2sqrt (example 3.1)
Time bar (total: 9.1s)
| 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)| 864.0ms | 3337× | 2 | valid |
| 843.0ms | 4756× | 1 | valid |
| 12.0ms | 163× | 0 | valid |
ival-sqrt: 400.0ms (32.2% of total)ival-add: 173.0ms (13.9% of total)backward-pass: 168.0ms (13.5% of total)...c/correct-round.rkt:119:19: 163.0ms (13.1% of total)ival-sub: 129.0ms (10.4% of total)ival->: 126.0ms (10.1% of total)ival-<: 42.0ms (3.4% of total)ival-and: 25.0ms (2% of total)const: 16.0ms (1.3% 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)) |
| 52.0ms | 300× | 1 | valid |
| 48.0ms | 202× | 2 | valid |
| 1.0ms | 10× | 0 | valid |
Compiled 48 to 20 computations (58.3% saved)
ival-sqrt: 25.0ms (42.2% of total)ival-add: 17.0ms (28.7% of total)backward-pass: 10.0ms (16.9% of total)ival-sub: 6.0ms (10.1% of total)const: 1.0ms (1.7% of total)Compiled 8 to 6 computations (25% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 6.3% | (-.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 | 6.3% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 28.0ms | 101× | 2 | valid |
| 20.0ms | 150× | 1 | valid |
| 0.0ms | 5× | 0 | valid |
Compiled 20 to 7 computations (65% saved)
ival-sqrt: 9.0ms (32.1% of total)ival-add: 9.0ms (32.1% of total)backward-pass: 5.0ms (17.8% of total)ival-sub: 4.0ms (14.2% of total)const: 1.0ms (3.6% 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 | (+ x 1) |
| 1× | batch-egg-rewrite |
| 2088× | *-lowering-*.f32 |
| 2088× | *-lowering-*.f64 |
| 1794× | fma-lowering-fma.f32 |
| 1794× | fma-lowering-fma.f64 |
| 1676× | fmsub-define |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 1 | 39 | 16 |
| 2 | 303 | 16 |
| 3 | 3722 | 16 |
| 0 | 8045 | 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 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.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))))) |
(-.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 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.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 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.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 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.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 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.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) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.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)) (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 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.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 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.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 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.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 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)) |
(*.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))) |
(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 (sqrt.f64 x) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
(*.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 | 1039 | 376 |
| 3 | 3226 | 373 |
| 4 | 7122 | 373 |
| 0 | 8132 | 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 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x))) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
(+.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 x #s(literal 1/16 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 #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 #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 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x 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 (*.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)))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) #s(literal 5/128 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 (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 (*.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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)))) |
(* -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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 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)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 x (-.f64 (+.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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)))) (*.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)))))) |
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 5806 to 837 computations (85.6% saved)
10 alts after pruning (9 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 259 | 9 | 268 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 259 | 10 | 269 |
| 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) | |
| ▶ | 8.7% | (/.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))) |
| ▶ | 6.3% | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 x)) |
| 6.3% | (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 x)) | |
| ▶ | 4.7% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (pow.f64 (*.f64 x x) #s(literal 1/4 binary64))) |
| ✓ | 6.3% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| ▶ | 1.6% | (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| 6.6% | (*.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))) | |
| 98.3% | (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
Compiled 268 to 182 computations (32.1% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 64 | (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 64 | (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
| ✓ | cost-diff | 256 | (+.f64 x (-.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 320 | (/.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 | (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))) |
| ✓ | cost-diff | 0 | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (pow.f64 (*.f64 x x) #s(literal 1/4 binary64)) |
| ✓ | 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))) (pow.f64 (*.f64 x x) #s(literal 1/4 binary64))) |
| ✓ | 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) |
| 2222× | sum3-define |
| 1806× | fma-lowering-fma.f32 |
| 1806× | fma-lowering-fma.f64 |
| 1572× | fmsub-define |
| 1502× | fnmadd-define |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 33 | 185 |
| 1 | 66 | 185 |
| 2 | 107 | 181 |
| 3 | 167 | 180 |
| 4 | 221 | 180 |
| 5 | 345 | 180 |
| 6 | 605 | 180 |
| 7 | 964 | 180 |
| 8 | 1416 | 180 |
| 9 | 2179 | 180 |
| 10 | 5263 | 180 |
| 0 | 8026 | 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 |
(- (sqrt (+ x 1)) (pow (* x x) 1/4)) |
(sqrt (+ x 1)) |
(+ x 1) |
x |
1 |
(pow (* x x) 1/4) |
(* x x) |
1/4 |
(- (/ 1 (sqrt (/ 1 (+ x 1)))) (sqrt x)) |
(/ 1 (sqrt (/ 1 (+ x 1)))) |
1 |
(sqrt (/ 1 (+ x 1))) |
(/ 1 (+ x 1)) |
(+ x 1) |
x |
(sqrt x) |
(/ (+ 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 |
(- (sqrt (+ x 1)) (pow (* x x) 1/4)) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (pow.f64 (*.f64 x x) #s(literal 1/4 binary64))) |
(sqrt (+ x 1)) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+ x 1) |
(+.f64 #s(literal 1 binary64) x) |
x |
1 |
#s(literal 1 binary64) |
(pow (* x x) 1/4) |
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64)) |
(* x x) |
(*.f64 x x) |
1/4 |
#s(literal 1/4 binary64) |
(- (/ 1 (sqrt (/ 1 (+ x 1)))) (sqrt x)) |
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 x)) |
(/ 1 (sqrt (/ 1 (+ x 1)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) |
1 |
#s(literal 1 binary64) |
(sqrt (/ 1 (+ x 1))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) |
(/ 1 (+ x 1)) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) |
(+ x 1) |
(+.f64 #s(literal 1 binary64) x) |
x |
(sqrt x) |
(sqrt.f64 x) |
(/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(+ 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) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(pow (+ x 1) 1/2) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+ x 1) |
(+.f64 #s(literal 1 binary64) x) |
1/2 |
#s(literal 1/2 binary64) |
(sqrt x) |
(sqrt.f64 x) |
Found 18 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 | 8.0% | (+.f64 x (-.f64 #s(literal 1 binary64) x)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))) |
| ✓ | accuracy | 99.6% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))) |
| ✓ | accuracy | 6.3% | (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 x)) |
| ✓ | accuracy | 100.0% | (*.f64 x x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
| ✓ | accuracy | 51.6% | (pow.f64 (*.f64 x x) #s(literal 1/4 binary64)) |
| ✓ | accuracy | 6.3% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (pow.f64 (*.f64 x x) #s(literal 1/4 binary64))) |
| ✓ | 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 | 99.4% | (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
| ✓ | accuracy | 65.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
| 202.0ms | 101× | 2 | valid |
| 151.0ms | 150× | 1 | valid |
| 6.0ms | 5× | 0 | valid |
Compiled 236 to 34 computations (85.6% saved)
ival-pow: 60.0ms (25.8% of total)ival-div: 38.0ms (16.3% of total)ival-mult: 38.0ms (16.3% of total)ival-sqrt: 35.0ms (15% of total)backward-pass: 24.0ms (10.3% of total)ival-sub: 21.0ms (9% of total)ival-add: 15.0ms (6.4% of total)const: 2.0ms (0.9% 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 (- (sqrt (+ x 1)) (pow (* x x) 1/4))> |
#<alt (sqrt (+ x 1))> |
#<alt (+ x 1)> |
#<alt (pow (* x x) 1/4)> |
#<alt (- (/ 1 (sqrt (/ 1 (+ x 1)))) (sqrt x))> |
#<alt (/ 1 (sqrt (/ 1 (+ x 1))))> |
#<alt (sqrt (/ 1 (+ x 1)))> |
#<alt (/ 1 (+ x 1))> |
#<alt (/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x)))> |
#<alt (+ x (- 1 x))> |
#<alt (+ (pow (+ x 1) 1/2) (sqrt x))> |
#<alt (pow (+ x 1) 1/2)> |
#<alt (sqrt (/ 1 (* x (* x x))))> |
#<alt (/ 1 (* x (* x x)))> |
#<alt (* 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 (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 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))> |
#<alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (sqrt -1)))))> |
#<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)))) (* (sqrt (/ 1 x)) (sqrt -1)))))> |
#<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))))) (* (sqrt (/ 1 x)) (sqrt -1)))))> |
