 (PI.f64) n) (/.f64 (*.f64 n (/.f64 (PI.f64) (PI.f64))) (*.f64 n (/.f64 (PI.f64) (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) 0) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
(+.f64 0 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) 0) |
(-.f64 (*.f64 0 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) 1) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
| Outputs |
|---|
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(*.f64 -1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(*.f64 -1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(*.f64 -1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))) |
(*.f64 -1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(*.f64 -1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(*.f64 -1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
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(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)))))) |
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (+.f64 1 (*.f64 -1/2 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) k)))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))))) |
(*.f64 (sqrt.f64 2) (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))) |
(+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) 0) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) |
(+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (*.f64 0 (*.f64 (sqrt.f64 2) (*.f64 -1/2 k)))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) |
(+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (*.f64 0 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) |
(+.f64 0 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k)))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) |
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k)))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) |
(+.f64 (*.f64 0 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k)))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) |
(-.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) 0) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) |
(-.f64 (*.f64 0 (neg.f64 (sqrt.f64 2))) (*.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) |
(-.f64 (*.f64 0 (neg.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (neg.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k))) (sqrt.f64 2))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) 1) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 k k)) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k)) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k)))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k))) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k))))) |
(/.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) k))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (neg.f64 k))) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (neg.f64 k))))) |
(/.f64 (*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) (/.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (neg.f64 (sqrt.f64 2)))) (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (neg.f64 (sqrt.f64 2)))))) |
(/.f64 (*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) (/.f64 (*.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (neg.f64 k)) (*.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (neg.f64 k)))) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))) |
(/.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) k))) (/.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))) |
(/.f64 (*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) (/.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))) |
(/.f64 (*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) (/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (neg.f64 k))) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (neg.f64 k))))) |
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/2 k)) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k)))) |
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) |
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) |
(+.f64 (*.f64 (PI.f64) n) 0) |
(*.f64 (PI.f64) n) |
(+.f64 (*.f64 (PI.f64) n) (*.f64 0 (*.f64 n (/.f64 (PI.f64) (PI.f64))))) |
(*.f64 (PI.f64) n) |
(+.f64 0 (*.f64 (PI.f64) n)) |
(*.f64 (PI.f64) n) |
(+.f64 (*.f64 0 (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (*.f64 (PI.f64) n)) |
(*.f64 (PI.f64) n) |
(-.f64 (*.f64 (PI.f64) n) 0) |
(*.f64 (PI.f64) n) |
(-.f64 (*.f64 0 (neg.f64 (PI.f64))) (*.f64 (neg.f64 (PI.f64)) n)) |
(*.f64 (PI.f64) n) |
(-.f64 (*.f64 0 (neg.f64 n)) (*.f64 (neg.f64 n) (PI.f64))) |
(*.f64 (PI.f64) n) |
(/.f64 (*.f64 (PI.f64) n) 1) |
(*.f64 (PI.f64) n) |
(/.f64 (*.f64 (PI.f64) n) (/.f64 (PI.f64) (PI.f64))) |
(*.f64 (PI.f64) n) |
(/.f64 (*.f64 (PI.f64) n) (/.f64 n n)) |
(*.f64 (PI.f64) n) |
(/.f64 (*.f64 (PI.f64) n) (/.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) |
(*.f64 (PI.f64) n) |
(/.f64 (*.f64 (PI.f64) n) (/.f64 (*.f64 n (/.f64 (PI.f64) (PI.f64))) (*.f64 n (/.f64 (PI.f64) (PI.f64))))) |
(*.f64 (PI.f64) n) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) 0) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) |
(+.f64 0 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) |
(+.f64 (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) |
(-.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) 0) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) |
(-.f64 (*.f64 0 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) |
(-.f64 (*.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) 1) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.3b | (/.f64 1 (sqrt.f64 k)) | |
| ✓ | 0.3b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2))) |
| ✓ | 0.3b | (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))) |
| ✓ | 0.3b | (pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2)) |
Compiled 322 to 223 computations (30.7% saved)
15 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 47.0ms | n | @ | -inf | (pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2)) |
| 15.0ms | n | @ | 0 | (pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2)) |
| 7.0ms | n | @ | inf | (pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2)) |
| 1.0ms | k | @ | 0 | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2))) |
| 1.0ms | k | @ | -inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2))) |
| 1× | batch-egg-rewrite |
| 1770× | rational_best_oopsla_all_46_json-2 |
| 1770× | rational_best_oopsla_all_46_json-1 |
| 1770× | rational_best_oopsla_all_46_json-4 |
| 1770× | rational_best_oopsla_all_46_json-3 |
| 1148× | rational_best_oopsla_all_46_json_45_simplify-72 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 28 | 387 |
| 1 | 192 | 387 |
| 2 | 704 | 375 |
| 3 | 4007 | 375 |
| 1× | node limit |
| Inputs |
|---|
(pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2)) |
(*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2))) |
| Outputs |
|---|
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| 1× | egg-herbie |
| 1270× | rational_best_oopsla_all_46_json_45_simplify-23 |
| 762× | rational_best_oopsla_all_46_json_45_simplify-72 |
| 682× | rational_best_oopsla_all_46_json_45_simplify-49 |
| 670× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 582× | rational_best_oopsla_all_46_json_45_simplify-7 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 184 | 8606 |
| 1 | 675 | 8564 |
| 2 | 2960 | 8478 |
| 1× | node limit |
| Inputs |
|---|
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
