
Time bar (total: 8.6s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 25% | 75% | 0% | 0% | 0% | 0 |
| 0% | 0% | 25% | 75% | 0% | 0% | 0% | 1 |
| 50% | 12.5% | 12.5% | 75% | 0% | 0% | 0% | 2 |
| 75% | 18.7% | 6.2% | 75% | 0% | 0% | 0% | 3 |
| 87.5% | 21.9% | 3.1% | 75% | 0% | 0% | 0% | 4 |
| 93.8% | 23.4% | 1.6% | 75% | 0% | 0% | 0% | 5 |
| 96.9% | 24.2% | 0.8% | 75% | 0% | 0% | 0% | 6 |
| 98.4% | 24.6% | 0.4% | 75% | 0% | 0% | 0% | 7 |
| 99.2% | 24.8% | 0.2% | 75% | 0% | 0% | 0% | 8 |
| 99.6% | 24.9% | 0.1% | 75% | 0% | 0% | 0% | 9 |
| 99.8% | 24.9% | 0% | 75% | 0% | 0% | 0% | 10 |
| 99.9% | 25% | 0% | 75% | 0% | 0% | 0% | 11 |
| 100% | 25% | 0% | 75% | 0% | 0% | 0% | 12 |
Compiled 15 to 10 computations (33.3% saved)
ival-add: 0.0ms (0% of total)ival-sub: 0.0ms (0% of total)ival-and: 0.0ms (0% of total)ival-sqrt: 0.0ms (0% of total)...c/correct-round.rkt:119:19: 0.0ms (0% of total)const: 0.0ms (0% of total)ival->: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)ival-<: 0.0ms (0% of total)| 872.0ms | 3400× | 2 | valid |
| 715.0ms | 4673× | 1 | valid |
| 18.0ms | 183× | 0 | valid |
ival-sqrt: 322.0ms (27.4% of total)ival->: 172.0ms (14.6% of total)ival-sub: 166.0ms (14.1% of total)ival-add: 154.0ms (13.1% of total)...c/correct-round.rkt:119:19: 140.0ms (11.9% of total)backward-pass: 138.0ms (11.7% of total)ival-<: 42.0ms (3.6% of total)ival-and: 25.0ms (2.1% of total)const: 17.0ms (1.4% of total)| 2× | egg-herbie |
| 270× | sum3-define |
| 244× | fnmadd-define |
| 184× | fmsub-define |
| 168× | fnmsub-define |
| 168× | fma-define |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 12 | 26 |
| 1 | 25 | 24 |
| 2 | 52 | 23 |
| 3 | 99 | 23 |
| 4 | 190 | 23 |
| 5 | 387 | 23 |
| 6 | 579 | 23 |
| 7 | 755 | 23 |
| 8 | 849 | 23 |
| 9 | 955 | 23 |
| 10 | 1033 | 23 |
| 11 | 1039 | 23 |
| 0 | 6 | 7 |
| 1 | 11 | 7 |
| 2 | 15 | 7 |
| 3 | 22 | 7 |
| 4 | 32 | 7 |
| 5 | 64 | 7 |
| 6 | 122 | 7 |
| 7 | 210 | 7 |
| 8 | 295 | 7 |
| 9 | 401 | 7 |
| 10 | 479 | 7 |
| 11 | 485 | 7 |
| 0 | 485 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | saturated |
| Inputs |
|---|
(- (sqrt (+ x 1)) (sqrt x)) |
| Outputs |
|---|
(- (sqrt (+ x 1)) (sqrt x)) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Inputs |
|---|
(- (sqrt (+ x 1)) (sqrt x)) |
(- (sqrt (+ (neg x) 1)) (sqrt (neg x))) |
(neg (- (sqrt (+ (neg x) 1)) (sqrt (neg x)))) |
| Outputs |
|---|
(- (sqrt (+ x 1)) (sqrt x)) |
(- (sqrt (+ (neg x) 1)) (sqrt (neg x))) |
(- (sqrt (- 1 x)) (sqrt (neg x))) |
(neg (- (sqrt (+ (neg x) 1)) (sqrt (neg x)))) |
(- (sqrt (neg x)) (sqrt (- 1 x))) |
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 256 | 0 | - | 0 | - | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 0 | 0 | - | 0 | - | x |
| 0 | 0 | - | 0 | - | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (sqrt.f64 x) |
| 0 | 0 | - | 0 | - | (+.f64 x #s(literal 1 binary64)) |
| 60.0ms | 226× | 2 | valid |
| 35.0ms | 276× | 1 | valid |
| 1.0ms | 10× | 0 | valid |
Compiled 48 to 20 computations (58.3% saved)
ival-sqrt: 23.0ms (38.1% of total)ival-sub: 16.0ms (26.5% of total)backward-pass: 11.0ms (18.2% of total)ival-add: 9.0ms (14.9% of total)const: 1.0ms (1.7% of total)Compiled 8 to 6 computations (25% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 6.0% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
Compiled 8 to 6 computations (25% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | (+.f64 x #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
| ✓ | cost-diff | 0 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 124× | fnmadd-define |
| 122× | sum3-define |
| 80× | fma-lowering-fma.f32 |
| 80× | fnmsub-define |
| 80× | fmsub-define |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 1 | 11 | 18 |
| 2 | 15 | 18 |
| 3 | 22 | 18 |
| 4 | 32 | 18 |
| 5 | 64 | 18 |
| 6 | 122 | 18 |
| 7 | 210 | 18 |
| 8 | 295 | 18 |
| 9 | 401 | 18 |
| 10 | 479 | 18 |
| 11 | 485 | 18 |
| 0 | 485 | 18 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(- (sqrt (+ x 1)) (sqrt x)) |
(sqrt (+ x 1)) |
(+ x 1) |
x |
1 |
(sqrt x) |
| Outputs |
|---|
(- (sqrt (+ x 1)) (sqrt x)) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(sqrt (+ x 1)) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+ x 1) |
(+.f64 x #s(literal 1 binary64)) |
x |
1 |
#s(literal 1 binary64) |
(sqrt x) |
(sqrt.f64 x) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (+.f64 x #s(literal 1 binary64)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 6.0% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 22.0ms | 113× | 2 | valid |
| 21.0ms | 138× | 1 | valid |
| 0.0ms | 5× | 0 | valid |
Compiled 20 to 7 computations (65% saved)
ival-sqrt: 9.0ms (37.8% of total)backward-pass: 6.0ms (25.2% of total)ival-add: 4.0ms (16.8% of total)ival-sub: 3.0ms (12.6% of total)const: 1.0ms (4.2% of total)| Inputs |
|---|
#<alt (- (sqrt (+ x 1)) (sqrt x))> |
#<alt (sqrt (+ x 1))> |
#<alt (+ x 1)> |
#<alt (sqrt x)> |
| Outputs |
|---|
#<alt (- 1 (sqrt x))> |
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))> |
#<alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))> |
#<alt (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)> |
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)> |
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)> |
#<alt (* -1/2 (sqrt (/ 1 x)))> |
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))> |
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))> |
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))> |
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))> |
#<alt 1> |
#<alt (+ 1 x)> |
#<alt (+ 1 x)> |
#<alt (+ 1 x)> |
#<alt x> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt x> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (- (sqrt (+ x 1)) (sqrt x)) |
| 1.0ms | x | @ | inf | (- (sqrt (+ x 1)) (sqrt x)) |
| 0.0ms | x | @ | 0 | (- (sqrt (+ x 1)) (sqrt x)) |
| 0.0ms | x | @ | -inf | (sqrt x) |
| 0.0ms | x | @ | -inf | (sqrt (+ x 1)) |
| 1× | batch-egg-rewrite |
| 2378× | *-lowering-*.f32 |
| 2378× | *-lowering-*.f64 |
| 1782× | fma-lowering-fma.f32 |
| 1782× | fma-lowering-fma.f64 |
| 1676× | fmsub-define |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 1 | 39 | 16 |
| 2 | 300 | 16 |
| 3 | 3704 | 16 |
| 0 | 8338 | 16 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- (sqrt (+ x 1)) (sqrt x)) |
(sqrt (+ x 1)) |
(+ x 1) |
(sqrt x) |
| Outputs |
|---|
(+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) |
(+.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (sqrt.f64 x))) |
(+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) |
(+.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))))))) |
(+.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) #s(literal -1 binary64))) |
(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
(-.f64 #s(literal 0 binary64) (-.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))) |
(-.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))))) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))))))) |
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 x (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) |
(-.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) #s(literal 0 binary64)) (sqrt.f64 x)) |
(fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))) |
(fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))))))) |
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))))))) |
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))) |
(fma.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))) |
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))))))) |
(fma.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))) |
(fma.f64 #s(literal -1 binary64) (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) |
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) |
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) |
(fma.f64 (pow.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) |
(fma.f64 (pow.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) |
(fma.f64 (pow.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) |
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/4 binary64)) (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/4 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))))))) |
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) |
(fma.f64 (sqrt.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) |
(fma.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (+.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (pow.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal 3 binary64)))) (+.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (*.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))) (-.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))) (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))))))) |
(fma.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (pow.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64)))) (+.f64 x (-.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))))))) |
(fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) (neg.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))) |
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(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) (+.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) |
(/.f64 (*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (pow.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) |
(/.f64 (*.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))) (+.f64 (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) |
(/.f64 (*.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(/.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) |
(pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) |
(*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) |
(*.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) |
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))) |
(*.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) |
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))) |
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 (*.f64 x x) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))) |
(*.f64 (*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) |
(*.f64 (/.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x))))) |
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) x))) (+.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) x)) |
(*.f64 (/.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) (+.f64 (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))) |
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 x)) #s(literal 2 binary64))) |
(fabs.f64 (sqrt.f64 x)) |
(sqrt.f64 x) |
(pow.f64 x #s(literal 1/2 binary64)) |
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(*.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))) |
| 1× | egg-herbie |
| 2970× | *-lowering-*.f32 |
| 2970× | *-lowering-*.f64 |
| 2056× | +-lowering-+.f64 |
| 2056× | +-lowering-+.f32 |
| 1514× | sum3-define |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 113 | 434 |
| 1 | 325 | 384 |
| 2 | 1037 | 376 |
| 3 | 3221 | 373 |
| 4 | 7103 | 373 |
| 0 | 8112 | 373 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- 1 (sqrt x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x) |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x)) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
1 |
(+ 1 x) |
(+ 1 x) |
(+ 1 x) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
| Outputs |
|---|
(- 1 (sqrt x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64))) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
(+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (sqrt.f64 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x) |
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x) |
(/.f64 (+.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal -5/128 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) x) |