#<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) (sqrt -1)))> |
#<alt (* -1 (* (sqrt x) (sqrt -1)))> |
#<alt (* -1 (* (sqrt x) (sqrt -1)))> |
#<alt (* -1 (* (sqrt x) (sqrt -1)))> |
#<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 (* -1/2 x))> |
#<alt (+ 1 (* x (- (* 3/8 x) 1/2)))> |
#<alt (+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))> |
#<alt (sqrt (/ 1 x))> |
#<alt (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))> |
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))> |
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))> |
#<alt (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))> |
#<alt 1> |
#<alt (+ 1 (* -1 x))> |
#<alt (+ 1 (* x (- x 1)))> |
#<alt (+ 1 (* x (- (* x (+ 1 (* -1 x))) 1)))> |
#<alt (/ 1 x)> |
#<alt (/ (- 1 (/ 1 x)) x)> |
#<alt (/ (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)) x)> |
#<alt (/ (- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3)))) x)> |
#<alt (/ 1 x)> |
#<alt (* -1 (/ (- (/ 1 x) 1) x))> |
#<alt (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x))> |
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) 1) x))> |
#<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 (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 (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))> |
#<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)> |
63 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 62.0ms | x | @ | 0 | (- (sqrt (+ x 1)) (pow (* x x) 1/4)) |
| 13.0ms | 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) |
| 1.0ms | x | @ | inf | (/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x))) |
| 1× | batch-egg-rewrite |
| 3198× | *-lowering-*.f32 |
| 3198× | *-lowering-*.f64 |
| 2140× | +-lowering-+.f64 |
| 2140× | +-lowering-+.f32 |
| 2132× | fma-lowering-fma.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 33 | 124 |
| 1 | 221 | 107 |
| 2 | 1976 | 106 |
| 0 | 8727 | 106 |
| 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) |
(- (sqrt (+ x 1)) (pow (* x x) 1/4)) |
(sqrt (+ x 1)) |
(+ x 1) |
(pow (* x x) 1/4) |
(- (/ 1 (sqrt (/ 1 (+ x 1)))) (sqrt x)) |
(/ 1 (sqrt (/ 1 (+ x 1)))) |
(sqrt (/ 1 (+ x 1))) |
(/ 1 (+ x 1)) |
(/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x))) |
(+ x (- 1 x)) |
(+ (pow (+ x 1) 1/2) (sqrt x)) |
(pow (+ x 1) 1/2) |
(sqrt (/ 1 (* x (* x x)))) |
(/ 1 (* x (* x 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))) |
(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 (+.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 (-.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 (*.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)))))) |
(/.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))) (/.f64 #s(literal 1 binary64) 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)))))) |
(pow.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)) |
(pow.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)) #s(literal -1 binary64)) |
(*.f64 #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 #s(literal 1 binary64) 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 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 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)))))) #s(literal -1 binary64))) |
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(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))) |
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))) |
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))) |
(/.f64 (pow.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) |
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x)))) |
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x))))) |
(/.f64 (sqrt.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64))) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(/.f64 (sqrt.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (*.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) |
(/.f64 (sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (neg.f64 (+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x))))) |
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)))) (sqrt.f64 (neg.f64 (+.f64 x #s(literal -1 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))) |
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) |
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) |
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 x)) |
(*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) 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) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))) |
(*.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))) |
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (sqrt.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.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 (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) #s(literal -1 binary64))) |
(*.f64 (sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) |
(*.f64 (sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64)))) |
(*.f64 (sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))) |
(exp.f64 (*.f64 (*.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal -1/2 binary64))) #s(literal 3 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal -1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 3/2 binary64))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 3 binary64))) |
(exp.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64)) #s(literal -1 binary64))) |
(exp.f64 (neg.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64)))) |
(exp.f64 (-.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (log.f64 x))) |
(fabs.f64 (pow.f64 x #s(literal -3/2 binary64))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/2 binary64))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))))) |
(/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) |
(/.f64 (pow.f64 x #s(literal -1/2 binary64)) x) |
(/.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3/2 binary64)))) |
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)))) |
(/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)) #s(literal 3 binary64))) |
(/.f64 (sqrt.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (neg.f64 (*.f64 x x)))) |
(pow.f64 x #s(literal -3/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) |
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 3 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 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 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 1/4 binary64)) |
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -3/2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 x #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (/.f64 (*.f64 x x) #s(literal 1 binary64)) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1 binary64)) |
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))))) |
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) (pow.f64 x #s(literal -3/4 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 (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 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -1 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)))) |
(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 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (*.f64 x x))) |
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) 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 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/4 binary64)) |
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x 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 #s(literal 0 binary64) (*.f64 x (*.f64 x x))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -3 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -3 binary64))) |
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -3 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -3 binary64))) |
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x))) |
(sqrt.f64 (*.f64 (*.f64 x x) (*.f64 x x))) |
(pow.f64 x #s(literal 2 binary64)) |
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 1 binary64)) |
(pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1/4 binary64)) |
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x)) |
(*.f64 #s(literal 1 binary64) (*.f64 x x)) |
(*.f64 x x) |
(*.f64 (sqrt.f64 x) (pow.f64 x #s(literal 3/2 binary64))) |
(*.f64 (*.f64 x x) #s(literal 1 binary64)) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x)) |
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 x)) |
| 1× | egg-herbie |
| 4156× | +-lowering-+.f64 |
| 4156× | +-lowering-+.f32 |
| 3296× | *-lowering-*.f32 |
| 3296× | *-lowering-*.f64 |
| 1468× | sum3-define |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 339 | 2650 |
| 1 | 1071 | 2268 |
| 2 | 3782 | 2250 |
| 0 | 8323 | 2250 |
| 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 (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 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* -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)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* -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))))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
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) (sqrt -1))) |
(* -1 (* (sqrt x) (sqrt -1))) |
(* -1 (* (sqrt x) (sqrt -1))) |
(* -1 (* (sqrt x) (sqrt -1))) |
(- 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 (* -1/2 x)) |
(+ 1 (* x (- (* 3/8 x) 1/2))) |
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2))) |
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
1 |
(+ 1 (* -1 x)) |
(+ 1 (* x (- x 1))) |
(+ 1 (* x (- (* x (+ 1 (* -1 x))) 1))) |
(/ 1 x) |
(/ (- 1 (/ 1 x)) x) |
(/ (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)) x) |
(/ (- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3)))) x) |
(/ 1 x) |
(* -1 (/ (- (/ 1 x) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) 1) x)) |
(/ 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 (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))))))) |
(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)) |
(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) |
