Time bar (total: 2.5s)
| 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% | 99.9% | 0.1% | 0% | 0% | 0% | 2 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 3 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 4 |
| 25% | 25% | 74.9% | 0.1% | 0% | 0% | 0% | 5 |
| 37.5% | 37.5% | 62.4% | 0.1% | 0% | 0% | 0% | 6 |
| 48% | 37.5% | 40.6% | 0.1% | 21.9% | 0% | 0% | 7 |
| 57.1% | 43.7% | 32.8% | 0.1% | 23.4% | 0% | 0% | 8 |
| 71.4% | 54.6% | 21.9% | 0.1% | 23.4% | 0% | 0% | 9 |
| 77.3% | 58.5% | 17.2% | 0.1% | 24.2% | 0% | 0% | 10 |
| 85.1% | 64.4% | 11.3% | 0.1% | 24.2% | 0% | 0% | 11 |
| 88.3% | 66.5% | 8.8% | 0.1% | 24.6% | 0% | 0% | 12 |
Compiled 8 to 5 computations (37.5% saved)
| 1.9s | 8256× | body | 256 | valid |
| 3.0ms | 43× | body | 256 | infinite |
| 2× | egg-herbie |
| 1084× | rational.json-simplify-2 |
| 944× | rational.json-simplify-19 |
| 906× | rational.json-simplify-44 |
| 902× | rational.json-simplify-37 |
| 848× | rational.json-simplify-39 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 26 |
| 1 | 11 | 26 |
| 2 | 19 | 26 |
| 3 | 55 | 26 |
| 4 | 354 | 26 |
| 5 | 3913 | 26 |
| 6 | 6160 | 26 |
| 7 | 7208 | 26 |
| 8 | 7866 | 26 |
| 0 | 2 | 2 |
| 1× | saturated |
| 1× | node limit |
| Inputs |
|---|
0 |
1 |
| Outputs |
|---|
0 |
1 |
| Inputs |
|---|
(-.f64 x (*.f64 y y)) |
(-.f64 y (*.f64 x x)) |
| Outputs |
|---|
(-.f64 x (*.f64 y y)) |
(-.f64 y (*.f64 x x)) |
Compiled 9 to 6 computations (33.3% saved)
| 1× | egg-herbie |
| 1812× | rational.json-simplify-35 |
| 1348× | rational.json-simplify-53 |
| 1016× | rational.json-simplify-39 |
| 866× | rational.json-simplify-59 |
| 642× | rational.json-simplify-1 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 13 |
| 1 | 8 | 13 |
| 2 | 12 | 13 |
| 3 | 30 | 13 |
| 4 | 180 | 13 |
| 5 | 1954 | 13 |
| 6 | 5908 | 13 |
| 7 | 7751 | 13 |
| 1× | node limit |
| Inputs |
|---|
(-.f64 x (*.f64 y y)) |
| Outputs |
|---|
(-.f64 x (*.f64 y y)) |
Compiled 7 to 4 computations (42.9% saved)
2 alts after pruning (2 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 0 | 1 | 1 |
| Fresh | 0 | 1 | 1 |
| Picked | 0 | 0 | 0 |
| Done | 0 | 0 | 0 |
| Total | 0 | 2 | 2 |
| Status | Error | Program |
|---|---|---|
| ▶ | 0.0b | (-.f64 x (*.f64 y y)) |
Compiled 7 to 4 computations (42.9% saved)
Found 1 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (-.f64 x (*.f64 y y)) |
Compiled 12 to 4 computations (66.7% saved)
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | y | @ | inf | (-.f64 x (*.f64 y y)) |
| 0.0ms | x | @ | 0 | (-.f64 x (*.f64 y y)) |
| 0.0ms | x | @ | inf | (-.f64 x (*.f64 y y)) |
| 0.0ms | y | @ | 0 | (-.f64 x (*.f64 y y)) |
| 0.0ms | x | @ | -inf | (-.f64 x (*.f64 y y)) |
| 1× | batch-egg-rewrite |
| 1358× | rational.json-simplify-2 |
| 1306× | rational.json-1 |
| 1306× | rational.json-2 |
| 1306× | rational.json-4 |
| 1306× | rational.json-3 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 13 |
| 1 | 40 | 13 |
| 2 | 105 | 13 |
| 3 | 271 | 13 |
| 4 | 1071 | 13 |
| 5 | 4299 | 13 |
| 1× | node limit |
| Inputs |
|---|
(-.f64 x (*.f64 y y)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 y (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (*.f64 y y)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y (neg.f64 y)) x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 1 (-.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 x (-.f64 1 (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (-.f64 x (*.f64 y y))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (-.f64 x (*.f64 y y)) 2) (/.f64 (-.f64 x (*.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x (-.f64 1 (*.f64 y y))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 x (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (-.f64 x (*.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 x (*.f64 y y)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 y y) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (-.f64 (*.f64 y y) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (-.f64 x (*.