(* -1/2 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x)) |
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -1/16 binary64)))) x) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x)) |
(/.f64 (-.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -5/128 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))))))) x) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 x (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 x (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 x (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 x (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
1 |
#s(literal 1 binary64) |
(+ 1 x) |
(+.f64 #s(literal 1 binary64) x) |
(+ 1 x) |
(+.f64 #s(literal 1 binary64) x) |
(+ 1 x) |
(+.f64 #s(literal 1 binary64) x) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
Compiled 6005 to 884 computations (85.3% saved)
6 alts after pruning (5 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 276 | 5 | 281 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 276 | 6 | 282 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.4% | (/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) x) |
| ▶ | 99.0% | (/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
| ▶ | 7.7% | (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
| ✓ | 6.0% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| ▶ | 1.6% | (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ▶ | 98.4% | (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
Compiled 140 to 104 computations (25.7% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (-.f64 #s(literal 1 binary64) x) |
| ✓ | cost-diff | 256 | (+.f64 x (-.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 256 | (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
| ✓ | cost-diff | 0 | (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) x) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
| ✓ | cost-diff | 0 | (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
| ✓ | cost-diff | 0 | (/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) x) |
| 2262× | fnmsub-define |
| 1560× | sum4-define |
| 1156× | *-lowering-*.f32 |
| 1156× | *-lowering-*.f64 |
| 992× | fnmadd-define |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 28 | 185 |
| 1 | 56 | 185 |
| 2 | 94 | 181 |
| 3 | 140 | 180 |
| 4 | 177 | 180 |
| 5 | 235 | 180 |
| 6 | 361 | 180 |
| 7 | 545 | 180 |
| 8 | 818 | 180 |
| 9 | 1259 | 180 |
| 10 | 2668 | 180 |
| 11 | 5938 | 180 |
| 0 | 8106 | 180 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* (sqrt x) 1/2) (* 1/16 (sqrt (/ 1 (* x (* x x))))))) x) |
(+ (* -1/8 (sqrt (/ 1 x))) (+ (* (sqrt x) 1/2) (* 1/16 (sqrt (/ 1 (* x (* x x))))))) |
(* -1/8 (sqrt (/ 1 x))) |
-1/8 |
(sqrt (/ 1 x)) |
(/ 1 x) |
1 |
x |
(+ (* (sqrt x) 1/2) (* 1/16 (sqrt (/ 1 (* x (* x x)))))) |
(* (sqrt x) 1/2) |
(sqrt x) |
1/2 |
(* 1/16 (sqrt (/ 1 (* x (* x x))))) |
1/16 |
(sqrt (/ 1 (* x (* x x)))) |
(/ 1 (* x (* x x))) |
(* x (* x x)) |
(* x x) |
(- 1 (sqrt x)) |
1 |
(sqrt x) |
x |
(* 1/2 (sqrt (/ 1 x))) |
1/2 |
(sqrt (/ 1 x)) |
(/ 1 x) |
1 |
x |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) |
(+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) |
(* -1/8 (sqrt (/ 1 x))) |
-1/8 |
(sqrt (/ 1 x)) |
(/ 1 x) |
1 |
x |
(* (sqrt x) 1/2) |
(sqrt x) |
1/2 |
(/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x))) |
(+ x (- 1 x)) |
x |
(- 1 x) |
1 |
(+ (pow (+ x 1) 1/2) (sqrt x)) |
(pow (+ x 1) 1/2) |
(+ x 1) |
1/2 |
(sqrt x) |
| Outputs |
|---|
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* (sqrt x) 1/2) (* 1/16 (sqrt (/ 1 (* x (* x x))))))) x) |
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) x) |
(+ (* -1/8 (sqrt (/ 1 x))) (+ (* (sqrt x) 1/2) (* 1/16 (sqrt (/ 1 (* x (* x x))))))) |
(+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
(* -1/8 (sqrt (/ 1 x))) |
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
-1/8 |
#s(literal -1/8 binary64) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
1 |
#s(literal 1 binary64) |
x |
(+ (* (sqrt x) 1/2) (* 1/16 (sqrt (/ 1 (* x (* x x)))))) |
(+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) |
(* (sqrt x) 1/2) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
1/2 |
#s(literal 1/2 binary64) |
(* 1/16 (sqrt (/ 1 (* x (* x x))))) |
(*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) |
1/16 |
#s(literal 1/16 binary64) |
(sqrt (/ 1 (* x (* x x)))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(/ 1 (* x (* x x))) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(* x (* x x)) |
(*.f64 x (*.f64 x x)) |
(* x x) |
(*.f64 x x) |
(- 1 (sqrt x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
1 |
#s(literal 1 binary64) |
(sqrt x) |
(sqrt.f64 x) |
x |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
1 |
#s(literal 1 binary64) |
x |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) |
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
(+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) |
(+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
(* -1/8 (sqrt (/ 1 x))) |
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
-1/8 |
#s(literal -1/8 binary64) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
1 |
#s(literal 1 binary64) |
x |
(* (sqrt x) 1/2) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
1/2 |
#s(literal 1/2 binary64) |
(/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) |
(+ x (- 1 x)) |
#s(literal 1 binary64) |
x |
(- 1 x) |
(-.f64 #s(literal 1 binary64) x) |
1 |
#s(literal 1 binary64) |
(+ (pow (+ x 1) 1/2) (sqrt x)) |
(+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) |
(pow (+ x 1) 1/2) |
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) |
(+ x 1) |
(+.f64 #s(literal 1 binary64) x) |
1/2 |
#s(literal 1/2 binary64) |
(sqrt x) |
(sqrt.f64 x) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 100.0% | (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
| ✓ | accuracy | 99.6% | (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
| ✓ | accuracy | 7.0% | (+.f64 x (-.f64 #s(literal 1 binary64) x)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 100.0% | (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
| ✓ | accuracy | 99.6% | (/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 1 binary64) x) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
| ✓ | accuracy | 100.0% | (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
| ✓ | accuracy | 99.6% | (/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) x) |
| ✓ | accuracy | 99.2% | (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
| ✓ | accuracy | 71.1% | (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
| 614.0ms | 238× | 1 | valid |
| 10.0ms | 18× | 0 | valid |
Compiled 234 to 29 computations (87.6% saved)
ival-add: 424.0ms (77.9% of total)ival-div: 37.0ms (6.8% of total)ival-sub: 22.0ms (4% of total)ival-mult: 20.0ms (3.7% of total)backward-pass: 16.0ms (2.9% of total)ival-pow: 14.0ms (2.6% of total)ival-sqrt: 11.0ms (2% of total)const: 1.0ms (0.2% of total)| Inputs |
|---|
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* (sqrt x) 1/2) (* 1/16 (sqrt (/ 1 (* x (* x x))))))) x)> |
#<alt (+ (* -1/8 (sqrt (/ 1 x))) (+ (* (sqrt x) 1/2) (* 1/16 (sqrt (/ 1 (* x (* x x)))))))> |
#<alt (* -1/8 (sqrt (/ 1 x)))> |
#<alt (sqrt (/ 1 x))> |
#<alt (- 1 (sqrt x))> |
#<alt (sqrt x)> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (/ 1 x)> |
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)> |
#<alt (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2))> |
#<alt (/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x)))> |
#<alt (+ x (- 1 x))> |
#<alt (- 1 x)> |
#<alt (+ (pow (+ x 1) 1/2) (sqrt x))> |
#<alt (sqrt (/ 1 (* x (* x x))))> |
#<alt (/ 1 (* x (* x x)))> |
| Outputs |
|---|
#<alt (* 1/16 (sqrt (/ 1 (pow x 5))))> |
#<alt (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3))> |
#<alt (/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3))> |
#<alt (/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))> |
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))> |
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))> |
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))> |
#<alt (+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))> |
#<alt (+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))> |
#<alt (* 1/16 (sqrt (/ 1 (pow x 3))))> |
#<alt (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2))> |
#<alt (/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2))> |
#<alt (/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))> |
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1/8 (sqrt (/ 1 x)))> |
#<alt (* -1/8 (sqrt (/ 1 x)))> |
#<alt (* -1/8 (sqrt (/ 1 x)))> |
#<alt (* -1/8 (sqrt (/ 1 x)))> |
#<alt (* -1/8 (sqrt (/ 1 x)))> |
#<alt (* -1/8 (sqrt (/ 1 x)))> |
#<alt (* -1/8 (sqrt (/ 1 x)))> |
#<alt (* -1/8 (sqrt (/ 1 x)))> |
#<alt (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (- 1 (sqrt x))> |
#<alt (- 1 (sqrt x))> |
#<alt (- 1 (sqrt x))> |
#<alt (- 1 (sqrt x))> |
#<alt (* -1 (sqrt x))> |
#<alt (* x (- (/ 1 x) (sqrt (/ 1 x))))> |
#<alt (* x (- (/ 1 x) (sqrt (/ 1 x))))> |
#<alt (* x (- (/ 1 x) (sqrt (/ 1 x))))> |
#<alt (* (sqrt x) (pow (sqrt -1) 2))> |
#<alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))> |
#<alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))> |
#<alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (* -1/8 (sqrt (/ 1 (pow x 3))))> |
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))> |
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))> |
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))> |
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))> |
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))> |
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))> |
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))> |
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))> |
#<alt (* -1/8 (sqrt (/ 1 x)))> |
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)> |
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)> |
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))> |
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (/ 1 (+ 1 (sqrt x)))> |
#<alt (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))> |
#<alt (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))> |
#<alt (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)> |
#<alt (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)> |
#<alt (/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)> |
#<alt (* -1/2 (sqrt (/ 1 x)))> |
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))> |
#<alt (* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))> |
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt (+ 1 (* -1 x))> |
#<alt (+ 1 (* -1 x))> |
#<alt (+ 1 (* -1 x))> |
#<alt (* -1 x)> |
#<alt (* x (- (/ 1 x) 1))> |
#<alt (* x (- (/ 1 x) 1))> |
#<alt (* x (- (/ 1 x) 1))> |
#<alt (* -1 x)> |
#<alt (* -1 (* x (- 1 (/ 1 x))))> |
#<alt (* -1 (* x (- 1 (/ 1 x))))> |
#<alt (* -1 (* x (- 1 (/ 1 x))))> |
#<alt (+ 1 (sqrt x))> |
#<alt (+ 1 (+ (sqrt x) (* 1/2 x)))> |
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))> |
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))> |
#<alt (* 2 (sqrt x))> |
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))> |
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))> |
#<alt (sqrt (/ 1 (pow x 3)))> |
#<alt (sqrt (/ 1 (pow x 3)))> |
#<alt (sqrt (/ 1 (pow x 3)))> |
#<alt (sqrt (/ 1 (pow x 3)))> |
#<alt (sqrt (/ 1 (pow x 3)))> |
#<alt (sqrt (/ 1 (pow x 3)))> |
#<alt (sqrt (/ 1 (pow x 3)))> |
#<alt (sqrt (/ 1 (pow x 3)))> |
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))> |
#<alt (/ 1 (pow x 3))> |
#<alt (/ 1 (pow x 3))> |
#<alt (/ 1 (pow x 3))> |
#<alt (/ 1 (pow x 3))> |
#<alt (/ 1 (pow x 3))> |
#<alt (/ 1 (pow x 3))> |
#<alt (/ 1 (pow x 3))> |
#<alt (/ 1 (pow x 3))> |
#<alt (/ 1 (pow x 3))> |
#<alt (/ 1 (pow x 3))> |