| 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 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 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 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 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 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 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 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 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 1/16 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)))))))) |
(* 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 1/16 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 x) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 x (+.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 (* 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 x (+.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 (* 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 x (+.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))) |
(* -1/8 (sqrt (/ 1 x))) |
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1/8 (sqrt (/ 1 x))) |
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1/8 (sqrt (/ 1 x))) |
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1/8 (sqrt (/ 1 x))) |
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1/8 (sqrt (/ 1 x))) |
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1/8 (sqrt (/ 1 x))) |
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
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(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
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(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
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(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
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(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
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(* (sqrt x) (pow (sqrt -1) 2)) |
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(- (+ 1 (* 1/2 x)) (sqrt x)) |
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(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
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(* -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)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
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(* -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))))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
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1 |
#s(literal 1 binary64) |
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(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
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(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))))))) |
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1 |
#s(literal 1 binary64) |
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(sqrt.f64 x) |
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(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
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1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
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(+.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 #s(literal 1/16 binary64) x)))))) |
(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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 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 (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 (*.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)))))))) |
(* -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)))))) |
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(* -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)) |
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#s(literal 1 binary64) |
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#s(literal 1 binary64) |
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#s(literal 1 binary64) |
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#s(literal 1 binary64) |
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#s(literal 1 binary64) |
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#s(literal 1 binary64) |
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#s(literal 1 binary64) |
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#s(literal 1 binary64) |
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#s(literal 1 binary64) |
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#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
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(+ 1 (+ (sqrt x) (* 1/2 x))) |
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(* 2 (sqrt x)) |
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(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))) |
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(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
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(* -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))))))) |
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(* -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)))))))) |
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(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
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(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
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(sqrt x) |
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(* 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)))))))) |
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(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
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(* -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))))))) |
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(sqrt (/ 1 (pow x 3))) |
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(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))) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
Compiled 29881 to 3593 computations (88% saved)
11 alts after pruning (9 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1420 | 8 | 1428 |
| Fresh | 3 | 1 | 4 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1427 | 11 | 1438 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 32.9% | (/.f64 (+.f64 (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x x))) |
| 99.0% | (/.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x) | |
| 8.7% | (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x x) #s(literal 1/4 binary64)))) | |
| ▶ | 7.2% | (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
| 98.1% | (/.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))) |
| ✓ | 6.3% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| ✓ | 1.6% | (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ▶ | 99.2% | (+.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)))))) |
| 99.2% | (*.f64 (/.f64 #s(literal 1 binary64) 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)))))) | |
| ▶ | 98.3% | (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
Compiled 277 to 196 computations (29.2% saved)
| 1× | egg-herbie |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) |
| ✓ | cost-diff | 0 | (+.f64 (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 0 | (/.f64 (+.f64 (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x 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 | (+.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)))))) |
| ✓ | cost-diff | 0 | (*.f64 (sqrt.f64 x) #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (-.f64 #s(literal 1 binary64) x) |
| ✓ | cost-diff | 256 | (+.f64 x (-.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 384 | (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
| ✓ | 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 | (+.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))) |
| 1946× | sum3-define |
| 1500× | *-lowering-*.f32 |
| 1500× | *-lowering-*.f64 |
| 1272× | sum5-define |
| 1178× | +-lowering-+.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 32 | 188 |
| 1 | 73 | 184 |
| 2 | 140 | 178 |
| 3 | 238 | 178 |
| 4 | 317 | 178 |
| 5 | 407 | 178 |
| 6 | 637 | 178 |
| 7 | 1249 | 178 |
| 8 | 1866 | 178 |
| 9 | 2587 | 178 |
| 10 | 5985 | 178 |
| 0 | 8113 | 178 |
| 1× | iter limit |
| 1× | node limit |
| 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 (/ 1 x))) |
1/2 |
(sqrt (/ 1 x)) |
(/ 1 x) |
1 |
x |
(/ (+ x (- 1 x)) (* (sqrt x) 2)) |
(+ x (- 1 x)) |
x |
(- 1 x) |
1 |
(* (sqrt x) 2) |
(sqrt x) |
2 |
(+ (* 1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (* x (* x x)))))) |
(* 1/2 (sqrt (/ 1 x))) |
1/2 |
(sqrt (/ 1 x)) |
(/ 1 x) |
1 |
x |
(* -1/8 (sqrt (/ 1 (* x (* x x))))) |
-1/8 |
(sqrt (/ 1 (* x (* x x)))) |
(/ 1 (* x (* x x))) |
(* x (* x x)) |
(* x x) |
(/ (+ (* (sqrt x) (+ 1/16 (* x -1/8))) (* (sqrt (* x (* x x))) (* x 1/2))) (* x (* x x))) |
(+ (* (sqrt x) (+ 1/16 (* x -1/8))) (* (sqrt (* x (* x x))) (* x 1/2))) |
(* (sqrt x) (+ 1/16 (* x -1/8))) |
(sqrt x) |
x |
(+ 1/16 (* x -1/8)) |
1/16 |
(* x -1/8) |
-1/8 |
(* (sqrt (* x (* x x))) (* x 1/2)) |
(sqrt (* x (* x x))) |
(* x (* x x)) |
(* x x) |
(* x 1/2) |
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 (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
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 |
(/ (+ x (- 1 x)) (* (sqrt x) 2)) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(+ x (- 1 x)) |
#s(literal 1 binary64) |
x |
(- 1 x) |
(-.f64 #s(literal 1 binary64) x) |
1 |
#s(literal 1 binary64) |
(* (sqrt x) 2) |
(*.f64 (sqrt.f64 x) #s(literal 2 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
2 |
#s(literal 2 binary64) |
(+ (* 1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (* x (* 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 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
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 (* x x))))) |
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) |
-1/8 |
#s(literal -1/8 binary64) |
(sqrt (/ 1 (* x (* x x)))) |
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) |
(/ 1 (* x (* x x))) |
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x) |
(* x (* x x)) |
(*.f64 x (*.f64 x x)) |
(* x x) |
(*.f64 x x) |