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 x (*.f64 y y)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 x (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 x (*.f64 y y)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 y y) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 x (*.f64 y y)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 x (*.f64 y y)) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (-.f64 (*.f64 y y) x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 x (*.f64 y y)) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 x (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (*.f64 y y) x)))))) |
| 1× | egg-herbie |
| 1126× | rational.json-simplify-2 |
| 968× | rational.json-simplify-41 |
| 804× | rational.json-simplify-48 |
| 722× | rational.json-simplify-59 |
| 696× | rational.json-simplify-51 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 57 | 826 |
| 1 | 115 | 784 |
| 2 | 239 | 784 |
| 3 | 590 | 784 |
| 4 | 1800 | 680 |
| 5 | 4813 | 680 |
| 6 | 6928 | 680 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 -1 (pow.f64 y 2)) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
x |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
x |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
x |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(*.f64 -1 (pow.f64 y 2)) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(*.f64 -1 (pow.f64 y 2)) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(+.f64 (-.f64 x (*.f64 y y)) 0) |
(+.f64 0 (-.f64 x (*.f64 y y))) |
(+.f64 (*.f64 y (neg.f64 y)) x) |
(+.f64 -1 (+.f64 1 (-.f64 x (*.f64 y y)))) |
(+.f64 -1 (+.f64 x (-.f64 1 (*.f64 y y)))) |
(+.f64 (+.f64 1 (-.f64 x (*.f64 y y))) -1) |
(+.f64 (/.f64 (-.f64 x (*.f64 y y)) 2) (/.f64 (-.f64 x (*.f64 y y)) 2)) |
(+.f64 (+.f64 x (-.f64 1 (*.f64 y y))) -1) |
(*.f64 (-.f64 x (*.f64 y y)) 1) |
(*.f64 1 (-.f64 x (*.f64 y y))) |
(*.f64 2 (/.f64 (-.f64 x (*.f64 y y)) 2)) |
(*.f64 (*.f64 (-.f64 x (*.f64 y y)) 2) 1/2) |
(*.f64 (-.f64 (*.f64 y y) x) -1) |
(*.f64 -1 (-.f64 (*.f64 y y) x)) |
(*.f64 1/2 (*.f64 (-.f64 x (*.f64 y y)) 2)) |
(*.f64 (/.f64 (-.f64 x (*.f64 y y)) 2) 2) |
(/.f64 (-.f64 x (*.f64 y y)) 1) |
(/.f64 (*.f64 (-.f64 x (*.f64 y y)) 2) 2) |
(/.f64 (-.f64 (*.f64 y y) x) -1) |
(/.f64 (*.f64 (-.f64 x (*.f64 y y)) 4) 4) |
(/.f64 (*.f64 2 (*.f64 (-.f64 x (*.f64 y y)) 4)) 8) |
(/.f64 (*.f64 2 (-.f64 (*.f64 y y) x)) -2) |
(/.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 x (*.f64 y y)) 4))) 16) |
(pow.f64 (-.f64 x (*.f64 y y)) 1) |
(neg.f64 (-.f64 (*.f64 y y) x)) |
| Outputs |
|---|
(*.f64 -1 (pow.f64 y 2)) |
(neg.f64 (pow.f64 y 2)) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
x |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
x |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
x |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
(*.f64 -1 (pow.f64 y 2)) |
(neg.f64 (pow.f64 y 2)) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
(*.f64 -1 (pow.f64 y 2)) |
(neg.f64 (pow.f64 y 2)) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
(+.f64 (*.f64 -1 (pow.f64 y 2)) x) |
(+.f64 (neg.f64 (pow.f64 y 2)) x) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(+.f64 (-.f64 x (*.f64 y y)) 0) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(+.f64 0 (-.f64 x (*.f64 y y))) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(+.f64 (*.f64 y (neg.f64 y)) x) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(+.f64 -1 (+.f64 1 (-.f64 x (*.f64 y y)))) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(+.f64 -1 (+.f64 x (-.f64 1 (*.f64 y y)))) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(+.f64 (+.f64 1 (-.f64 x (*.f64 y y))) -1) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(+.f64 (/.f64 (-.f64 x (*.f64 y y)) 2) (/.f64 (-.f64 x (*.f64 y