#<alt (/ 1 (pow x 3))> |
#<alt (/ 1 (pow x 3))> |
48 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | x | @ | -inf | (/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x))) |
| 2.0ms | x | @ | 0 | (/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x))) |
| 1.0ms | x | @ | 0 | (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* (sqrt x) 1/2) (* 1/16 (sqrt (/ 1 (* x (* x x))))))) x) |
| 1.0ms | x | @ | inf | (/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x))) |
| 1.0ms | x | @ | -inf | (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* (sqrt x) 1/2) (* 1/16 (sqrt (/ 1 (* x (* x x))))))) x) |
| 1× | batch-egg-rewrite |
| 2838× | /-lowering-/.f32 |
| 2838× | /-lowering-/.f64 |
| 2652× | *-lowering-*.f32 |
| 2652× | *-lowering-*.f64 |
| 2158× | fma-lowering-fma.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 28 | 112 |
| 1 | 182 | 93 |
| 2 | 1660 | 92 |
| 0 | 8386 | 92 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* (sqrt x) 1/2) (* 1/16 (sqrt (/ 1 (* x (* x x))))))) x) |
(+ (* -1/8 (sqrt (/ 1 x))) (+ (* (sqrt x) 1/2) (* 1/16 (sqrt (/ 1 (* x (* x x))))))) |
(* -1/8 (sqrt (/ 1 x))) |
(sqrt (/ 1 x)) |
(- 1 (sqrt x)) |
(sqrt x) |
(* 1/2 (sqrt (/ 1 x))) |
(/ 1 x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) |
(+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) |
(/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x))) |
(+ x (- 1 x)) |
(- 1 x) |
(+ (pow (+ x 1) 1/2) (sqrt x)) |
(sqrt (/ 1 (* x (* x x)))) |
(/ 1 (* x (* x x))) |
| Outputs |
|---|
(exp.f64 (*.f64 (log.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))))))) #s(literal -1 binary64))) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))))) (-.f64 #s(literal 0 binary64) x))) |
(-.f64 (/.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))))) x) (/.f64 (/.f64 (pow.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 2 binary64)) (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))))) x)) |
(-.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (*.f64 x (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))))))) (/.f64 (pow.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 2 binary64)) (*.f64 x (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))))))) |
(neg.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))))) (-.f64 #s(literal 0 binary64) x))) |
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))))) x)) |
(/.f64 #s(literal 1 binary64) (/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))))))))) |
(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))))) x) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))))) #s(literal 1 binary64)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))))) (-.f64 #s(literal 0 binary64) x)) |
(/.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 3 binary64))) (*.f64 x (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (*.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))) |
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (pow.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 2 binary64))) (*.f64 x (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))))))) |
(/.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (*.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) x)) |
(/.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 3 binary64))) #s(literal -1 binary64)) (*.f64 (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (*.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) (-.f64 #s(literal 0 binary64) x))) |
(/.f64 (*.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (pow.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))))) x)) |
(/.f64 (*.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (pow.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 2 binary64))) #s(literal -1 binary64)) (*.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))))) (-.f64 #s(literal 0 binary64) x))) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))))))) (neg.f64 (-.f64 #s(literal 0 binary64) x))) |
(/.f64 (neg.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 3 binary64)))) (neg.f64 (*.f64 x (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (*.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (pow.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 2 binary64)))) (neg.f64 (*.f64 x (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))))))) |
(/.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))))) #s(literal 1 binary64)) x) |
(/.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x)) |
(/.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (*.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))) |
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(/.f64 (neg.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 3 binary64))) #s(literal 1 binary64))) (neg.f64 (*.f64 (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (*.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) x))) |
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(*.f64 (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 3 binary64))) |
(*.f64 (sqrt.f64 (pow.f64 x #s(literal -3/2 binary64))) (sqrt.f64 (pow.f64 x #s(literal -3/2 binary64)))) |
(exp.f64 (*.f64 #s(literal -3 binary64) (log.f64 x))) |
(exp.f64 (*.f64 (log.f64 x) #s(literal -3 binary64))) |
(exp.f64 (+.f64 (*.f64 (*.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64)))) |
(exp.f64 (-.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) (*.f64 (log.f64 x) #s(literal 2 binary64)))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x)))) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x))))) |
(/.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 x x)) |
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))))) |
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (*.f64 x x))) |
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x) |
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x))) (neg.f64 (neg.f64 (*.f64 x x)))) |
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x)) |
(pow.f64 x #s(literal -3 binary64)) |
(pow.f64 (sqrt.f64 x) #s(literal -6 binary64)) |
(pow.f64 (*.f64 x x) #s(literal -3/2 binary64)) |
(pow.f64 (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) |
(pow.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -2 binary64)) |
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal -1/2 binary64)) |
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x))) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (*.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) |
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 x #s(literal -3/2 binary64))) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) x)) |
| 1× | egg-herbie |
| 4088× | *-lowering-*.f32 |
| 4088× | *-lowering-*.f64 |
| 2234× | +-lowering-+.f64 |
| 2234× | +-lowering-+.f32 |
| 1510× | --lowering--.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 222 | 1784 |
| 1 | 680 | 1513 |
| 2 | 2440 | 1494 |
| 3 | 6905 | 1494 |
| 0 | 8243 | 1494 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/16 (sqrt (/ 1 (pow x 5)))) |
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) |
(* 1/2 (sqrt (/ 1 x))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2)) |
(* 1/2 (sqrt x)) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1/8 (sqrt (/ 1 x))) |
(* -1/8 (sqrt (/ 1 x))) |
(* -1/8 (sqrt (/ 1 x))) |
(* -1/8 (sqrt (/ 1 x))) |
(* -1/8 (sqrt (/ 1 x))) |
(* -1/8 (sqrt (/ 1 x))) |
(* -1/8 (sqrt (/ 1 x))) |
(* -1/8 (sqrt (/ 1 x))) |
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(- 1 (sqrt x)) |
(- 1 (sqrt x)) |
(- 1 (sqrt x)) |
(- 1 (sqrt x)) |
(* -1 (sqrt x)) |
(* x (- (/ 1 x) (sqrt (/ 1 x)))) |
(* x (- (/ 1 x) (sqrt (/ 1 x)))) |
(* x (- (/ 1 x) (sqrt (/ 1 x)))) |
(* (sqrt x) (pow (sqrt -1) 2)) |
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))) |
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))) |
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(* -1/8 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(* 1/2 (sqrt (/ 1 x))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(* -1/8 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(* 1/2 (sqrt x)) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(/ 1 (+ 1 (sqrt x))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x) |
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x) |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) |
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x)) |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
(+ 1 (* -1 x)) |
(+ 1 (* -1 x)) |
(+ 1 (* -1 x)) |
(* -1 x) |
(* x (- (/ 1 x) 1)) |
(* x (- (/ 1 x) 1)) |
(* x (- (/ 1 x) 1)) |
(* -1 x) |
(* -1 (* x (- 1 (/ 1 x)))) |
(* -1 (* x (- 1 (/ 1 x)))) |
(* -1 (* x (- 1 (/ 1 x)))) |
(+ 1 (sqrt x)) |
(+ 1 (+ (sqrt x) (* 1/2 x))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))) |
(* 2 (sqrt x)) |
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
| Outputs |
|---|
(* 1/16 (sqrt (/ 1 (pow x 5)))) |
(*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) |
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3)) |
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (*.f64 x (*.f64 x x))) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x (*.f64 x x))) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x (*.f64 x x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) |
(+.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) |
(+.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/8 binary64))) |
(+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))) x)) |
(+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))) x)) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) |
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2)) |
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (*.f64 x x)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2)) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x x)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2)) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x x)) |
(* 1/2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) |
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(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x) |
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) |
(/.f64 (-.f64 (-.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))) x) |
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x)) |
(/.f64 (-.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 (*.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) #s(literal -5/128 binary64)) (pow.f64 x #s(literal 6 binary64))))) x) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1 x)) |
(-.f64 #s(literal 1 binary64) x) |
(+ 1 (* -1 x)) |
(-.f64 #s(literal 1 binary64) x) |
(+ 1 (* -1 x)) |
(-.f64 #s(literal 1 binary64) x) |
(* -1 x) |
(-.f64 #s(literal 0 binary64) x) |
(* x (- (/ 1 x) 1)) |
(-.f64 #s(literal 1 binary64) x) |
(* x (- (/ 1 x) 1)) |
(-.f64 #s(literal 1 binary64) x) |
(* x (- (/ 1 x) 1)) |
(-.f64 #s(literal 1 binary64) x) |
(* -1 x) |
(-.f64 #s(literal 0 binary64) x) |
(* -1 (* x (- 1 (/ 1 x)))) |
(-.f64 #s(literal 1 binary64) x) |
(* -1 (* x (- 1 (/ 1 x)))) |
(-.f64 #s(literal 1 binary64) x) |
(* -1 (* x (- 1 (/ 1 x)))) |
(-.f64 #s(literal 1 binary64) x) |
(+ 1 (sqrt x)) |
(+.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(+ 1 (+ (sqrt x) (* 1/2 x))) |
(+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 x #s(literal 1/2 binary64)))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))) |
(+.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))) |
(+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 #s(literal 1/16 binary64) x)))))) |
(* 2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 2 binary64)) |
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))) |
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))) |
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))) |