(/ (+ (* (sqrt x) (+ 1/16 (* x -1/8))) (* (sqrt (* x (* x x))) (* x 1/2))) (* x (* x x))) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 x #s(literal 2 binary64)))) (*.f64 x (*.f64 x x))) |
(+ (* (sqrt x) (+ 1/16 (* x -1/8))) (* (sqrt (* x (* x x))) (* x 1/2))) |
(+.f64 (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 x #s(literal 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) |
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) |
(* (sqrt (* x (* x x))) (* x 1/2)) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 x #s(literal 2 binary64))) |
(sqrt (* x (* x x))) |
(sqrt.f64 (*.f64 x (*.f64 x x))) |
(* x (* x x)) |
(*.f64 x (*.f64 x x)) |
(* x x) |
(*.f64 x x) |
(* x 1/2) |
(/.f64 x #s(literal 2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.7% | (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) |
| ✓ | accuracy | 76.0% | (+.f64 (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 65.8% | (sqrt.f64 (*.f64 x (*.f64 x x))) |
| ✓ | accuracy | 34.7% | (/.f64 (+.f64 (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x x))) |
| ✓ | accuracy | 99.9% | (*.f64 x (*.f64 x x)) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
| ✓ | accuracy | 99.4% | (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
| ✓ | accuracy | 65.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) |
| ✓ | accuracy | 100.0% | (*.f64 (sqrt.f64 x) #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 99.6% | (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
| ✓ | accuracy | 8.0% | (+.f64 x (-.f64 #s(literal 1 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 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))) |
| 191.0ms | 236× | 1 | valid |
| 7.0ms | 20× | 0 | valid |
Compiled 236 to 33 computations (86% saved)
ival-mult: 32.0ms (26.8% of total)ival-div: 20.0ms (16.8% of total)ival-add: 18.0ms (15.1% of total)backward-pass: 17.0ms (14.3% of total)ival-pow: 15.0ms (12.6% of total)ival-sqrt: 14.0ms (11.7% of total)ival-sub: 3.0ms (2.5% of total)const: 2.0ms (1.7% 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 (/ 1 x)))> |
#<alt (sqrt (/ 1 x))> |
#<alt (/ 1 x)> |
#<alt (/ (+ x (- 1 x)) (* (sqrt x) 2))> |
#<alt (+ x (- 1 x))> |
#<alt (- 1 x)> |
#<alt (* (sqrt x) 2)> |
#<alt (+ (* 1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (* x (* x x))))))> |
#<alt (/ (+ (* (sqrt x) (+ 1/16 (* x -1/8))) (* (sqrt (* x (* x x))) (* x 1/2))) (* x (* x x)))> |
#<alt (+ (* (sqrt x) (+ 1/16 (* x -1/8))) (* (sqrt (* x (* x x))) (* x 1/2)))> |
#<alt (* (sqrt x) (+ 1/16 (* x -1/8)))> |
#<alt (sqrt x)> |
#<alt (sqrt (/ 1 (* x (* x x))))> |
#<alt (/ 1 (* x (* x x)))> |
#<alt (* x (* x x))> |
#<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 (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 (* 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 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 (* 2 (sqrt x))> |
#<alt (* 2 (sqrt x))> |
#<alt (* 2 (sqrt x))> |
#<alt (* 2 (sqrt x))> |
#<alt (* 2 (sqrt x))> |
#<alt (* 2 (sqrt x))> |
#<alt (* 2 (sqrt x))> |
#<alt (* 2 (sqrt x))> |
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<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 (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 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 (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))> |
#<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 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 (* 1/16 (sqrt x))> |
#<alt (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x)))> |
#<alt (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x)))> |
#<alt (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x)))> |
#<alt (* -1/8 (sqrt (pow x 3)))> |
#<alt (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 x))) (* 1/16 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 x))) (* 1/16 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 x))) (* 1/16 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* 1/8 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))> |
#<alt (* (pow x 2) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* (pow x 2) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* (pow x 2) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<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 (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))> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (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))> |
#<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 | (/ (+ x (- 1 x)) (* (sqrt x) 2)) |
| 1.0ms | x | @ | -inf | (/ (+ (* (sqrt x) (+ 1/16 (* x -1/8))) (* (sqrt (* x (* x x))) (* x 1/2))) (* x (* x x))) |
| 0.0ms | x | @ | inf | (/ (+ (* (sqrt x) (+ 1/16 (* x -1/8))) (* (sqrt (* x (* x x))) (* x 1/2))) (* x (* x x))) |
| 0.0ms | x | @ | 0 | (/ (+ (* (sqrt x) (+ 1/16 (* x -1/8))) (* (sqrt (* x (* x x))) (* x 1/2))) (* x (* x x))) |
| 0.0ms | x | @ | -inf | (* x (* x x)) |
| 1× | batch-egg-rewrite |
| 2688× | *-lowering-*.f32 |
| 2688× | *-lowering-*.f64 |
| 2528× | /-lowering-/.f32 |
| 2528× | /-lowering-/.f64 |
| 2226× | fma-lowering-fma.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 32 | 128 |
| 1 | 199 | 115 |
| 2 | 1709 | 110 |
| 0 | 8433 | 110 |
| 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 (/ 1 x))) |
(sqrt (/ 1 x)) |
(/ 1 x) |
(/ (+ x (- 1 x)) (* (sqrt x) 2)) |
(+ x (- 1 x)) |
(- 1 x) |
(* (sqrt x) 2) |
(+ (* 1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (* x (* x x)))))) |
(/ (+ (* (sqrt x) (+ 1/16 (* x -1/8))) (* (sqrt (* x (* x x))) (* x 1/2))) (* x (* x x))) |
(+ (* (sqrt x) (+ 1/16 (* x -1/8))) (* (sqrt (* x (* x x))) (* x 1/2))) |
(* (sqrt x) (+ 1/16 (* x -1/8))) |
(sqrt x) |
(sqrt (/ 1 (* x (* x x)))) |
(/ 1 (* x (* x x))) |
(* x (* x x)) |
(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)))))) |
(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 (/.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) 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 (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 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) 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 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))) #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 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (/.f64 (-.f64 x 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 (*.f64 x x) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (/.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (/.f64 (-.f64 x x) (*.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))) |
(-.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 (/.f64 (*.f64 x x) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (*.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (/.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (*.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (-.f64 #s(literal 0 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 (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)) |
(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))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) |
(/.f64 (neg.f64 (*.f64 x x)) (neg.f64 (/.f64 #s(literal 1 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 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) |
(*.f64 x (*.f64 x x)) |
(*.f64 x (/.f64 (*.f64 x x) #s(literal 1 binary64))) |
(*.f64 (*.f64 x x) x) |
(*.f64 (*.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))) |
(exp.f64 (*.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)) #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))) |
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -3/2 binary64))) |
(/.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)) |
(/.f64 (neg.f64 (pow.f64 x #s(literal 3/2 binary64))) #s(literal -1 binary64)) |
(/.f64 (*.f64 x (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))) |
(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 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 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 (sqrt.f64 x) (pow.f64 (/.f64 (*.f64 x x) #s(literal 1 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 (*.f64 x x) #s(literal 1 binary64)))) |
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 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 (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 |
| 3238× | *-lowering-*.f32 |
| 3238× | *-lowering-*.f64 |
| 2558× | +-lowering-+.f64 |
| 2558× | +-lowering-+.f32 |
| 2048× | fma-lowering-fma.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 246 | 2017 |
| 1 | 784 | 1768 |
| 2 | 2980 | 1745 |
| 3 | 7332 | 1745 |
| 0 | 8589 | 1745 |
| 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))) |
(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) |
(* 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))) |
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)))) |
(* 2 (sqrt x)) |
(* 2 (sqrt x)) |
(* 2 (sqrt x)) |
(* 2 (sqrt x)) |
(* 2 (sqrt x)) |
(* 2 (sqrt x)) |
(* 2 (sqrt x)) |
(* 2 (sqrt x)) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -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))) |
(+ (* 1/8 (* (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))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(* 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 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)))))) |
(* 1/16 (sqrt x)) |
(+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) |
(+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) |
(+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) |
(* -1/8 (sqrt (pow x 3))) |
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 x))) (* 1/16 (sqrt (/ 1 (pow x 3)))))) |
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 x))) (* 1/16 (sqrt (/ 1 (pow x 3)))))) |
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 x))) (* 1/16 (sqrt (/ 1 (pow x 3)))))) |
(* 1/8 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) |
(* (pow x 2) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* (pow x 2) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* (pow x 2) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(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))) |
(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)) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(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)) |