y)) 2)) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(+.f64 (+.f64 x (-.f64 1 (*.f64 y y))) -1) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(*.f64 (-.f64 x (*.f64 y y)) 1) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(*.f64 1 (-.f64 x (*.f64 y y))) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(*.f64 2 (/.f64 (-.f64 x (*.f64 y y)) 2)) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(*.f64 (*.f64 (-.f64 x (*.f64 y y)) 2) 1/2) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(*.f64 (-.f64 (*.f64 y y) x) -1) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(*.f64 -1 (-.f64 (*.f64 y y) x)) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(*.f64 1/2 (*.f64 (-.f64 x (*.f64 y y)) 2)) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(*.f64 (/.f64 (-.f64 x (*.f64 y y)) 2) 2) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(/.f64 (-.f64 x (*.f64 y y)) 1) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(/.f64 (*.f64 (-.f64 x (*.f64 y y)) 2) 2) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(/.f64 (-.f64 (*.f64 y y) x) -1) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(/.f64 (*.f64 (-.f64 x (*.f64 y y)) 4) 4) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(/.f64 (*.f64 2 (*.f64 (-.f64 x (*.f64 y y)) 4)) 8) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(/.f64 (*.f64 2 (-.f64 (*.f64 y y) x)) -2) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(/.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 x (*.f64 y y)) 4))) 16) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(pow.f64 (-.f64 x (*.f64 y y)) 1) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
(neg.f64 (-.f64 (*.f64 y y) x)) |
(+.f64 x (*.f64 y (neg.f64 y))) |
(-.f64 x (*.f64 y y)) |
Compiled 249 to 109 computations (56.2% saved)
2 alts after pruning (1 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 31 | 1 | 32 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 31 | 2 | 33 |
| Status | Error | Program |
|---|---|---|
| ✓ | 0.0b | (-.f64 x (*.f64 y y)) |
| 20.8b | x |
Compiled 10 to 6 computations (40% saved)
Compiled 2 to 2 computations (0% saved)
2 alts after pruning (1 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 0 | 0 | 0 |
| Fresh | 0 | 1 | 1 |
| Picked | 0 | 0 | 0 |
| Done | 0 | 1 | 1 |
| Total | 0 | 2 | 2 |
| Status | Error | Program |
|---|---|---|
| ✓ | 0.0b | (-.f64 x (*.f64 y y)) |
| 20.8b | x |
Compiled 10 to 6 computations (40% saved)
Compiled 2 to 2 computations (0% saved)
2 alts after pruning (1 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 0 | 0 | 0 |
| Fresh | 0 | 1 | 1 |
| Picked | 0 | 0 | 0 |
| Done | 0 | 1 | 1 |
| Total | 0 | 2 | 2 |
| Status | Error | Program |
|---|---|---|
| ✓ | 0.0b | (-.f64 x (*.f64 y y)) |
| 20.8b | x |
Compiled 10 to 6 computations (40% saved)
Compiled 2 to 2 computations (0% saved)
2 alts after pruning (1 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 0 | 0 | 0 |
| Fresh | 0 | 1 | 1 |
| Picked | 0 | 0 | 0 |
| Done | 0 | 1 | 1 |
| Total | 0 | 2 | 2 |
| Status | Error | Program |
|---|---|---|
| ✓ | 0.0b | (-.f64 x (*.f64 y y)) |
| 20.8b | x |
Compiled 10 to 6 computations (40% saved)
Total -20.8b remaining (-266515.7%)
Threshold costs -20.8b (-266515.7%)
| Inputs |
|---|
x |
(-.f64 x (*.f64 y y)) |
| Outputs |
|---|
(-.f64 x (*.f64 y y)) |
4 calls:
| 3.0ms | (-.f64 x (*.f64 y y)) |
| 3.0ms | y |
| 3.0ms | x |
| 3.0ms | (*.f64 y y) |
| Error | Segments | Branch |
|---|---|---|
| 0.0b | 1 | x |
| 0.0b | 1 | y |
| 0.0b | 1 | (-.f64 x (*.f64 y y)) |
| 0.0b | 1 | (*.f64 y y) |
Compiled 26 to 15 computations (42.3% saved)
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 14 |
| 1× | fuel |
| 1× | saturated |
| Inputs |
|---|
(-.f64 x (*.f64 y y)) |
x |
| Outputs |
|---|
(-.f64 x (*.f64 y y)) |
x |
Compiled 10 to 6 computations (40% saved)
Compiled 8 to 4 computations (50% saved)
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