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 x) #s(literal 2 binary64)) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64)) (*.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
Compiled 24534 to 2801 computations (88.6% saved)
8 alts after pruning (6 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1040 | 6 | 1046 |
| Fresh | 0 | 0 | 0 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1044 | 8 | 1052 |
| Status | Accuracy | Program |
|---|---|---|
| 32.0% | (/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x x)) x) | |
| ▶ | 98.2% | (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
| ▶ | 99.6% | (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
| ▶ | 98.2% | (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
| ✓ | 6.0% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| ▶ | 98.6% | (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
| ✓ | 98.4% | (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
| ▶ | 91.1% | (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))) |
Compiled 141 to 102 computations (27.7% saved)
| 1× | egg-herbie |
Found 15 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (log.f64 x) |
| ✓ | cost-diff | 0 | (*.f64 (log.f64 x) #s(literal -1/2 binary64)) |
| ✓ | cost-diff | 6464 | (exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64))) |
| ✓ | cost-diff | 6464 | (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
| ✓ | cost-diff | 0 | (pow.f64 x #s(literal -1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (+.f64 x #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
| 20× | *-lowering-*.f32 |
| 20× | *-lowering-*.f64 |
| 10× | *-commutative |
| 10× | /-lowering-/.f32 |
| 10× | /-lowering-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 77 |
| 1 | 31 | 77 |
| 2 | 36 | 77 |
| 3 | 37 | 77 |
| 0 | 37 | 77 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(/ 1 (+ (pow (+ x 1) 1/2) (sqrt x))) |
1 |
(+ (pow (+ x 1) 1/2) (sqrt x)) |
(pow (+ x 1) 1/2) |
(+ x 1) |
x |
1/2 |
(sqrt x) |
(/ 1/2 (sqrt x)) |
1/2 |
(sqrt x) |
x |
(* (pow x -1/2) 1/2) |
(pow x -1/2) |
x |
-1/2 |
1/2 |
(/ (* (sqrt x) 1/2) x) |
(* (sqrt x) 1/2) |
(sqrt x) |
x |
1/2 |
(* 1/2 (exp (* (log x) -1/2))) |
1/2 |
(exp (* (log x) -1/2)) |
(* (log x) -1/2) |
(log x) |
x |
-1/2 |
| Outputs |
|---|
(/ 1 (+ (pow (+ x 1) 1/2) (sqrt x))) |
(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
1 |
#s(literal 1 binary64) |
(+ (pow (+ x 1) 1/2) (sqrt x)) |
(+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
(pow (+ x 1) 1/2) |
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) |
(+ x 1) |
(+.f64 #s(literal 1 binary64) x) |
x |
1/2 |
#s(literal 1/2 binary64) |
(sqrt x) |
(sqrt.f64 x) |
(/ 1/2 (sqrt x)) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
1/2 |
#s(literal 1/2 binary64) |
(sqrt x) |
(sqrt.f64 x) |
x |
(* (pow x -1/2) 1/2) |
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))) |
(pow x -1/2) |
(pow.f64 x #s(literal -1/2 binary64)) |
x |
-1/2 |
#s(literal -1/2 binary64) |
1/2 |
#s(literal 1/2 binary64) |
(/ (* (sqrt x) 1/2) x) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x) |
(* (sqrt x) 1/2) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(sqrt x) |
(sqrt.f64 x) |
x |
1/2 |
#s(literal 1/2 binary64) |
(* 1/2 (exp (* (log x) -1/2))) |
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))) |
1/2 |
#s(literal 1/2 binary64) |
(exp (* (log x) -1/2)) |
(pow.f64 x #s(literal -1/2 binary64)) |
(* (log x) -1/2) |
(*.f64 #s(literal -1/2 binary64) (log.f64 x)) |
(log x) |
(log.f64 x) |
x |
-1/2 |
#s(literal -1/2 binary64) |
Found 15 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.f64 (log.f64 x) #s(literal -1/2 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))) |
| ✓ | accuracy | 100.0% | (log.f64 x) |
| ✓ | accuracy | 92.3% | (exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64))) |
| ✓ | accuracy | 100.0% | (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 99.6% | (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
| ✓ | accuracy | 100.0% | (pow.f64 x #s(literal -1/2 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 99.6% | (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
| ✓ | accuracy | 100.0% | (+.f64 x #s(literal 1 binary64)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 100.0% | (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
| ✓ | accuracy | 99.6% | (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
| 68.0ms | 256× | 0 | valid |
Compiled 87 to 19 computations (78.2% saved)
ival-pow: 17.0ms (40.9% of total)ival-mult: 7.0ms (16.8% of total)ival-div: 5.0ms (12% of total)ival-add: 4.0ms (9.6% of total)ival-exp: 3.0ms (7.2% of total)ival-log: 3.0ms (7.2% of total)ival-sqrt: 2.0ms (4.8% of total)const: 1.0ms (2.4% of total)backward-pass: 0.0ms (0% of total)| Inputs |
|---|
#<alt (/ 1 (+ (pow (+ x 1) 1/2) (sqrt x)))> |
#<alt (+ (pow (+ x 1) 1/2) (sqrt x))> |
#<alt (pow (+ x 1) 1/2)> |
#<alt (+ x 1)> |
#<alt (/ 1/2 (sqrt x))> |
#<alt (sqrt x)> |
#<alt (* (pow x -1/2) 1/2)> |
#<alt (pow x -1/2)> |
#<alt (/ (* (sqrt x) 1/2) x)> |
#<alt (* (sqrt x) 1/2)> |
#<alt (* 1/2 (exp (* (log x) -1/2)))> |
#<alt (exp (* (log x) -1/2))> |
#<alt (* (log x) -1/2)> |
#<alt (log x)> |
| Outputs |
|---|
#<alt (/ 1 (+ 1 (sqrt x)))> |
#<alt (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))> |
#<alt (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))> |
#<alt (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)> |
#<alt (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)> |
#<alt (/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)> |
#<alt (* -1/2 (sqrt (/ 1 x)))> |
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))> |
#<alt (* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))> |
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))> |
#<alt (+ 1 (sqrt x))> |
#<alt (+ 1 (+ (sqrt x) (* 1/2 x)))> |
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))> |
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))> |
#<alt (* 2 (sqrt x))> |
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))> |
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))> |
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))> |
#<alt 1> |
#<alt (+ 1 x)> |
#<alt (+ 1 x)> |
#<alt (+ 1 x)> |
#<alt x> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt x> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (* -1/2 (log x))> |
#<alt (* -1/2 (log x))> |
#<alt (* -1/2 (log x))> |
#<alt (* -1/2 (log x))> |
#<alt (* 1/2 (log (/ 1 x)))> |
#<alt (* 1/2 (log (/ 1 x)))> |
#<alt (* 1/2 (log (/ 1 x)))> |
#<alt (* 1/2 (log (/ 1 x)))> |
#<alt (* -1/2 (+ (log -1) (* -1 (log (/ -1 x)))))> |
#<alt (* -1/2 (+ (log -1) (* -1 (log (/ -1 x)))))> |
#<alt (* -1/2 (+ (log -1) (* -1 (log (/ -1 x)))))> |
#<alt (* -1/2 (+ (log -1) (* -1 (log (/ -1 x)))))> |
#<alt (log x)> |
#<alt (log x)> |
#<alt (log x)> |
#<alt (log x)> |
#<alt (* -1 (log (/ 1 x)))> |
#<alt (* -1 (log (/ 1 x)))> |
#<alt (* -1 (log (/ 1 x)))> |
#<alt (* -1 (log (/ 1 x)))> |
#<alt (+ (log -1) (* -1 (log (/ -1 x))))> |
#<alt (+ (log -1) (* -1 (log (/ -1 x))))> |
#<alt (+ (log -1) (* -1 (log (/ -1 x))))> |
#<alt (+ (log -1) (* -1 (log (/ -1 x))))> |
42 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 31.0ms | x | @ | 0 | (* (log x) -1/2) |
| 18.0ms | x | @ | -inf | (* (log x) -1/2) |
| 6.0ms | x | @ | inf | (* (log x) -1/2) |
| 1.0ms | x | @ | -inf | (/ 1/2 (sqrt x)) |
| 0.0ms | x | @ | 0 | (pow x -1/2) |
| 1× | batch-egg-rewrite |
| 2794× | *-lowering-*.f32 |
| 2794× | *-lowering-*.f64 |
| 2124× | fma-lowering-fma.f32 |
| 2124× | fma-lowering-fma.f64 |
| 2072× | /-lowering-/.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 56 |
| 1 | 91 | 54 |
| 2 | 513 | 54 |
| 3 | 5191 | 54 |
| 0 | 8027 | 54 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ 1 (+ (pow (+ x 1) 1/2) (sqrt x))) |
(+ (pow (+ x 1) 1/2) (sqrt x)) |
(pow (+ x 1) 1/2) |
(+ x 1) |
(/ 1/2 (sqrt x)) |
(sqrt x) |
(* (pow x -1/2) 1/2) |
(pow x -1/2) |
(/ (* (sqrt x) 1/2) x) |
(* (sqrt x) 1/2) |
(* 1/2 (exp (* (log x) -1/2))) |
(exp (* (log x) -1/2)) |
(* (log x) -1/2) |
(log x) |
| Outputs |
|---|
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (+.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))) |
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (+.f64 #s(literal 1 binary64) x))) |
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))) |
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) (*.f64 (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))))) |
(+.f64 (*.f64 (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))))) |
(+.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x x)))) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x x))))) |
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))) |
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(-.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (-.f64 x x))) (/.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (-.f64 x x)))) |
(-.f64 (/.f64 (+.f64 x (+.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (/.f64 (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (-.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (-.f64 (+.f64 x (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) |
(/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x x)) (*.f64 (+.f64 #s(literal 1 binary64) (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (-.f64 x x))) |
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (+.f64 x (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) |
(/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) (+.f64 (neg.f64 (+.f64 #s(literal 1 binary64) x)) x)) |
(/.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (pow.f64 (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 3 binary64))) (*.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (-.f64 (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64))) (*.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 x x)) (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 x (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (-.f64 x x)) (+.f64 (+.f64 x (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (pow.f64 (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 3 binary64)))) (*.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (-.f64 (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64)))) (*.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 x x)) (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x x))) (*.f64 (+.f64 #s(literal 1 binary64) (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (-.f64 x x)) (+.f64 (+.f64 x (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (pow.f64 (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 3 binary64)))) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (-.f64 (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64)))) (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 x x)) (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x x))) (+.f64 #s(literal 1 binary64) (-.f64 x x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x x))) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (+.f64 (+.f64 x (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(/.f64 (/.f64 (-.f64 (+.f64 x (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (-.f64 (+.f64 x (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1/2 binary64)) |
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(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) |
(neg.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) |
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(/.f64 (sqrt.f64 x) (/.f64 x #s(literal 1/2 binary64))) |
(/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) |
(/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x) |
(/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) |
(/.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) x)) |