(* (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)))) |
(+.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 #s(literal 1/16 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))) (/.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 #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 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.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 (/ (+ (* 1/128 (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) |
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(*.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)))))) |
(+ (* 1/8 (* (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)))))) |
(+ (* 1/8 (* (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)))))) |
(* 1/16 (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 -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 #s(literal 1/2 binary64) (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 5 binary64))))))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) |
(+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 #s(literal 1/2 binary64) (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 5 binary64))))))) |
(* 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 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 -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 #s(literal 1/2 binary64) (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 5 binary64)))))))) |
(* (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 -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 #s(literal 1/2 binary64) (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 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 (* (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 (*.f64 x x)) (+.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 (* (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 (*.f64 x x)) (+.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 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))) |
(+ (* -1/8 (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))) |
(+ (* -1/8 (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))) |
(* -1/8 (sqrt (pow x 3))) |
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))) |
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 x))) (* 1/16 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 (*.f64 x x) (+.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))))))) |
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 x))) (* 1/16 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 (*.f64 x x) (+.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))))))) |
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 x))) (* 1/16 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 (*.f64 x x) (+.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))))))) |
(* 1/8 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))) |
(* (pow x 2) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 (*.f64 x x) (+.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))))))) |
(* (pow x 2) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 (*.f64 x x) (+.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))))))) |
(* (pow x 2) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 (*.f64 x x) (+.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))))))) |
(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) |
(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))) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.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)) |
(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 26552 to 3125 computations (88.2% saved)
25 alts after pruning (24 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1194 | 23 | 1217 |
| Fresh | 3 | 1 | 4 |
| Picked | 5 | 0 | 5 |
| Done | 1 | 1 | 2 |
| Total | 1203 | 25 | 1228 |
| Status | Accuracy | Program |
|---|---|---|
| 98.5% | (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) | |
| 4.8% | (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 3.6% | (/.f64 (/.f64 (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 3.5% | (/.f64 (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)) #s(literal 1 binary64))) (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)) (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 3.6% | (/.f64 (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 x x)) (+.f64 (+.f64 #s(literal 1 binary64) x) x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| ▶ | 5.1% | (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) x)) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
| 3.2% | (/.f64 (/.f64 (+.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 2.9% | (/.f64 (/.f64 (+.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))) x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 40.0% | (/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64)))) x) (*.f64 x x)) | |
| 5.1% | (/.f64 (-.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 #s(literal 1 binary64) x) x)) (/.f64 (*.f64 x x) (+.f64 (+.f64 #s(literal 1 binary64) x) x))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 32.9% | (/.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x))))) (*.f64 x x)) | |
| 3.3% | (/.f64 (+.f64 x (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 5.1% | (/.f64 (+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 7.2% | (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 2 binary64))) | |
| 5.1% | (/.f64 (+.f64 x (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 5.4% | (/.f64 (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| ▶ | 3.6% | (/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) |
| 98.1% | (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) | |
| 99.5% | (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 x)))) | |
| ▶ | 99.6% | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
| ▶ | 98.1% | (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
| ✓ | 6.3% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 99.0% | (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) | |
| ▶ | 97.8% | (*.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))) |
| 91.0% | (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))) |
Compiled 986 to 560 computations (43.2% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (pow.f64 x #s(literal -1/4 binary64)) |
| ✓ | cost-diff | 6464 | (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64)) |
| ✓ | cost-diff | 6464 | (*.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))) |
| ✓ | cost-diff | 384 | (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) x) |
| ✓ | cost-diff | 384 | (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) x)) |
| ✓ | cost-diff | 1536 | (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) x)) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) |
| ✓ | cost-diff | 1664 | (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) x)) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 x x) |
| ✓ | cost-diff | 384 | (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) |
| ✓ | cost-diff | 384 | (*.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
| ✓ | cost-diff | 1152 | (/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1/2 binary64) (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))) |
| 3508× | *-lowering-*.f32 |
| 3508× | *-lowering-*.f64 |
| 2304× | +-lowering-+.f64 |
| 2304× | +-lowering-+.f32 |
| 2068× | /-lowering-/.f32 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 31 | 167 |
| 1 | 90 | 163 |
| 2 | 262 | 162 |
| 3 | 1344 | 136 |
| 0 | 9662 | 136 |
| 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 (sqrt x)) |
1/2 |
(sqrt x) |
x |
(/ (* (- (* x x) (* (- 1 x) (- 1 x))) (/ 1/2 (sqrt x))) (+ (+ x -1) x)) |
(* (- (* x x) (* (- 1 x) (- 1 x))) (/ 1/2 (sqrt x))) |
(- (* x x) (* (- 1 x) (- 1 x))) |
(* x x) |
x |
(* (- 1 x) (- 1 x)) |
(- 1 x) |
1 |
(/ 1/2 (sqrt x)) |
1/2 |
(sqrt x) |
(+ (+ x -1) x) |
(+ x -1) |
-1 |
(/ (/ (- 1 (* (/ (+ x -1) (+ (* x x) -1)) x)) (* (/ (+ x -1) (+ (* x x) -1)) 1)) (* (sqrt x) 2)) |
(/ (- 1 (* (/ (+ x -1) (+ (* x x) -1)) x)) (* (/ (+ x -1) (+ (* x x) -1)) 1)) |
(- 1 (* (/ (+ x -1) (+ (* x x) -1)) x)) |
1 |
(* (/ (+ x -1) (+ (* x x) -1)) x) |
(/ (+ x -1) (+ (* x x) -1)) |
(+ x -1) |
x |
-1 |
(+ (* x x) -1) |
(* x x) |
(* (/ (+ x -1) (+ (* x x) -1)) 1) |
(* (sqrt x) 2) |
(sqrt x) |
2 |
(* 1/2 (pow (pow x -1/4) 2)) |
1/2 |
(pow (pow x -1/4) 2) |
(pow x -1/4) |
x |
-1/4 |
2 |
| 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 (sqrt x)) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
1/2 |
#s(literal 1/2 binary64) |
(sqrt x) |
(sqrt.f64 x) |
x |
(/ (* (- (* x x) (* (- 1 x) (- 1 x))) (/ 1/2 (sqrt x))) (+ (+ x -1) x)) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(* (- (* x x) (* (- 1 x) (- 1 x))) (/ 1/2 (sqrt x))) |
(/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 x)) |
(- (* x x) (* (- 1 x) (- 1 x))) |
(+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 2 binary64))) |
(* x x) |
(*.f64 x x) |
x |
(* (- 1 x) (- 1 x)) |
(*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) |
(- 1 x) |
(-.f64 #s(literal 1 binary64) x) |
1 |
#s(literal 1 binary64) |
(/ 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 -1) x) |
(+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 2 binary64))) |
(+ x -1) |
(+.f64 x #s(literal -1 binary64)) |
-1 |
#s(literal -1 binary64) |
(/ (/ (- 1 (* (/ (+ x -1) (+ (* x x) -1)) x)) (* (/ (+ x -1) (+ (* x x) -1)) 1)) (* (sqrt x) 2)) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(/ (- 1 (* (/ (+ x -1) (+ (* x x) -1)) x)) (* (/ (+ x -1) (+ (* x x) -1)) 1)) |
#s(literal 1 binary64) |
(- 1 (* (/ (+ x -1) (+ (* x x) -1)) x)) |
(-.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1 binary64) x))) |
1 |
#s(literal 1 binary64) |
(* (/ (+ x -1) (+ (* x x) -1)) x) |
(/.f64 x (+.f64 #s(literal 1 binary64) x)) |
(/ (+ x -1) (+ (* x x) -1)) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) |
(+ x -1) |
(+.f64 x #s(literal -1 binary64)) |
x |
-1 |
#s(literal -1 binary64) |
(+ (* x x) -1) |
(+.f64 (*.f64 x x) #s(literal -1 binary64)) |
(* x x) |
(*.f64 x x) |
(* (/ (+ x -1) (+ (* x x) -1)) 1) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) |