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(/.f64 (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 2 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2))))))) (/.f64 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2))))) |
(/.f64 (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 2 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2))))))) (/.f64 (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 2 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2))))))) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 2 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2))))))))) |
(/.f64 (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 2 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2))))))) (/.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2))))))) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2))))))))) |
(+.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 0) |
(+.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 0 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) |
(+.f64 0 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 0 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 0) |
(-.f64 (*.f64 0 (neg.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)))) (*.f64 (neg.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 1) |
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) |
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) |
| Outputs |
|---|
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64)))))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64)))))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2))))))) |
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(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (pow.f64 (neg.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 1) |
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (pow.f64 (neg.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (pow.f64 (neg.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)))) |
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (pow.f64 (neg.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (neg.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (pow.f64 (neg.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) |
Compiled 33579 to 21711 computations (35.3% saved)
15 alts after pruning (8 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 821 | 4 | 825 |
| Fresh | 3 | 4 | 7 |
| Picked | 1 | 0 | 1 |
| Done | 1 | 7 | 8 |
| Total | 826 | 15 | 841 |
| Status | Error | Program |
|---|---|---|
| ▶ | 21.7b | (+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) |
| ▶ | 0.6b | (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
| ✓ | 0.5b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2))) |
| ✓ | 0.5b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| 21.7b | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (*.f64 1/8 (pow.f64 k 2))))))))) | |
| ▶ | 21.9b | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)))))))) |
| ✓ | 22.0b | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))) |
| 21.1b | (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)))))) | |
| ✓ | 22.2b | (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
| ✓ | 3.3b | (*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) |
| ▶ | 21.9b | (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))))) |
| ✓ | 3.7b | (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))) |
| 25.2b | (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) | |
| ✓ | 22.2b | (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
| ▶ | 22.2b | (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
Compiled 850 to 611 computations (28.1% saved)
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.3b | (/.f64 1 (sqrt.f64 k)) | |
| ✓ | 0.3b | (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
| ✓ | 0.3b | (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) |
| ✓ | 0.5b | (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2))))))) |
Compiled 267 to 183 computations (31.5% saved)
15 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | k | @ | 0 | (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
| 0.0ms | k | @ | -inf | (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
| 0.0ms | k | @ | inf | (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
| 0.0ms | k | @ | 0 | (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) |
| 0.0ms | n | @ | inf | (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
| 1× | batch-egg-rewrite |
| 1674× | rational_best_oopsla_all_46_json-2 |
| 1674× | rational_best_oopsla_all_46_json-1 |
| 1674× | rational_best_oopsla_all_46_json-4 |
| 1674× | rational_best_oopsla_all_46_json-3 |
| 970× | rational_best_oopsla_all_46_json_45_simplify-7 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 27 | 375 |
| 1 | 185 | 375 |
| 2 | 680 | 375 |
| 3 | 3785 | 375 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2))))))) |
(pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) |
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
| Outputs |
|---|
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| 1× | egg-herbie |
| 1432× | rational_best_oopsla_all_46_json_45_simplify-23 |
| 778× | rational_best_oopsla_all_46_json_45_simplify-72 |
| 704× | rational_best_oopsla_all_46_json_45_simplify-49 |
| 650× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 552× | rational_best_oopsla_all_46_json_45_simplify-24 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 192 | 9253 |
| 1 | 679 | 9213 |
| 2 | 2903 | 9159 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
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(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
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(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
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(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) |
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(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))) |
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(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) (+.f64 1 (*.f64 -1 k))))) |
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(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) (+.f64 1 (*.f64 -1 k))))) |
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) (+.f64 1 (*.f64 -1 k))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))))))) |
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(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))) |
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(+.f64 (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2))))) (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 0) |
(-.f64 (*.f64 0 (neg.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)))) (*.f64 (neg.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 1) |
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)))))) |
| Outputs |
|---|
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 n -2)) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 n -2)) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 n -2)) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 n -2)) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 n -2)) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 n -2)) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 n -2)) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 n -2)) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 n -2)) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 n -2)) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 n -2)) |