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) |
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) x) |
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 x)) |
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x)) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) x)) |
(/.f64 (/.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) #s(literal -1 binary64)) x) |
(/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64))) |
(pow.f64 (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) x))) |
(*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x)) |
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) |
(*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) x)) |
(*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 x) (/.f64 #s(literal -1 binary64) x))) |
(*.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) x))) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (sqrt.f64 x) (sqrt.f64 x))) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) |
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x))) |
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) x))) |
(*.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x)) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/4 binary64)))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) |
(*.f64 (/.f64 #s(literal -1 binary64) x) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64)) |
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1/2 binary64) x))) |
(*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/4 binary64))))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64))) |
(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (pow.f64 x #s(literal -1/2 binary64))) |
(*.f64 (/.f64 (sqrt.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) x)) |
(*.f64 (pow.f64 (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) (/.f64 #s(literal -1 binary64) x)) |
(*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/4 binary64)))) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/4 binary64)))) (pow.f64 x #s(literal -1/4 binary64))) |
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/8 binary64))) (pow.f64 x #s(literal -1/8 binary64))) |
(-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) |
(neg.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) |
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) |
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64)) |
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) |
(neg.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) |
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(/.f64 (sqrt.f64 x) (/.f64 x #s(literal 1/2 binary64))) |
(/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) |
(/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x) |
(/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) |
(/.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) x)) |
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) |
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) x) |
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 x)) |
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x)) |
(/.f64 (*.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) x)) |
(/.f64 (/.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) #s(literal -1 binary64)) x) |
(/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64))) |
(pow.f64 (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) x))) |
(*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x)) |
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) |
(*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) x)) |
(*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 x) (/.f64 #s(literal -1 binary64) x))) |
(*.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) x))) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (sqrt.f64 x) (sqrt.f64 x))) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) |
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x))) |
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) x))) |
(*.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x)) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/4 binary64)))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) |
(*.f64 (/.f64 #s(literal -1 binary64) x) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64)) |
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1/2 binary64) x))) |
(*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/4 binary64))))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64))) |
(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (pow.f64 x #s(literal -1/2 binary64))) |
(*.f64 (/.f64 (sqrt.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) x)) |
(*.f64 (pow.f64 (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) (/.f64 #s(literal -1 binary64) x)) |
(*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/4 binary64)))) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/4 binary64)))) (pow.f64 x #s(literal -1/4 binary64))) |
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/8 binary64))) (pow.f64 x #s(literal -1/8 binary64))) |
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x))) |
(exp.f64 (*.f64 (log.f64 (*.f64 x x)) #s(literal -1/4 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal -1/4 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal -1/2 binary64))) (log.f64 x))) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal -1/4 binary64)) #s(literal 2 binary64))) |
(exp.f64 (+.f64 (*.f64 (log.f64 x) #s(literal -1/4 binary64)) (*.f64 (log.f64 x) #s(literal -1/4 binary64)))) |
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))) |
(exp.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) (log.f64 x))) |
(sqrt.f64 (/.f64 x (*.f64 x x))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 (sqrt.f64 x) x) |
(/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) |
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (-.f64 #s(literal 0 binary64) x)) |
(/.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) (sqrt.f64 x)) |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64))) |
(pow.f64 x #s(literal -1/2 binary64)) |
(pow.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64)) |
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 x)) |
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) |
(*.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) |
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) x)) |
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) x))) |
(*.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal -1/8 binary64)) (pow.f64 x #s(literal -1/4 binary64)))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) x)) |
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) x) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x)) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x))) |
(*.f64 (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (/.f64 (log.f64 x) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (/.f64 (log.f64 x) #s(literal 2 binary64)))) |
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64))) |
(*.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/8 binary64))) (pow.f64 x #s(literal -1/8 binary64))) |
(*.f64 #s(literal -1/2 binary64) (log.f64 x)) |
(*.f64 (log.f64 x) #s(literal -1/2 binary64)) |
(log.f64 x) |
(+.f64 (log.f64 x) #s(literal 0 binary64)) |
(+.f64 #s(literal 0 binary64) (log.f64 x)) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) (*.f64 #s(literal 1/2 binary64) (log.f64 x))) |
(*.f64 #s(literal 1 binary64) (log.f64 x)) |
(*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 x x))) |
(*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 x))) |
| 1× | egg-herbie |
| 3912× | *-lowering-*.f32 |
| 3912× | *-lowering-*.f64 |
| 2246× | +-lowering-+.f64 |
| 2246× | +-lowering-+.f32 |
| 1500× | fnmsub-define |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 200 | 1272 |
| 1 | 625 | 1155 |
| 2 | 2176 | 1137 |
| 3 | 6879 | 1136 |
| 0 | 8144 | 1136 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ 1 (+ 1 (sqrt x))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x) |
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x) |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) |
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x)) |
(+ 1 (sqrt x)) |
(+ 1 (+ (sqrt x) (* 1/2 x))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))) |
(* 2 (sqrt x)) |
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
1 |
(+ 1 x) |
(+ 1 x) |
(+ 1 x) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (sqrt x)) |
(* 1/2 (sqrt x)) |
(* 1/2 (sqrt x)) |
(* 1/2 (sqrt x)) |
(* 1/2 (sqrt x)) |
(* 1/2 (sqrt x)) |
(* 1/2 (sqrt x)) |
(* 1/2 (sqrt x)) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* -1/2 (log x)) |
(* -1/2 (log x)) |
(* -1/2 (log x)) |
(* -1/2 (log x)) |
(* 1/2 (log (/ 1 x))) |
(* 1/2 (log (/ 1 x))) |
(* 1/2 (log (/ 1 x))) |
(* 1/2 (log (/ 1 x))) |
(* -1/2 (+ (log -1) (* -1 (log (/ -1 x))))) |
(* -1/2 (+ (log -1) (* -1 (log (/ -1 x))))) |
(* -1/2 (+ (log -1) (* -1 (log (/ -1 x))))) |
(* -1/2 (+ (log -1) (* -1 (log (/ -1 x))))) |
(log x) |
(log x) |
(log x) |
(log x) |
(* -1 (log (/ 1 x))) |
(* -1 (log (/ 1 x))) |
(* -1 (log (/ 1 x))) |
(* -1 (log (/ 1 x))) |
(+ (log -1) (* -1 (log (/ -1 x)))) |
(+ (log -1) (* -1 (log (/ -1 x)))) |
(+ (log -1) (* -1 (log (/ -1 x)))) |
(+ (log -1) (* -1 (log (/ -1 x)))) |
| Outputs |
|---|
(/ 1 (+ 1 (sqrt x))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (*.f64 x (+.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)))))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (*.f64 x (+.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))) (*.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))))))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)))))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x) |
(/.f64 (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) x) |
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (+.f64 (-.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) x) |
(* -1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x) |
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) x) |
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x)) |
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (-.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64)))) (*.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))) (-.f64 #s(literal 0 binary64) x)) |
(+ 1 (sqrt x)) |
(+.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(+ 1 (+ (sqrt x) (* 1/2 x))) |
(+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 x #s(literal 1/2 binary64)))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))) |
(+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))) |
(+.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))) |
(* 2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 2 binary64)) |
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))) |
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))) |
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))) |
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 x) #s(literal 2 binary64)) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
(*.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (+.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (/.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))) (-.f64 #s(literal 0 binary64) x)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (+.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))) |
1 |
#s(literal 1 binary64) |
(+ 1 x) |
(+.f64 #s(literal 1 binary64) x) |
(+ 1 x) |
(+.f64 #s(literal 1 binary64) x) |
(+ 1 x) |
(+.f64 #s(literal 1 binary64) x) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* 1/2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* 1/2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* 1/2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* 1/2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* 1/2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* 1/2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* 1/2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1/2 (log x)) |