(* (sqrt x) 2) |
(*.f64 (sqrt.f64 x) #s(literal 2 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
2 |
#s(literal 2 binary64) |
(* 1/2 (pow (pow x -1/4) 2)) |
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))) |
1/2 |
#s(literal 1/2 binary64) |
(pow (pow x -1/4) 2) |
(pow.f64 x #s(literal -1/2 binary64)) |
(pow x -1/4) |
(pow.f64 x #s(literal -1/4 binary64)) |
x |
-1/4 |
#s(literal -1/4 binary64) |
2 |
#s(literal 2 binary64) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))) |
| ✓ | accuracy | 100.0% | (pow.f64 x #s(literal -1/4 binary64)) |
| ✓ | accuracy | 99.2% | (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64)) |
| ✓ | accuracy | 99.7% | (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) x) |
| ✓ | accuracy | 99.6% | (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) x)) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
| ✓ | accuracy | 52.9% | (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) |
| ✓ | accuracy | 8.0% | (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) x)) |
| ✓ | accuracy | 99.6% | (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
| ✓ | accuracy | 99.6% | (/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) |
| ✓ | accuracy | 99.6% | (*.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
| ✓ | accuracy | 7.4% | (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 99.6% | (/.f64 #s(literal 1/2 binary64) (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))) |
| 168.0ms | 157× | 1 | valid |
| 104.0ms | 92× | 2 | valid |
| 2.0ms | 7× | 0 | valid |
Compiled 256 to 32 computations (87.5% saved)
ival-div: 29.0ms (20.3% of total)ival-mult: 27.0ms (18.9% of total)backward-pass: 24.0ms (16.8% of total)ival-add: 23.0ms (16.1% of total)ival-pow: 21.0ms (14.7% of total)ival-sub: 9.0ms (6.3% of total)ival-sqrt: 8.0ms (5.6% of total)const: 2.0ms (1.4% 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 (sqrt x))> |
#<alt (sqrt x)> |
#<alt (/ (* (- (* x x) (* (- 1 x) (- 1 x))) (/ 1/2 (sqrt x))) (+ (+ x -1) x))> |
#<alt (* (- (* x x) (* (- 1 x) (- 1 x))) (/ 1/2 (sqrt x)))> |
#<alt (- (* x x) (* (- 1 x) (- 1 x)))> |
#<alt (* x x)> |
#<alt (/ (/ (- 1 (* (/ (+ x -1) (+ (* x x) -1)) x)) (* (/ (+ x -1) (+ (* x x) -1)) 1)) (* (sqrt x) 2))> |
#<alt (/ (- 1 (* (/ (+ x -1) (+ (* x x) -1)) x)) (* (/ (+ x -1) (+ (* x x) -1)) 1))> |
#<alt (- 1 (* (/ (+ x -1) (+ (* x x) -1)) x))> |
#<alt (* (/ (+ x -1) (+ (* x x) -1)) x)> |
#<alt (* 1/2 (pow (pow x -1/4) 2))> |
#<alt (pow (pow x -1/4) 2)> |
#<alt (pow x -1/4)> |
#<alt (/ (+ x -1) (+ (* x x) -1))> |
| 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)))> |
#<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 (pow x 3)) (* -1/2 (sqrt x))) x)> |
#<alt (/ (+ (sqrt (pow x 3)) (* -1/2 (sqrt x))) x)> |
#<alt (/ (+ (sqrt (pow x 3)) (* -1/2 (sqrt x))) x)> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))> |
#<alt (sqrt x)> |
#<alt (* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))> |
#<alt (* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))> |
#<alt (* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))> |
#<alt -1> |
#<alt (- (* 2 x) 1)> |
#<alt (- (* 2 x) 1)> |
#<alt (- (* 2 x) 1)> |
#<alt (* 2 x)> |
#<alt (* x (- 2 (/ 1 x)))> |
#<alt (* x (- 2 (/ 1 x)))> |
#<alt (* x (- 2 (/ 1 x)))> |
#<alt (* 2 x)> |
#<alt (* -1 (* x (- (/ 1 x) 2)))> |
#<alt (* -1 (* x (- (/ 1 x) 2)))> |
#<alt (* -1 (* x (- (/ 1 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 (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 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 (* x (- x 1)))> |
#<alt (+ 1 (* x (- (* x (+ 1 (* -1 x))) 1)))> |
#<alt (/ 1 x)> |
#<alt (/ (- 1 (/ 1 x)) x)> |
#<alt (/ (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)) x)> |
#<alt (/ (- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3)))) x)> |
#<alt (/ 1 x)> |
#<alt (* -1 (/ (- (/ 1 x) 1) x))> |
#<alt (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x))> |
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) 1) x))> |
#<alt x> |
#<alt (* x (+ 1 (* -1 x)))> |
#<alt (* x (+ 1 (* x (- x 1))))> |
#<alt (* x (+ 1 (* x (- (* x (+ 1 (* -1 x))) 1))))> |
#<alt 1> |
#<alt (- 1 (/ 1 x))> |
#<alt (- (+ 1 (/ 1 (pow x 2))) (/ 1 x))> |
#<alt (- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3))))> |
#<alt 1> |
#<alt (- 1 (/ 1 x))> |
#<alt (+ 1 (* -1 (/ (- 1 (/ 1 x)) x)))> |
#<alt (+ 1 (* -1 (/ (+ 1 (* -1 (/ (- 1 (/ 1 x)) x))) 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 (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 (pow (/ 1 x) 1/4)> |
#<alt (pow (/ 1 x) 1/4)> |
#<alt (pow (/ 1 x) 1/4)> |
#<alt (pow (/ 1 x) 1/4)> |
#<alt (pow (/ 1 x) 1/4)> |
#<alt (pow (/ 1 x) 1/4)> |
#<alt (pow (/ 1 x) 1/4)> |
#<alt (pow (/ 1 x) 1/4)> |
#<alt (exp (* 1/4 (+ (log -1) (log (/ -1 x)))))> |
#<alt (exp (* 1/4 (+ (log -1) (log (/ -1 x)))))> |
#<alt (exp (* 1/4 (+ (log -1) (log (/ -1 x)))))> |
#<alt (exp (* 1/4 (+ (log -1) (log (/ -1 x)))))> |
#<alt 1> |
#<alt (+ 1 (* -1 x))> |
#<alt (+ 1 (* x (- x 1)))> |
#<alt (+ 1 (* x (- (* x (+ 1 (* -1 x))) 1)))> |
#<alt (/ 1 x)> |
#<alt (/ (- 1 (/ 1 x)) x)> |
#<alt (/ (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)) x)> |
#<alt (/ (- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3)))) x)> |
#<alt (/ 1 x)> |
#<alt (* -1 (/ (- (/ 1 x) 1) x))> |
#<alt (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x))> |
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) 1) x))> |
54 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 33.0ms | x | @ | -inf | (pow x -1/4) |
| 9.0ms | x | @ | 0 | (pow x -1/4) |
| 7.0ms | x | @ | inf | (pow x -1/4) |
| 3.0ms | x | @ | -inf | (sqrt (+ 1 x)) |
| 2.0ms | x | @ | inf | (/ (/ (- 1 (* (/ (+ x -1) (+ (* x x) -1)) x)) (* (/ (+ x -1) (+ (* x x) -1)) 1)) (* (sqrt x) 2)) |
| 1× | batch-egg-rewrite |
| 3660× | *-lowering-*.f32 |
| 3660× | *-lowering-*.f64 |
| 2514× | /-lowering-/.f32 |
| 2514× | /-lowering-/.f64 |
| 1834× | +-lowering-+.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 31 | 144 |
| 1 | 230 | 105 |
| 2 | 2097 | 99 |
| 0 | 8950 | 99 |
| 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 (sqrt x)) |
(sqrt x) |
(/ (* (- (* x x) (* (- 1 x) (- 1 x))) (/ 1/2 (sqrt x))) (+ (+ x -1) x)) |
(* (- (* x x) (* (- 1 x) (- 1 x))) (/ 1/2 (sqrt x))) |
(- (* x x) (* (- 1 x) (- 1 x))) |
(* x x) |
(/ (/ (- 1 (* (/ (+ x -1) (+ (* x x) -1)) x)) (* (/ (+ x -1) (+ (* x x) -1)) 1)) (* (sqrt x) 2)) |
(/ (- 1 (* (/ (+ x -1) (+ (* x x) -1)) x)) (* (/ (+ x -1) (+ (* x x) -1)) 1)) |
(- 1 (* (/ (+ x -1) (+ (* x x) -1)) x)) |
(* (/ (+ x -1) (+ (* x x) -1)) x) |
(* 1/2 (pow (pow x -1/4) 2)) |
(pow (pow x -1/4) 2) |
(pow x -1/4) |
(/ (+ x -1) (+ (* x x) -1)) |
| Outputs |
|---|
(exp.f64 (*.f64 (log.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) #s(literal -1 binary64))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))) |
(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))))) |
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))) |
(pow.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) #s(literal -1 binary64)) |
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) #s(literal -1/2 binary64)) |
(pow.f64 (exp.f64 (log.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) #s(literal -1/2 binary64))) |
(*.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) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))) |
(*.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)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))) #s(literal -1 binary64))) |
(+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
(+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) |
(exp.f64 (neg.f64 (*.f64 (log.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) #s(literal -1 binary64)))) |
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 x (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))) |
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) |
(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 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 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 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) (+.f64 x (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) #s(literal 1 binary64)) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (neg.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 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 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 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 x (-.f64 (+.f64 #s(literal 1 binary64) x) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 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 #s(literal 1 binary64) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
(/.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 1/2 binary64)) (sqrt.f64 x)))) |
(/.f64 (neg.f64 (+.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 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))) |
(/.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x)) (-.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) (*.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) x)) (*.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))) |
(pow.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) #s(literal 1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) (+.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) |
(*.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 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 #s(literal 1 binary64) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))) |
(*.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 1/2 binary64)) (sqrt.f64 x)))) |
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x))) |
(hypot.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(fabs.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) |
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(/.f64 (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 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) |
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (sqrt.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64))))) |
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))) (sqrt.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 0 binary64) x))))))) |