(*.f64 -2 (*.f64 n (PI.f64))) |
(*.f64 (PI.f64) (*.f64 n -2)) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n))))))) |
(exp.f64 (*.f64 (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k)))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 2 (PI.f64)))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2))))))) |
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) (*.f64 (sqrt.f64 2) k))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))))))) |
(+.f64 (*.f64 (*.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) (*.f64 (sqrt.f64 2) k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
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(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (neg.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (neg.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (neg.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)))))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (neg.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.3b | (/.f64 1 (sqrt.f64 k)) | |
| ✓ | 0.3b | (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
| 0.3b | (*.f64 n (PI.f64)) | |
| ✓ | 0.5b | (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
Compiled 43 to 21 computations (51.2% saved)
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 5.0ms | n | @ | 0 | (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
| 0.0ms | n | @ | -inf | (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
| 0.0ms | k | @ | -inf | (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
| 0.0ms | k | @ | 0 | (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
| 0.0ms | n | @ | inf | (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
| 1× | batch-egg-rewrite |
| 944× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 788× | rational_best_oopsla_all_46_json_45_simplify-23 |
| 758× | rational_best_oopsla_all_46_json_45_simplify-87 |
| 754× | rational_best_oopsla_all_46_json_45_simplify-37 |
| 746× | rational_best_oopsla_all_46_json_45_simplify-13 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 68 |
| 1 | 98 | 68 |
| 2 | 328 | 68 |
| 3 | 1601 | 68 |
| 4 | 7396 | 68 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) |
| Outputs |
|---|
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| 1× | egg-herbie |
| 1220× | rational_best_oopsla_all_46_json_45_simplify-10 |
| 1198× | rational_best_oopsla_all_46_json_45_simplify-30 |
| 644× | rational_best_oopsla_all_46_json_45_simplify-72 |
| 634× | rational_best_oopsla_all_46_json_45_simplify-35 |
| 596× | rational_best_oopsla_all_46_json_45_simplify-23 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 188 | 4944 |
| 1 | 618 | 4944 |
| 2 | 2190 | 4936 |
| 3 | 5796 | 4932 |
| 1× | node limit |
| Inputs |
|---|
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(neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))) |
(neg.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 2))))) |
(neg.f64 (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(neg.f64 (*.f64 -1 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))))) |
(neg.f64 (*.f64 (*.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 1 (sqrt.f64 k)))) |
(neg.f64 (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) (sqrt.f64 2))) |
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) 0) |
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) 0)) |
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) 0)) |
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) 0)) |
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) 0)) |
(+.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 0 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) 0) |
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) 0)) |
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) 0)) |
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) 0)) |
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) 0)) |
(-.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))) |
(-.f64 0 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))) |
(-.f64 0 (*.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))) |
(-.f64 0 (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (sqrt.f64 k)))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) 1) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) -1) |
(neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))) |
(neg.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))) |
(neg.f64 (*.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))) |
(neg.f64 (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (sqrt.f64 k)))) |
| Outputs |
|---|
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) 0) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 2))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 0 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 0 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 0 (*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 2) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 2)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 2) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(+.f64 (*.f64 0 (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) 0) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 2))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) 0)) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 0 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 2)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 0 (*.f64 1 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 2))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
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(neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))) |
(-.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) 0) |
(-.f64 0 (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) 1) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) -1) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) |
(neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) |
(neg.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) |
(neg.f64 (*.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))) |
(neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))) |
(-.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) 0) |
(neg.f64 (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.3b | (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) | |
| 0.3b | (*.f64 (*.f64 2 (PI.f64)) n) | |
| 0.3b | (*.f64 (PI.f64) n) | |
| ✓ | 0.7b | (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))))) |
Compiled 116 to 74 computations (36.2% saved)
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | n | @ | -inf | (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))))) |
| 1.0ms | n | @ | 0 | (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))))) |
| 1.0ms | n | @ | inf | (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))))) |
| 1.0ms | k | @ | -inf | (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))))) |
| 1.0ms | k | @ | inf | (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))))) |
| 1× | batch-egg-rewrite |
| 1584× | rational_best_oopsla_all_46_json-2 |
| 1584× | rational_best_oopsla_all_46_json-1 |
| 1584× | rational_best_oopsla_all_46_json-4 |
| 1584× | rational_best_oopsla_all_46_json-3 |
| 910× | rational_best_oopsla_all_46_json_45_simplify-72 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 81 |
| 1 | 163 | 81 |
| 2 | 629 | 81 |