(*.f64 #s(literal -1/2 binary64) (log.f64 x)) |
(* -1/2 (log x)) |
(*.f64 #s(literal -1/2 binary64) (log.f64 x)) |
(* -1/2 (log x)) |
(*.f64 #s(literal -1/2 binary64) (log.f64 x)) |
(* -1/2 (log x)) |
(*.f64 #s(literal -1/2 binary64) (log.f64 x)) |
(* 1/2 (log (/ 1 x))) |
(*.f64 #s(literal -1/2 binary64) (log.f64 x)) |
(* 1/2 (log (/ 1 x))) |
(*.f64 #s(literal -1/2 binary64) (log.f64 x)) |
(* 1/2 (log (/ 1 x))) |
(*.f64 #s(literal -1/2 binary64) (log.f64 x)) |
(* 1/2 (log (/ 1 x))) |
(*.f64 #s(literal -1/2 binary64) (log.f64 x)) |
(* -1/2 (+ (log -1) (* -1 (log (/ -1 x))))) |
(*.f64 #s(literal -1/2 binary64) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))) |
(* -1/2 (+ (log -1) (* -1 (log (/ -1 x))))) |
(*.f64 #s(literal -1/2 binary64) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))) |
(* -1/2 (+ (log -1) (* -1 (log (/ -1 x))))) |
(*.f64 #s(literal -1/2 binary64) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))) |
(* -1/2 (+ (log -1) (* -1 (log (/ -1 x))))) |
(*.f64 #s(literal -1/2 binary64) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))) |
(log x) |
(log.f64 x) |
(log x) |
(log.f64 x) |
(log x) |
(log.f64 x) |
(log x) |
(log.f64 x) |
(* -1 (log (/ 1 x))) |
(log.f64 x) |
(* -1 (log (/ 1 x))) |
(log.f64 x) |
(* -1 (log (/ 1 x))) |
(log.f64 x) |
(* -1 (log (/ 1 x))) |
(log.f64 x) |
(+ (log -1) (* -1 (log (/ -1 x)))) |
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) |
(+ (log -1) (* -1 (log (/ -1 x)))) |
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) |
(+ (log -1) (* -1 (log (/ -1 x)))) |
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) |
(+ (log -1) (* -1 (log (/ -1 x)))) |
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) |
Compiled 12865 to 1792 computations (86.1% saved)
8 alts after pruning (5 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 914 | 4 | 918 |
| Fresh | 0 | 1 | 1 |
| Picked | 3 | 2 | 5 |
| Done | 1 | 1 | 2 |
| Total | 918 | 8 | 926 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 32.0% | (/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x x)) x) |
| ▶ | 99.6% | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
| ✓ | 98.2% | (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
| ▶ | 91.0% | (/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))) |
| ✓ | 6.0% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| ✓ | 98.6% | (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
| ▶ | 98.1% | (*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) |
| ▶ | 48.8% | (*.f64 (sqrt.f64 (/.f64 x (*.f64 x x))) #s(literal 1/2 binary64)) |
Compiled 139 to 95 computations (31.7% saved)
| 1× | egg-herbie |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (+.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) |
| ✓ | cost-diff | 0 | (/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x x)) |
| ✓ | cost-diff | 0 | (/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x x)) x) |
| ✓ | cost-diff | 0 | (log.f64 x) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) (log.f64 x)) |
| ✓ | cost-diff | 6528 | (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))) |
| ✓ | cost-diff | 6528 | (/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))) |
| ✓ | cost-diff | 0 | (*.f64 x x) |
| ✓ | cost-diff | 128 | (/.f64 x (*.f64 x x)) |
| ✓ | cost-diff | 192 | (sqrt.f64 (/.f64 x (*.f64 x x))) |
| ✓ | cost-diff | 256 | (*.f64 (sqrt.f64 (/.f64 x (*.f64 x x))) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1/2 binary64) x) |
| ✓ | cost-diff | 128 | (*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) x) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 0 | (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
| 1630× | fma-lowering-fma.f32 |
| 1630× | fma-lowering-fma.f64 |
| 1524× | sum5-define |
| 1522× | fnmadd-define |
| 1474× | *-lowering-*.f32 |
Useful iterations: 10 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 30 | 176 |
| 1 | 65 | 167 |
| 2 | 111 | 165 |
| 3 | 160 | 165 |
| 4 | 196 | 165 |
| 5 | 218 | 165 |
| 6 | 247 | 162 |
| 7 | 297 | 162 |
| 8 | 486 | 159 |
| 9 | 2388 | 159 |
| 10 | 4958 | 158 |
| 0 | 8072 | 158 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ 1 (+ (sqrt (+ 1 x)) (sqrt x))) |
1 |
(+ (sqrt (+ 1 x)) (sqrt x)) |
(sqrt (+ 1 x)) |
(+ 1 x) |
x |
(sqrt x) |
(* (/ 1/2 x) (sqrt x)) |
(/ 1/2 x) |
1/2 |
x |
(sqrt x) |
(* (sqrt (/ x (* x x))) 1/2) |
(sqrt (/ x (* x x))) |
(/ x (* x x)) |
x |
(* x x) |
1/2 |
(/ 1/2 (exp (* 1/2 (log x)))) |
1/2 |
(exp (* 1/2 (log x))) |
(* 1/2 (log x)) |
(log x) |
x |
(/ (/ (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8)))) (* x x)) x) |
(/ (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8)))) (* x x)) |
(+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8)))) |
(* (sqrt (* x (* x x))) (* x 1/2)) |
(sqrt (* x (* x x))) |
(* x (* x x)) |
x |
(* x x) |
(* x 1/2) |
1/2 |
(* (sqrt x) (+ 1/16 (* x -1/8))) |
(sqrt x) |
(+ 1/16 (* x -1/8)) |
1/16 |
(* x -1/8) |
-1/8 |
| Outputs |
|---|
(/ 1 (+ (sqrt (+ 1 x)) (sqrt x))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
1 |
#s(literal 1 binary64) |
(+ (sqrt (+ 1 x)) (sqrt x)) |
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(sqrt (+ 1 x)) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+ 1 x) |
(+.f64 #s(literal 1 binary64) x) |
x |
(sqrt x) |
(sqrt.f64 x) |
(* (/ 1/2 x) (sqrt x)) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(/ 1/2 x) |
(/.f64 #s(literal 1/2 binary64) x) |
1/2 |
#s(literal 1/2 binary64) |
x |
(sqrt x) |
(sqrt.f64 x) |
(* (sqrt (/ x (* x x))) 1/2) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(sqrt (/ x (* x x))) |
(pow.f64 x #s(literal -1/2 binary64)) |
(/ x (* x x)) |
(/.f64 #s(literal 1 binary64) x) |
x |
(* x x) |
(*.f64 x x) |
1/2 |
#s(literal 1/2 binary64) |
(/ 1/2 (exp (* 1/2 (log x)))) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
1/2 |
#s(literal 1/2 binary64) |
(exp (* 1/2 (log x))) |
(sqrt.f64 x) |
(* 1/2 (log x)) |
(*.f64 #s(literal 1/2 binary64) (log.f64 x)) |
(log x) |
(log.f64 x) |
x |
(/ (/ (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8)))) (* x x)) x) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x (*.f64 x x))) |
(/ (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8)))) (* x x)) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x x)) |
(+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8)))) |
(+.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) |
(* (sqrt (* x (* x x))) (* x 1/2)) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) |
(sqrt (* x (* x x))) |
(sqrt.f64 (*.f64 x (*.f64 x x))) |
(* x (* x x)) |
(*.f64 x (*.f64 x x)) |
x |
(* x x) |
(*.f64 x x) |
(* x 1/2) |
(*.f64 x #s(literal 1/2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(* (sqrt x) (+ 1/16 (* x -1/8))) |
(*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) |
(sqrt x) |
(sqrt.f64 x) |
(+ 1/16 (* x -1/8)) |
(+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) |
1/16 |
#s(literal 1/16 binary64) |
(* x -1/8) |
(*.f64 x #s(literal -1/8 binary64)) |
-1/8 |
#s(literal -1/8 binary64) |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.6% | (/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x x)) x) |
| ✓ | accuracy | 71.9% | (sqrt.f64 (*.f64 x (*.f64 x x))) |
| ✓ | accuracy | 70.1% | (+.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) |
| ✓ | accuracy | 41.7% | (/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x x)) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal 1/2 binary64) (log.f64 x)) |
| ✓ | accuracy | 100.0% | (log.f64 x) |
| ✓ | accuracy | 99.6% | (/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))) |
| ✓ | accuracy | 92.3% | (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))) |
| ✓ | accuracy | 100.0% | (*.f64 (sqrt.f64 (/.f64 x (*.f64 x x))) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 x x) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (/.f64 x (*.f64 x x))) |
| ✓ | accuracy | 51.5% | (/.f64 x (*.f64 x x)) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 1/2 binary64) x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 99.4% | (*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 100.0% | (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
| ✓ | accuracy | 99.6% | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
| 118.0ms | 256× | 0 | valid |
Compiled 202 to 31 computations (84.7% saved)
ival-mult: 15.0ms (34.1% of total)ival-div: 10.0ms (22.8% of total)ival-sqrt: 7.0ms (15.9% of total)ival-add: 6.0ms (13.7% of total)ival-log: 3.0ms (6.8% of total)ival-exp: 3.0ms (6.8% of total)const: 1.0ms (2.3% of total)backward-pass: 0.0ms (0% of total)| Inputs |
|---|
#<alt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))> |
#<alt (+ (sqrt (+ 1 x)) (sqrt x))> |
#<alt (sqrt (+ 1 x))> |
#<alt (+ 1 x)> |
#<alt (* (/ 1/2 x) (sqrt x))> |
#<alt (/ 1/2 x)> |
#<alt (sqrt x)> |
#<alt (* (sqrt (/ x (* x x))) 1/2)> |
#<alt (sqrt (/ x (* x x)))> |
#<alt (/ x (* x x))> |
#<alt (* x x)> |
#<alt (/ 1/2 (exp (* 1/2 (log x))))> |
#<alt (exp (* 1/2 (log x)))> |
#<alt (* 1/2 (log x))> |
#<alt (log x)> |
#<alt (/ (/ (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8)))) (* x x)) x)> |
#<alt (/ (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8)))) (* x x))> |
#<alt (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8))))> |
#<alt (* (sqrt (* x (* x x))) (* x 1/2))> |
#<alt (sqrt (* x (* x x)))> |
| Outputs |
|---|
#<alt (/ 1 (+ 1 (sqrt x)))> |
#<alt (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))> |
#<alt (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))> |
#<alt (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)> |
#<alt (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)> |
#<alt (/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)> |
#<alt (* -1/2 (sqrt (/ 1 x)))> |
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))> |
#<alt (* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))> |
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))> |
#<alt (+ 1 (sqrt x))> |
#<alt (+ 1 (+ (sqrt x) (* 1/2 x)))> |
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))> |
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))> |
#<alt (* 2 (sqrt x))> |
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))> |
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))> |
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))> |
#<alt 1> |
#<alt (+ 1 x)> |
#<alt (+ 1 x)> |
#<alt (+ 1 x)> |
#<alt x> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt x> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (sqrt (/ 1 x))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (log x))> |
#<alt (* 1/2 (log x))> |
#<alt (* 1/2 (log x))> |
#<alt (* 1/2 (log x))> |
#<alt (* -1/2 (log (/ 1 x)))> |
#<alt (* -1/2 (log (/ 1 x)))> |
#<alt (* -1/2 (log (/ 1 x)))> |
#<alt (* -1/2 (log (/ 1 x)))> |
#<alt (* 1/2 (+ (log -1) (* -1 (log (/ -1 x)))))> |
#<alt (* 1/2 (+ (log -1) (* -1 (log (/ -1 x)))))> |
#<alt (* 1/2 (+ (log -1) (* -1 (log (/ -1 x)))))> |
#<alt (* 1/2 (+ (log -1) (* -1 (log (/ -1 x)))))> |
#<alt (log x)> |
#<alt (log x)> |
#<alt (log x)> |
#<alt (log x)> |
#<alt (* -1 (log (/ 1 x)))> |
#<alt (* -1 (log (/ 1 x)))> |
#<alt (* -1 (log (/ 1 x)))> |
#<alt (* -1 (log (/ 1 x)))> |
#<alt (+ (log -1) (* -1 (log (/ -1 x))))> |
#<alt (+ (log -1) (* -1 (log (/ -1 x))))> |
#<alt (+ (log -1) (* -1 (log (/ -1 x))))> |
#<alt (+ (log -1) (* -1 (log (/ -1 x))))> |
#<alt (* 1/16 (sqrt (/ 1 (pow x 5))))> |
#<alt (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3))> |
#<alt (/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3))> |
#<alt (/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))> |
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))> |