(/.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1 binary64))) (sqrt.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))))) |
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(pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) |
(pow.f64 (*.f64 x x) #s(literal -1/8 binary64)) |
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)) |
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 x #s(literal -1/8 binary64)) #s(literal 2 binary64)) |
(pow.f64 (exp.f64 #s(literal -1/4 binary64)) (log.f64 x)) |
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 x #s(literal -1/8 binary64)) (pow.f64 x #s(literal -1/8 binary64))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64))) |
(exp.f64 (*.f64 (log1p.f64 x) #s(literal -1 binary64))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) |
(/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (+.f64 #s(literal 1 binary64) x))) |
(/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) |
(/.f64 (+.f64 x #s(literal -1 binary64)) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(/.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) (*.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) x))) |
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x))) (*.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x x)))) |
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x x)) (+.f64 (*.f64 x x) #s(literal -1 binary64)))) |
(/.f64 (*.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (*.f64 x x) #s(literal -1 binary64)))) |
(/.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(literal -1 binary64))) |
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) |
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))) (+.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x x))) |
(/.f64 (*.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) x)) |
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal -2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) |
(*.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(*.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))) |
(*.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64))) (+.f64 x #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))) |
(*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 0 binary64) x))))) |
(*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1 binary64))) (+.f64 (*.f64 x x) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))) |
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal -1 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 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x x)))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) |
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) |
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))) |
| 1× | egg-herbie |
| 4156× | *-lowering-*.f32 |
| 4156× | *-lowering-*.f64 |
| 2558× | +-lowering-+.f64 |
| 2558× | +-lowering-+.f32 |
| 1062× | sum5-define |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 247 | 1632 |
| 1 | 774 | 1458 |
| 2 | 2556 | 1424 |
| 3 | 7624 | 1424 |
| 0 | 8156 | 1424 |
| 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))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* -1/2 (sqrt (/ 1 x))) |
(/ (+ (sqrt (pow x 3)) (* -1/2 (sqrt x))) x) |
(/ (+ (sqrt (pow x 3)) (* -1/2 (sqrt x))) x) |
(/ (+ (sqrt (pow x 3)) (* -1/2 (sqrt x))) x) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))) |
(sqrt x) |
(* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
-1 |
(- (* 2 x) 1) |
(- (* 2 x) 1) |
(- (* 2 x) 1) |
(* 2 x) |
(* x (- 2 (/ 1 x))) |
(* x (- 2 (/ 1 x))) |
(* x (- 2 (/ 1 x))) |
(* 2 x) |
(* -1 (* x (- (/ 1 x) 2))) |
(* -1 (* x (- (/ 1 x) 2))) |
(* -1 (* x (- (/ 1 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) |
(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))) |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
(+ 1 (* -1 x)) |
(+ 1 (* x (- x 1))) |
(+ 1 (* x (- (* x (+ 1 (* -1 x))) 1))) |
(/ 1 x) |
(/ (- 1 (/ 1 x)) x) |
(/ (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)) x) |
(/ (- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3)))) x) |
(/ 1 x) |
(* -1 (/ (- (/ 1 x) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) 1) x)) |
x |
(* x (+ 1 (* -1 x))) |
(* x (+ 1 (* x (- x 1)))) |
(* x (+ 1 (* x (- (* x (+ 1 (* -1 x))) 1)))) |
1 |
(- 1 (/ 1 x)) |
(- (+ 1 (/ 1 (pow x 2))) (/ 1 x)) |
(- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3)))) |
1 |
(- 1 (/ 1 x)) |
(+ 1 (* -1 (/ (- 1 (/ 1 x)) x))) |
(+ 1 (* -1 (/ (+ 1 (* -1 (/ (- 1 (/ 1 x)) x))) 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))) |
(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)) |
(pow (/ 1 x) 1/4) |
(pow (/ 1 x) 1/4) |
(pow (/ 1 x) 1/4) |
(pow (/ 1 x) 1/4) |
(pow (/ 1 x) 1/4) |
(pow (/ 1 x) 1/4) |
(pow (/ 1 x) 1/4) |
(pow (/ 1 x) 1/4) |
(exp (* 1/4 (+ (log -1) (log (/ -1 x))))) |
(exp (* 1/4 (+ (log -1) (log (/ -1 x))))) |
(exp (* 1/4 (+ (log -1) (log (/ -1 x))))) |
(exp (* 1/4 (+ (log -1) (log (/ -1 x))))) |
1 |
(+ 1 (* -1 x)) |
(+ 1 (* x (- x 1))) |
(+ 1 (* x (- (* x (+ 1 (* -1 x))) 1))) |
(/ 1 x) |
(/ (- 1 (/ 1 x)) x) |
(/ (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)) x) |
(/ (- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3)))) x) |
(/ 1 x) |
(* -1 (/ (- (/ 1 x) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) 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 (/.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 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) |
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#s(literal 1 binary64) |
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#s(literal 1 binary64) |
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#s(literal 1 binary64) |
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#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 (* x (- x 1))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) |
(+ 1 (* x (- (* x (+ 1 (* -1 x))) 1))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ (- 1 (/ 1 x)) x) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) x) |
(/ (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)) x) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x) |
(/ (- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3)))) x) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(* -1 (/ (- (/ 1 x) 1) x)) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) x) |
(* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) 1) x)) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)) x) |
x |
(* x (+ 1 (* -1 x))) |
(*.f64 x (-.f64 #s(literal 1 binary64) x)) |
(* x (+ 1 (* x (- x 1)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))) |
(* x (+ 1 (* x (- (* x (+ 1 (* -1 x))) 1)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))) |
1 |
#s(literal 1 binary64) |
(- 1 (/ 1 x)) |
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) |
(- (+ 1 (/ 1 (pow x 2))) (/ 1 x)) |
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) |
(- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3)))) |
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)) |
1 |
#s(literal 1 binary64) |
(- 1 (/ 1 x)) |
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) |
(+ 1 (* -1 (/ (- 1 (/ 1 x)) x))) |
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) |
(+ 1 (* -1 (/ (+ 1 (* -1 (/ (- 1 (/ 1 x)) x))) x))) |
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) 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))) |
(pow (/ 1 x) 1/4) |
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) |
(pow (/ 1 x) 1/4) |
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) |
(pow (/ 1 x) 1/4) |
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) |
(pow (/ 1 x) 1/4) |
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) |
(pow (/ 1 x) 1/4) |
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) |
(pow (/ 1 x) 1/4) |
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) |
(pow (/ 1 x) 1/4) |
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) |
(pow (/ 1 x) 1/4) |
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) |
(exp (* 1/4 (+ (log -1) (log (/ -1 x))))) |
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/4 binary64))) |
(exp (* 1/4 (+ (log -1) (log (/ -1 x))))) |
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/4 binary64))) |
(exp (* 1/4 (+ (log -1) (log (/ -1 x))))) |
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/4 binary64))) |
(exp (* 1/4 (+ (log -1) (log (/ -1 x))))) |
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/4 binary64))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1 x)) |
(-.f64 #s(literal 1 binary64) x) |
(+ 1 (* x (- x 1))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) |
(+ 1 (* x (- (* x (+ 1 (* -1 x))) 1))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ (- 1 (/ 1 x)) x) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) x) |
(/ (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)) x) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x) |
(/ (- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3)))) x) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(* -1 (/ (- (/ 1 x) 1) x)) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) x) |
(* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) 1) x)) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)) x) |
Compiled 35449 to 3411 computations (90.4% saved)
33 alts after pruning (29 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1271 | 15 | 1286 |
| Fresh | 5 | 14 | 19 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1278 | 33 | 1311 |
| Status | Accuracy | Program |
|---|---|---|
| 98.5% | (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) | |