| 3 | 3583 | 81 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))))) |
| Outputs |
|---|
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(/.f64 1 (sqrt.f64 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 1 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 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(*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 (*.f64 (PI.f64) n)))))))))) |
| 1× | egg-herbie |
| 1544× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 1224× | rational_best_oopsla_all_46_json_45_simplify-74 |
| 1118× | rational_best_oopsla_all_46_json_45_simplify-24 |
| 836× | rational_best_oopsla_all_46_json_45_simplify-13 |
| 810× | rational_best_oopsla_all_46_json_45_simplify-10 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 82 | 2197 |
| 1 | 301 | 2197 |
| 2 | 1423 | 2197 |
| 3 | 5826 | 2197 |
| 1× | node limit |
| Inputs |
|---|
(+.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) 0) |
(+.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
(+.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (*.f64 0 (*.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))))) |
(+.f64 0 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 1 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 2))) |
(+.f64 (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) |
(+.f64 (*.f64 1 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) |
(+.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) |
(+.f64 (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 (*.f64 (PI.f64) n))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) |
(+.f64 (*.f64 0 (*.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) |
(-.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) 0) |
(-.f64 (*.f64 0 (neg.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) |
(-.f64 (*.f64 0 (neg.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) 1) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
| Outputs |
|---|
(+.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) 0) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(+.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(+.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (*.f64 0 (*.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(+.f64 0 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 1 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 2))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(+.f64 (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(+.f64 (*.f64 1 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(+.f64 (*.f64 (*.f64 k (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(+.f64 (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 (*.f64 (PI.f64) n))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(+.f64 (*.f64 0 (*.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(-.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) 0) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(-.f64 (*.f64 0 (neg.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(-.f64 (*.f64 0 (neg.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) 1) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))))) |
(/.f64 (*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) (/.f64 (*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) (*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) |
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.4b | (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)) |
| ✓ | 0.5b | (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2) |
| ✓ | 2.1b | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)))))))) |
| ✓ | 3.2b | (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2))))))) |
Compiled 297 to 215 computations (27.6% saved)
18 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | n | @ | inf | (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2))))))) |
| 4.0ms | n | @ | -inf | (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2))))))) |
| 3.0ms | n | @ | inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)))))))) |
| 2.0ms | n | @ | -inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)))))))) |
| 2.0ms | n | @ | 0 | (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2))))))) |
| 1× | batch-egg-rewrite |
| 2042× | rational_best_oopsla_all_46_json-2 |
| 2042× | rational_best_oopsla_all_46_json-1 |
| 2042× | rational_best_oopsla_all_46_json-4 |
| 2042× | rational_best_oopsla_all_46_json-3 |
| 742× | rational_best_oopsla_all_46_json_45_simplify-89 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 34 | 390 |
| 1 | 242 | 354 |
| 2 | 967 | 346 |
| 3 | 4625 | 346 |
| 1× | node limit |
| Inputs |
|---|
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2))))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)))))))) |
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)) |
| Outputs |
|---|
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| 1× | egg-herbie |
| 1466× | rational_best_oopsla_all_46_json_45_simplify-37 |
| 1254× | rational_best_oopsla_all_46_json_45_simplify-72 |
| 1020× | rational_best_oopsla_all_46_json_45_simplify-49 |
| 828× | rational_best_oopsla_all_46_json_45_simplify-7 |
| 778× | rational_best_oopsla_all_46_json_45_simplify-89 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 221 | 11208 |
| 1 | 848 | 10510 |
| 2 | 3525 | 10366 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
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(*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) |
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(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(pow.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2) |
(pow.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2) |
(pow.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2) |
(pow.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2) |
(pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2) |
(pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2) |
(pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2) |
(pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2) |
(pow.f64 (+.f64 (log.f64 (neg.f64 (*.f64 2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 -1 n)))) 2) |
(pow.f64 (+.f64 (log.f64 (neg.f64 (*.f64 2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 -1 n)))) 2) |
(pow.f64 (+.f64 (log.f64 (neg.f64 (*.f64 2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 -1 n)))) 2) |
(pow.f64 (+.f64 (log.f64 (neg.f64 (*.f64 2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 -1 n)))) 2) |
(*.f64 (sqrt.f64 2) (pow.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2)) |
(*.f64 (pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2) (sqrt.f64 2)) |
(*.f64 (pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2) (sqrt.f64 2)) |
(*.f64 (pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2) (sqrt.f64 2)) |
(*.f64 (pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2) (sqrt.f64 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 2 (PI.f64))))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 2 (PI.f64))))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 2 (PI.f64))))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 2 (PI.f64))))) 2)) |
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(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))) (*.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
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(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))) |