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))> |
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))> |
#<alt (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))> |
#<alt (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))> |
#<alt (* 1/16 (sqrt (/ 1 (pow x 3))))> |
#<alt (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2))> |
#<alt (/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2))> |
#<alt (/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))> |
#<alt (* 1/2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* 1/16 (sqrt x))> |
#<alt (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x)))> |
#<alt (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))> |
#<alt (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))> |
#<alt (* 1/2 (sqrt (pow x 5)))> |
#<alt (* (pow x 3) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))> |
#<alt (* (pow x 3) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))> |
#<alt (* (pow x 3) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))> |
#<alt (* 1/2 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (pow x 3) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* 1/2 (sqrt (pow x 5)))> |
#<alt (* 1/2 (sqrt (pow x 5)))> |
#<alt (* 1/2 (sqrt (pow x 5)))> |
#<alt (* 1/2 (sqrt (pow x 5)))> |
#<alt (* 1/2 (sqrt (pow x 5)))> |
#<alt (* 1/2 (sqrt (pow x 5)))> |
#<alt (* 1/2 (sqrt (pow x 5)))> |
#<alt (* 1/2 (sqrt (pow x 5)))> |
#<alt (* 1/2 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))> |
#<alt (sqrt (pow x 3))> |
#<alt (sqrt (pow x 3))> |
#<alt (sqrt (pow x 3))> |
#<alt (sqrt (pow x 3))> |
#<alt (sqrt (pow x 3))> |
#<alt (sqrt (pow x 3))> |
#<alt (sqrt (pow x 3))> |
#<alt (sqrt (pow x 3))> |
#<alt (* (sqrt (pow x 3)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (pow x 3)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (pow x 3)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (pow x 3)) (pow (sqrt -1) 2))> |
60 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (/ (/ (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8)))) (* x x)) x) |
| 0.0ms | x | @ | 0 | (* (sqrt (* x (* x x))) (* x 1/2)) |
| 0.0ms | x | @ | inf | (/ (/ (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8)))) (* x x)) x) |
| 0.0ms | x | @ | 0 | (/ (/ (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8)))) (* x x)) x) |
| 0.0ms | x | @ | 0 | (/ 1/2 x) |
| 1× | batch-egg-rewrite |
| 4566× | *-lowering-*.f32 |
| 4566× | *-lowering-*.f64 |
| 3932× | /-lowering-/.f32 |
| 3932× | /-lowering-/.f64 |
| 1900× | frac-times |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 30 | 135 |
| 1 | 160 | 115 |
| 2 | 1226 | 105 |
| 0 | 8242 | 105 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ 1 (+ (sqrt (+ 1 x)) (sqrt x))) |
(+ (sqrt (+ 1 x)) (sqrt x)) |
(sqrt (+ 1 x)) |
(+ 1 x) |
(* (/ 1/2 x) (sqrt x)) |
(/ 1/2 x) |
(sqrt x) |
(* (sqrt (/ x (* x x))) 1/2) |
(sqrt (/ x (* x x))) |
(/ x (* x x)) |
(* x x) |
(/ 1/2 (exp (* 1/2 (log x)))) |
(exp (* 1/2 (log x))) |
(* 1/2 (log x)) |
(log x) |
(/ (/ (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8)))) (* x x)) x) |
(/ (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8)))) (* x x)) |
(+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8)))) |
(* (sqrt (* x (* x x))) (* x 1/2)) |
(sqrt (* x (* x x))) |
| Outputs |
|---|
(exp.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))) |
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64)))))) |
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (pow.f64 (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (*.f64 (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (-.f64 (pow.f64 (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64)))))))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (*.f64 (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64)))))) |
(pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1 binary64)) |
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1/2 binary64)) |
(pow.f64 (exp.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(*.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64))))) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64))) |
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(exp.f64 (neg.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64)))) |
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1 binary64))) |
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (/.f64 x (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(-.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal 1 binary64)) (/.f64 (/.f64 x (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal 1 binary64))) |
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (/.f64 x (*.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))) |
(-.f64 (/.f64 x (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(fma.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 x) #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 x) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64)))) (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (-.f64 (+.f64 #s(literal 1 binary64) x) x))) |
(/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64)))) (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (-.f64 (+.f64 #s(literal 1 binary64) x) x)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64)) |
(/.f64 (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64))))) |
(/.f64 (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 x (-.f64 (+.f64 #s(literal 1 binary64) x) (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64))))) |
(/.f64 (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (*.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64)))))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (*.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) #s(literal 1 binary64)) |
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64)))))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 x (-.f64 (+.f64 #s(literal 1 binary64) x) (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64)))))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (neg.f64 (*.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64))))))) |
(/.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (neg.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(/.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (neg.f64 (*.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))) |
(/.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x)) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (*.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) x)) (*.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 3/2 binary64)))) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64)))))) |
(/.f64 (*.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (*.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64)))))) |
(/.f64 (*.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (+.f64 #s(literal 1 binary64) x) x))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(/.f64 (*.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64))))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x))) (neg.f64 (neg.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))) |
(/.f64 (neg.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x))) (neg.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64)))) (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) #s(literal -1 binary64)) |
(*.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1 binary64)) |
(*.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(*.f64 (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64)))))) |
(*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
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(pow.f64 (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64)))) (-.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))))) (+.f64 (*.f64 (pow.f64 x #s(literal 9/2 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (pow.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) #s(literal 3/2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64)))) (*.f64 x (*.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))))) #s(literal -1 binary64)) |
(*.f64 (+.f64 (*.f64 (pow.f64 x #s(literal 9/2 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (pow.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64)))) (-.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))))))) |
(*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64)))) (*.f64 x (*.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))))) |
(*.f64 x (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3/2 binary64)))) |
(*.f64 (sqrt.f64 x) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) |
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) |
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 x #s(literal 1/2 binary64))) |
(*.f64 (*.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) |
(*.f64 (pow.f64 x #s(literal 5/2 binary64)) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) x) |
(*.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 x)) x) |
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64))) |
(exp.f64 (*.f64 (log.f64 x) #s(literal 3/2 binary64))) |
(fabs.f64 (pow.f64 x #s(literal 3/2 binary64))) |
(sqrt.f64 (*.f64 x (*.f64 x x))) |
(pow.f64 x #s(literal 3/2 binary64)) |
(pow.f64 (sqrt.f64 x) #s(literal 3 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 3/4 binary64)) |
(pow.f64 (*.f64 x (*.f64 x x)) #s(literal 1/2 binary64)) |
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 x) #s(literal 3 binary64))) |
(pow.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 2 binary64)) |
(*.f64 x (sqrt.f64 x)) |
(*.f64 (sqrt.f64 x) x) |
(*.f64 (*.f64 x (*.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) |
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64))) |
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) |
(*.f64 (pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 x) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 x) #s(literal 2 binary64)))) #s(literal 3 binary64))) |
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 3 binary64))) |
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64)))) |
| 1× | egg-herbie |
| 3282× | *-lowering-*.f32 |
| 3282× | *-lowering-*.f64 |
| 2554× | +-lowering-+.f64 |
| 2554× | +-lowering-+.f32 |
| 2272× | fma-lowering-fma.f32 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 254 | 2070 |
| 1 | 805 | 1798 |
| 2 | 3056 | 1768 |
| 3 | 7455 | 1765 |
| 0 | 8822 | 1765 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ 1 (+ 1 (sqrt x))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x) |
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x) |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) |
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x)) |
(+ 1 (sqrt x)) |
(+ 1 (+ (sqrt x) (* 1/2 x))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))) |
(* 2 (sqrt x)) |
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
1 |
(+ 1 x) |
(+ 1 x) |
(+ 1 x) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* 1/2 (log x)) |
(* 1/2 (log x)) |
(* 1/2 (log x)) |
(* 1/2 (log x)) |
(* -1/2 (log (/ 1 x))) |
(* -1/2 (log (/ 1 x))) |
(* -1/2 (log (/ 1 x))) |
(* -1/2 (log (/ 1 x))) |
(* 1/2 (+ (log -1) (* -1 (log (/ -1 x))))) |
(* 1/2 (+ (log -1) (* -1 (log (/ -1 x))))) |
(* 1/2 (+ (log -1) (* -1 (log (/ -1 x))))) |
(* 1/2 (+ (log -1) (* -1 (log (/ -1 x))))) |
(log x) |
(log x) |
(log x) |
(log x) |
(* -1 (log (/ 1 x))) |
(* -1 (log (/ 1 x))) |
(* -1 (log (/ 1 x))) |
(* -1 (log (/ 1 x))) |
(+ (log -1) (* -1 (log (/ -1 x)))) |
(+ (log -1) (* -1 (log (/ -1 x)))) |
(+ (log -1) (* -1 (log (/ -1 x)))) |
(+ (log -1) (* -1 (log (/ -1 x)))) |
(* 1/16 (sqrt (/ 1 (pow x 5)))) |
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) |
(* 1/2 (sqrt (/ 1 x))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2)) |