| 49.0% | (/.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) x) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 3.0% | (/.f64 (/.f64 (-.f64 (*.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 x (+.f64 #s(literal 1 binary64) x)))) (*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (*.f64 (+.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) x)) (/.f64 x (+.f64 #s(literal 1 binary64) x))))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 3.0% | (/.f64 (/.f64 (-.f64 (*.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 x (+.f64 #s(literal 1 binary64) x)))) (*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 2.6% | (/.f64 (/.f64 (-.f64 (*.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))) x)) (*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 3.6% | (/.f64 (/.f64 (-.f64 (*.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 x #s(literal -1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 3.5% | (/.f64 (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)) #s(literal 1 binary64))) (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)) (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 3.6% | (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x))) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 5.8% | (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) x)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 3.1% | (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 0 binary64) x)))))) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 6.0% | (/.f64 (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 x (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 2.9% | (/.f64 (/.f64 (+.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))) x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 40.0% | (/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64)))) x) (*.f64 x x)) | |
| 5.1% | (/.f64 (-.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 #s(literal 1 binary64) x) x)) (/.f64 (*.f64 x x) (+.f64 (+.f64 #s(literal 1 binary64) x) x))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 5.7% | (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1 binary64) x))) (/.f64 (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) x))) | |
| 32.9% | (/.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x))))) (*.f64 x x)) | |
| 3.3% | (/.f64 (+.f64 x (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 5.1% | (/.f64 (+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 7.2% | (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 2 binary64))) | |
| 5.1% | (/.f64 (+.f64 x (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 5.4% | (/.f64 (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| ✓ | 3.6% | (/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) |
| 98.1% | (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) | |
| 99.5% | (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 x)))) | |
| ✓ | 99.6% | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
| 97.7% | (/.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))) | |
| ✓ | 98.1% | (/.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)))) | |
| ✓ | 6.3% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 99.0% | (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) | |
| 5.7% | (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))) | |
| 7.2% | (*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 x (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 x (+.f64 x #s(literal -1 binary64))) (sqrt.f64 x))))) | |
| 97.2% | (*.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal -1/8 binary64)) #s(literal 4 binary64))) |
Compiled 1850 to 669 computations (63.8% 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 2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 2 binary64))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1 binary64) x))) (/.f64 (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) x))) |
(/.f64 (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 x (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 x (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 x (+.f64 x #s(literal -1 binary64))) (sqrt.f64 x))))) |
(/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) |
(/.f64 (+.f64 x (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 x x)) (+.f64 (+.f64 #s(literal 1 binary64) x) x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 x #s(literal -1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) x) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) x)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (+.f64 x (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (-.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 #s(literal 1 binary64) x) x)) (/.f64 (*.f64 x x) (+.f64 (+.f64 #s(literal 1 binary64) x) x))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x))) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) x)) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (+.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))) x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (+.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)) #s(literal 1 binary64))) (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)) (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))) x)) (*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 x (+.f64 #s(literal 1 binary64) x)))) (*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 0 binary64) x)))))) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 x (+.f64 #s(literal 1 binary64) x)))) (*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (*.f64 (+.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) x)) (/.f64 x (+.f64 #s(literal 1 binary64) x))))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))) |
(*.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))) |
(*.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal -1/8 binary64)) #s(literal 4 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 1/2 binary64) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (pow.f64 (*.f64 x x) #s(literal 1/4 binary64))) |
(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 x)) |
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (/.f64 x (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 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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 #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)))))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x x) #s(literal 1/4 binary64)))) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x))))) (*.f64 x x)) |
(/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64)))) x) (*.f64 x x)) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x x))) |
(*.f64 (/.f64 #s(literal 1 binary64) 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 (/.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) |
(*.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))) |
| Outputs |
|---|
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
2 calls:
| 15.0ms | x |
| 14.0ms | (-.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 2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 2 binary64))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1 binary64) x))) (/.f64 (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) x))) |
(/.f64 (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 x (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 x (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 x (+.f64 x #s(literal -1 binary64))) (sqrt.f64 x))))) |
(/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) |
(/.f64 (+.f64 x (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 x x)) (+.f64 (+.f64 #s(literal 1 binary64) x) x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 x #s(literal -1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x (-.f64 #s(literal 1 binary64) x))) (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) x) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) x)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (+.f64 x (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (-.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 #s(literal 1 binary64) x) x)) (/.f64 (*.f64 x x) (+.f64 (+.f64 #s(literal 1 binary64) x) x))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x))) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) x)) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (+.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))) x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (+.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)) #s(literal 1 binary64))) (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)) (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))) x)) (*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 x (+.f64 #s(literal 1 binary64) x)))) (*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 0 binary64) x)))))) (*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 x (+.f64 #s(literal 1 binary64) x)))) (*.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (*.f64 (+.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) x)) (/.f64 x (+.f64 #s(literal 1 binary64) x))))) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))) |
(*.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))) |
(*.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal -1/8 binary64)) #s(literal 4 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 1/2 binary64) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
| Outputs |
|---|
(/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
2 calls:
| 11.0ms | x |
| 9.0ms | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.5% | 1 | x |
| 98.5% | 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 |
|---|---|---|
| 98.1% | 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× | sub-neg_binary64 |
| 2× | *-commutative_binary64 |
| 2× | 1-exp_binary64 |
| 2× | neg-sub0_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 14 | 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 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 2 binary64)) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| 4156× | +-lowering-+.f64 |
| 4156× | +-lowering-+.f32 |
| 3296× | *-lowering-*.f32 |
| 3296× | *-lowering-*.f64 |
| 2970× | *-lowering-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 1 | 39 | 16 |
| 2 | 303 | 16 |
| 3 | 3722 | 16 |
| 0 | 8045 | 16 |
| 0 | 113 | 434 |
| 1 | 325 | 384 |
| 2 | 1039 | 376 |
| 3 | 3226 | 373 |
| 4 | 7122 | 373 |
| 0 | 8132 | 373 |
| 0 | 32 | 128 |
| 1 | 199 | 115 |
| 2 | 1709 | 110 |
| 0 | 8433 | 110 |
| 0 | 339 | 2650 |
| 1 | 1071 | 2268 |
| 2 | 3782 | 2250 |
| 0 | 8323 | 2250 |
| 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 |
Compiled 89 to 64 computations (28.1% saved)
Compiled 82 to 54 computations (34.1% saved)
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