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2))) (+.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k)))) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1/8))))) |
(+.f64 (*.f64 0 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) (/.f64 1 (sqrt.f64 k)))) |
(-.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) (/.f64 1 (sqrt.f64 k))) 0) |
(-.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) 0)) |
(-.f64 (*.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))))) |
(-.f64 (*.f64 0 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))) (/.f64 1 (sqrt.f64 k)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) (/.f64 1 (sqrt.f64 k))) 1) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) (/.f64 1 (sqrt.f64 k))))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) |
(+.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) 0) |
(+.f64 0 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) |
(-.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) 0) |
(*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) 1) |
(*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))) |
(*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 1 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))) |
(*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (*.f64 (/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))) |
(*.f64 1 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) |
(*.f64 -1 (neg.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))) |
(*.f64 (/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) |
(/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) 1) |
(/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))) |
(+.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) 0) |
(+.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (*.f64 (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) 0)) |
(+.f64 0 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))) |
(+.f64 (*.f64 0 (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))) |
(-.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) 0) |
(-.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (*.f64 (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) 0)) |
(-.f64 (*.f64 0 (neg.f64 (sqrt.f64 2))) (*.f64 (neg.f64 (sqrt.f64 2)) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))) |
(-.f64 (*.f64 0 (neg.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))) (*.f64 (neg.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (sqrt.f64 2))) |
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) 1) |
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) |
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))) |
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))) |
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) k))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2))))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2))))))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) |
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(*.f64 1 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) |
(pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2) |
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) |
(*.f64 -1 (neg.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))) |
(pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2) |
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) |
(*.f64 (/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) |
(pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2) |
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) |
(/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) 1) |
(pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2) |
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) |
(/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))) |
(pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2) |
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) |
(+.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) 0) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) |
(+.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (*.f64 (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) 0)) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) |
(+.f64 0 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) |
(+.f64 (*.f64 0 (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) |
(-.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) 0) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) |
(-.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (*.f64 (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) 0)) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) |
(-.f64 (*.f64 0 (neg.f64 (sqrt.f64 2))) (*.f64 (neg.f64 (sqrt.f64 2)) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) |
(-.f64 (*.f64 0 (neg.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))) (*.f64 (neg.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (sqrt.f64 2))) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) |
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) 1) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) |
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) |
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))) |
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)) (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)))) |
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) |
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)) |
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 1.6b | (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) |
| ✓ | 2.1b | (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
| ✓ | 5.7b | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))) |
| ✓ | 12.0b | (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))) |
Compiled 503 to 236 computations (53.1% saved)
24 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | n | @ | inf | (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))) |
| 4.0ms | n | @ | -inf | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))) |
| 4.0ms | n | @ | -inf | (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))) |
| 3.0ms | n | @ | 0 | (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))) |
| 2.0ms | n | @ | 0 | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))) |
| 1× | batch-egg-rewrite |
| 930× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 822× | rational_best_oopsla_all_46_json_45_simplify-74 |
| 782× | rational_best_oopsla_all_46_json_45_simplify-35 |
| 726× | rational_best_oopsla_all_46_json_45_simplify-37 |
| 684× | rational_best_oopsla_all_46_json-2 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 40 | 574 |
| 1 | 290 | 538 |
| 2 | 1181 | 538 |
| 3 | 5929 | 538 |
| 1× | node limit |
| Inputs |
|---|
(+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))) |
(*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64)))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 2) k)) -1/2) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 2) k)) -1/2) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 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| 1× | egg-herbie |
| 1878× | rational_best_oopsla_all_46_json_45_simplify-23 |
| 1538× | rational_best_oopsla_all_46_json_45_simplify-37 |
| 742× | rational_best_oopsla_all_46_json_45_simplify-89 |
| 716× | rational_best_oopsla_all_46_json_45_simplify-7 |
| 608× | rational_best_oopsla_all_46_json_45_simplify-10 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 193 | 13596 |
| 1 | 738 | 13128 |