(* 1/2 (sqrt x)) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) |
(* 1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* 1/16 (sqrt x)) |
(+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) |
(+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) |
(+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) |
(* 1/2 (sqrt (pow x 5))) |
(* (pow x 3) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* (pow x 3) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) |
(* (pow x 3) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) |
(* 1/2 (* (sqrt (pow x 5)) (pow (sqrt -1) 2))) |
(* -1 (* (pow x 3) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* 1/2 (sqrt (pow x 5))) |
(* 1/2 (sqrt (pow x 5))) |
(* 1/2 (sqrt (pow x 5))) |
(* 1/2 (sqrt (pow x 5))) |
(* 1/2 (sqrt (pow x 5))) |
(* 1/2 (sqrt (pow x 5))) |
(* 1/2 (sqrt (pow x 5))) |
(* 1/2 (sqrt (pow x 5))) |
(* 1/2 (* (sqrt (pow x 5)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (pow x 5)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (pow x 5)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (pow x 5)) (pow (sqrt -1) 2))) |
(sqrt (pow x 3)) |
(sqrt (pow x 3)) |
(sqrt (pow x 3)) |
(sqrt (pow x 3)) |
(sqrt (pow x 3)) |
(sqrt (pow x 3)) |
(sqrt (pow x 3)) |
(sqrt (pow x 3)) |
(* (sqrt (pow x 3)) (pow (sqrt -1) 2)) |
(* (sqrt (pow x 3)) (pow (sqrt -1) 2)) |
(* (sqrt (pow x 3)) (pow (sqrt -1) 2)) |
(* (sqrt (pow x 3)) (pow (sqrt -1) 2)) |
| Outputs |
|---|
(/ 1 (+ 1 (sqrt x))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (*.f64 x (+.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)))))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
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(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* 1/2 (log x)) |
(*.f64 #s(literal 1/2 binary64) (log.f64 x)) |
(* 1/2 (log x)) |
(*.f64 #s(literal 1/2 binary64) (log.f64 x)) |
(* 1/2 (log x)) |
(*.f64 #s(literal 1/2 binary64) (log.f64 x)) |
(* 1/2 (log x)) |
(*.f64 #s(literal 1/2 binary64) (log.f64 x)) |
(* -1/2 (log (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (log.f64 x)) |
(* -1/2 (log (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (log.f64 x)) |
(* -1/2 (log (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (log.f64 x)) |
(* -1/2 (log (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (log.f64 x)) |
(* 1/2 (+ (log -1) (* -1 (log (/ -1 x))))) |
(*.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))) |
(* 1/2 (+ (log -1) (* -1 (log (/ -1 x))))) |
(*.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))) |
(* 1/2 (+ (log -1) (* -1 (log (/ -1 x))))) |
(*.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))) |
(* 1/2 (+ (log -1) (* -1 (log (/ -1 x))))) |
(*.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))) |
(log x) |
(log.f64 x) |
(log x) |
(log.f64 x) |
(log x) |
(log.f64 x) |
(log x) |
(log.f64 x) |
(* -1 (log (/ 1 x))) |
(log.f64 x) |
(* -1 (log (/ 1 x))) |
(log.f64 x) |
(* -1 (log (/ 1 x))) |
(log.f64 x) |
(* -1 (log (/ 1 x))) |
(log.f64 x) |
(+ (log -1) (* -1 (log (/ -1 x)))) |
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) |
(+ (log -1) (* -1 (log (/ -1 x)))) |
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) |
(+ (log -1) (* -1 (log (/ -1 x)))) |
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) |
(+ (log -1) (* -1 (log (/ -1 x)))) |
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) |
(* 1/16 (sqrt (/ 1 (pow x 5)))) |
(*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) |
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3)) |
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 x) #s(literal 1/16 binary64))) (*.f64 x (*.f64 x x))) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) |
(/.f64 (+.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x (*.f64 x x))) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) |
(/.f64 (+.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x (*.f64 x x))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) |
(+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) x)) |
(+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) x)) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) |
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2)) |
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 x) #s(literal 1/16 binary64))) (*.f64 x x)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2)) |
(/.f64 (+.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x x)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2)) |
(/.f64 (+.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x x)) |
(* 1/2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) |
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) |
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))) |
(* 1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) |
(*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 x #s(literal -1/2 binary64)))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 x #s(literal -1/2 binary64)))) |
(* 1/16 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/16 binary64)) |
(+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) |
(+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 x) #s(literal 1/16 binary64))) |
(+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) |
(+.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) |
(+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) |
(+.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) |
(* 1/2 (sqrt (pow x 5))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 5 binary64)))) |
(* (pow x 3) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
(* (pow x 3) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))) |
(* (pow x 3) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))) |
(* 1/2 (* (sqrt (pow x 5)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 5 binary64)))) |
(* -1 (* (pow x 3) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 x #s(literal -1/2 binary64))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 x #s(literal -1/2 binary64))))) |
(* 1/2 (sqrt (pow x 5))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 5 binary64)))) |
(* 1/2 (sqrt (pow x 5))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 5 binary64)))) |
(* 1/2 (sqrt (pow x 5))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 5 binary64)))) |
(* 1/2 (sqrt (pow x 5))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 5 binary64)))) |
(* 1/2 (sqrt (pow x 5))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 5 binary64)))) |
(* 1/2 (sqrt (pow x 5))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 5 binary64)))) |
(* 1/2 (sqrt (pow x 5))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 5 binary64)))) |
(* 1/2 (sqrt (pow x 5))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 5 binary64)))) |
(* 1/2 (* (sqrt (pow x 5)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 5 binary64)))) |
(* 1/2 (* (sqrt (pow x 5)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 5 binary64)))) |
(* 1/2 (* (sqrt (pow x 5)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 5 binary64)))) |
(* 1/2 (* (sqrt (pow x 5)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 5 binary64)))) |
(sqrt (pow x 3)) |
(sqrt.f64 (*.f64 x (*.f64 x x))) |
(sqrt (pow x 3)) |
(sqrt.f64 (*.f64 x (*.f64 x x))) |
(sqrt (pow x 3)) |
(sqrt.f64 (*.f64 x (*.f64 x x))) |
(sqrt (pow x 3)) |
(sqrt.f64 (*.f64 x (*.f64 x x))) |
(sqrt (pow x 3)) |
(sqrt.f64 (*.f64 x (*.f64 x x))) |
(sqrt (pow x 3)) |
(sqrt.f64 (*.f64 x (*.f64 x x))) |
(sqrt (pow x 3)) |
(sqrt.f64 (*.f64 x (*.f64 x x))) |
(sqrt (pow x 3)) |
(sqrt.f64 (*.f64 x (*.f64 x x))) |
(* (sqrt (pow x 3)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (*.f64 x (*.f64 x x)))) |
(* (sqrt (pow x 3)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (*.f64 x (*.f64 x x)))) |
(* (sqrt (pow x 3)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (*.f64 x (*.f64 x x)))) |
(* (sqrt (pow x 3)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (*.f64 x (*.f64 x x)))) |
Compiled 35761 to 3259 computations (90.9% saved)
8 alts after pruning (1 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1368 | 1 | 1369 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 3 | 3 |
| Total | 1369 | 8 | 1377 |
| Status | Accuracy | Program |
|---|---|---|
| 39.2% | (/.f64 (/.f64 (+.f64 (*.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x x)) x) | |
| ✓ | 99.6% | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
| ✓ | 98.2% | (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
| ✓ | 91.0% | (/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))) |
| ✓ | 6.0% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| ✓ | 98.6% | (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
| ✓ | 98.1% | (*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) |
| ✓ | 48.8% | (*.f64 (sqrt.f64 (/.f64 x (*.f64 x x))) #s(literal 1/2 binary64)) |
Compiled 254 to 122 computations (52% saved)
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) |
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
(*.f64 (sqrt.f64 (/.f64 x (*.f64 x x))) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
(/.f64 (/.f64 (+.f64 (*.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x x)) x) |
(/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))) (*.f64 x x)) x) |
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) x) |
| Outputs |
|---|
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
2 calls:
| 5.0ms | x |
| 4.0ms | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | x |
| 99.6% | 1 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
Compiled 10 to 7 computations (30% saved)
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) |
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
(*.f64 (sqrt.f64 (/.f64 x (*.f64 x x))) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))) |
| Outputs |
|---|
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
2 calls:
| 6.0ms | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.6% | 1 | x |
| 98.6% | 1 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
Compiled 10 to 7 computations (30% saved)
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
| Outputs |
|---|
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
1 calls:
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.2% | 1 | x |
Compiled 2 to 1 computations (50% saved)
Total -0.0b remaining (-0%)
Threshold costs -0b (-0%)
| Inputs |
|---|
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| Outputs |
|---|
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
1 calls:
| 1.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 1.6% | 1 | x |
Compiled 2 to 1 computations (50% saved)
| 1× | egg-herbie |
| 8× | +-commutative_binary64 |
| 4× | *-commutative_binary64 |
| 4× | sub-neg_binary64 |
| 2× | 1-exp_binary64 |
| 2× | neg-sub0_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 22 |
| 1 | 21 | 22 |
| 2 | 25 | 22 |
| 3 | 27 | 22 |
| 4 | 28 | 22 |
| 1× | saturated |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| Outputs |
|---|
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| 4088× | *-lowering-*.f32 |
| 4088× | *-lowering-*.f64 |
| 2970× | *-lowering-*.f32 |
| 2970× | *-lowering-*.f64 |
| 2838× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 222 | 1784 |
| 1 | 680 | 1513 |
| 2 | 2440 | 1494 |
| 3 | 6905 | 1494 |
| 0 | 8243 | 1494 |
| 0 | 113 | 434 |
| 1 | 325 | 384 |
| 2 | 1037 | 376 |
| 3 | 3221 | 373 |
| 4 | 7103 | 373 |
| 0 | 8112 | 373 |
| 0 | 6 | 16 |
| 1 | 39 | 16 |
| 2 | 300 | 16 |
| 3 | 3704 | 16 |
| 0 | 8338 | 16 |
| 0 | 28 | 112 |
| 1 | 182 | 93 |
| 2 | 1660 | 92 |
| 0 | 8386 | 92 |
| 0 | 18 | 56 |
| 1 | 91 | 54 |
| 2 | 513 | 54 |
| 3 | 5191 | 54 |
| 0 | 8027 | 54 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 89 to 63 computations (29.2% saved)
Compiled 82 to 52 computations (36.6% saved)
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