| 2 | 3492 | 12078 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) |
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(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))) |
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(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
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(/.f64 (*.f64 (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 2) k)) -1/2) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 2) k)) -1/2) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 2) k)) -1/2) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) |
(+.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) 0) |
(+.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 0 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))) |
(+.f64 0 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n))))) |
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2)))))) (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n))))) |
(-.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) 0) |
(-.f64 (*.f64 0 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))) |
(-.f64 (*.f64 0 (neg.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))) (*.f64 (neg.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2)))) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) 1) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (sqrt.f64 2) (pow.f64 k 2)))) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))) |
(+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) 0) |
(+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (*.f64 0 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
(+.f64 0 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))))) |
(+.f64 (*.f64 0 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))))) |
(-.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) 0) |
(-.f64 (*.f64 0 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))))) |
(-.f64 (*.f64 0 (neg.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))))) (*.f64 (neg.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) 1) |
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) |
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3))) |
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))))) |
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))))) |
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (pow.f64 k 3))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (pow.f64 k 3))))) |
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))) |
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
| Outputs |
|---|
(*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(*.f64 -1/2 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 2) k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 1/8 (sqrt.f64 (*.f64 n (PI.f64)))))) |
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))))) |
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(*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (pow.f64 k 3))))) |
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))))) |
(*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) |
(*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (pow.f64 k 3))))) |
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (pow.f64 k 3))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (pow.f64 k 3))))) |
(*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) |
(*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (pow.f64 k 3))))) |
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))) |
(*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) |
(*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (pow.f64 k 3))))) |
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))))) |
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 -1/48 (pow.f64 k 3)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 -1/48 (pow.f64 k 3)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3))))) |
Compiled 35291 to 21418 computations (39.3% saved)
16 alts after pruning (6 fresh and 10 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 639 | 3 | 642 |
| Fresh | 0 | 3 | 3 |
| Picked | 1 | 0 | 1 |
| Done | 1 | 10 | 11 |
| Total | 641 | 16 | 657 |
| Status | Error | Program |
|---|---|---|
| 0.6b | (/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 1) | |
| 21.7b | (+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 -1/48 (pow.f64 k 3))) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) | |
| ✓ | 0.6b | (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
| ✓ | 0.5b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2))) |
| ✓ | 0.5b | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| 21.7b | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (*.f64 1/8 (pow.f64 k 2))))))))) | |
| ✓ | 22.0b | (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))) |
| 21.1b | (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)))))) | |
| ✓ | 22.2b | (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
| ✓ | 3.3b | (*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) |
| ✓ | 21.9b | (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))))) |
| ✓ | 3.7b | (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))) |
| 25.2b | (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) | |
| 21.9b | (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))) | |
| ✓ | 22.2b | (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
| ✓ | 22.2b | (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
Compiled 525 to 393 computations (25.1% saved)
Total -25.3b remaining (-4847.9%)
Threshold costs -25.3b (-4847.9%)
| Inputs |
|---|
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) |
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) 1) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))) |
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n))))))) |
(*.f64 (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))) |
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2))) |
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 1) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 0 (*.f64 (*.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n (*.f64 2 (PI.f64)))) (/.f64 (*.f64 2 (PI.f64)) (*.f64 (*.f64 2 (PI.f64)) (/.f64 n (*.f64 2 (PI.f64)))))) (*.f64 -2 (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2))) |
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)))))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (*.f64 1/8 (pow.f64 k 2))))))))) |
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 -1/48 (pow.f64 k 3))) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) |
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))) |
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) |
| Outputs |
|---|
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
4 calls:
| 95.0ms | (*.f64 (*.f64 2 (PI.f64)) n) |
| 16.0ms | k |
| 14.0ms | n |
| 8.0ms | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| Error | Segments | Branch |
|---|---|---|
| 0.5b | 1 | k |
| 0.5b | 1 | n |
| 0.5b | 1 | (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| 0.5b | 1 | (*.f64 (*.f64 2 (PI.f64)) n) |
Compiled 1018 to 646 computations (36.5% saved)
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 49 |
| 1× | fuel |
| 1× | saturated |
| Inputs |
|---|
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
| Outputs |
|---|
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))) |
Compiled 18 to 15 computations (16.7% saved)
Compiled 18 to 15 computations (16.7% saved)
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