Main:bigenough3 from C
Time bar (total: 10.6s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 100% | 0% | 0% | 0% | 0% | 0 |
| 0% | 0% | 100% | 0% | 0% | 0% | 0% | 1 |
| 50% | 50% | 50% | 0% | 0% | 0% | 0% | 2 |
| 66.7% | 50% | 25% | 0% | 0% | 25% | 0% | 3 |
| 80% | 50% | 12.5% | 0% | 0% | 37.5% | 0% | 4 |
| 88.9% | 50% | 6.2% | 0% | 0% | 43.7% | 0% | 5 |
| 94.1% | 50% | 3.1% | 0% | 0% | 46.9% | 0% | 6 |
| 97% | 50% | 1.6% | 0% | 0% | 48.4% | 0% | 7 |
| 98.5% | 50% | 0.8% | 0% | 0% | 49.2% | 0% | 8 |
| 99.2% | 50% | 0.4% | 0% | 0% | 49.6% | 0% | 9 |
| 99.6% | 50% | 0.2% | 0% | 0% | 49.8% | 0% | 10 |
| 99.8% | 50% | 0.1% | 0% | 0% | 49.9% | 0% | 11 |
| 99.9% | 50% | 0% | 0% | 0% | 49.9% | 0% | 12 |
Compiled 9 to 7 computations (22.2% saved)
ival-sub: 0.0ms (0% of total)ival-add: 0.0ms (0% of total)const: 0.0ms (0% of total)ival-sqrt: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| 274.0ms | 1624× | 2 | valid |
| 267.0ms | 2400× | 1 | valid |
| 208.0ms | 4232× | 0 | valid |
| 0.0ms | 7× | 0 | invalid |
ival-sqrt: 224.0ms (47.2% of total)ival-add: 91.0ms (19.2% of total)ival-sub: 78.0ms (16.5% of total)backward-pass: 66.0ms (13.9% of total)const: 15.0ms (3.2% 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 |
|---|---|---|---|---|---|
| 112 | 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)) |
| 22.0ms | 128× | 1 | valid |
| 18.0ms | 94× | 2 | valid |
| 17.0ms | 290× | 0 | valid |
Compiled 48 to 20 computations (58.3% saved)
ival-sqrt: 12.0ms (44% of total)ival-add: 5.0ms (18.3% of total)backward-pass: 5.0ms (18.3% of total)ival-sub: 4.0ms (14.7% of total)const: 1.0ms (3.7% of total)Compiled 8 to 6 computations (25% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 58.8% | (-.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 x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
| ✓ | accuracy | 58.8% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 16.0ms | 47× | 2 | valid |
| 9.0ms | 145× | 0 | valid |
| 8.0ms | 64× | 1 | valid |
Compiled 20 to 7 computations (65% saved)
backward-pass: 9.0ms (44.8% of total)ival-sqrt: 6.0ms (29.8% of total)ival-add: 3.0ms (14.9% of total)ival-sub: 2.0ms (9.9% of total)const: 0.0ms (0% 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))))) |
(fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.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))))) (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 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)
11 alts after pruning (10 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 258 | 10 | 268 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 258 | 11 | 269 |
| Status | Accuracy | Program |
|---|---|---|
| 58.3% | (/.f64 (-.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 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) x)) (*.f64 (+.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)))) | |
| ▶ | 43.9% | (/.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) |
| ▶ | 60.1% | (/.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))) |
| 57.6% | (-.f64 (+.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.f64 x)) | |
| 57.8% | (-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x)) | |
| ✓ | 58.8% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| ▶ | 55.4% | (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ▶ | 57.8% | (+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64))) |
| ▶ | 56.6% | (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x))) |
| 59.2% | (*.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)))))) | |
| 47.1% | (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
Compiled 328 to 196 computations (40.2% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
| ✓ | cost-diff | 0 | (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) |
| ✓ | cost-diff | 0 | (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x))) |
| ✓ | cost-diff | 0 | (*.f64 x #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (-.f64 #s(literal 1 binary64) x) |
| ✓ | cost-diff | 256 | (+.f64 x (-.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 256 | (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
| 2640× | sum3-define |
| 1798× | fnmadd-define |
| 1678× | fnmsub-define |
| 1554× | fma-lowering-fma.f32 |
| 1554× | fma-lowering-fma.f64 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 169 |
| 1 | 59 | 164 |
| 2 | 131 | 136 |
| 3 | 267 | 135 |
| 4 | 571 | 135 |
| 5 | 1569 | 135 |
| 6 | 3908 | 135 |
| 7 | 7272 | 135 |
| 0 | 8027 | 135 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (+ 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) |
(- 1 (sqrt x)) |
1 |
(sqrt x) |
x |
(+ (- 1 (sqrt x)) (* x 1/2)) |
(- 1 (sqrt x)) |
1 |
(sqrt x) |
x |
(* x 1/2) |
1/2 |
(+ 1 (- (* x (+ 1/2 (* x -1/8))) (sqrt x))) |
1 |
(- (* x (+ 1/2 (* x -1/8))) (sqrt x)) |
(* x (+ 1/2 (* x -1/8))) |
x |
(+ 1/2 (* x -1/8)) |
1/2 |
(* x -1/8) |
-1/8 |
(sqrt x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) |
(+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) |
(* -1/8 (sqrt (/ 1 x))) |
-1/8 |
(sqrt (/ 1 x)) |
(/ 1 x) |
1 |
x |
(* (sqrt x) 1/2) |
(sqrt x) |
1/2 |
| Outputs |
|---|
(/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x))) |
(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #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) |
(+ (pow (+ x 1) 1/2) (sqrt x)) |
(+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
(pow (+ x 1) 1/2) |
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) |
(+ x 1) |
(+.f64 x #s(literal 1 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(sqrt x) |
(sqrt.f64 x) |
(- 1 (sqrt x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
1 |
#s(literal 1 binary64) |
(sqrt x) |
(sqrt.f64 x) |
x |
(+ (- 1 (sqrt x)) (* x 1/2)) |
(+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 x))) |
(- 1 (sqrt x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
1 |
#s(literal 1 binary64) |
(sqrt x) |
(sqrt.f64 x) |
x |
(* x 1/2) |
(*.f64 x #s(literal 1/2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1 (- (* x (+ 1/2 (* x -1/8))) (sqrt x))) |
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))) |
1 |
#s(literal 1 binary64) |
(- (* x (+ 1/2 (* x -1/8))) (sqrt x)) |
(-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x)) |
(* x (+ 1/2 (* x -1/8))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) |
x |
(+ 1/2 (* x -1/8)) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))) |
1/2 |
#s(literal 1/2 binary64) |
(* x -1/8) |
(*.f64 x #s(literal -1/8 binary64)) |
-1/8 |
#s(literal -1/8 binary64) |
(sqrt x) |
(sqrt.f64 x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) |
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) |
(+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) |
(+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 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) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(sqrt x) |
(sqrt.f64 x) |
1/2 |
#s(literal 1/2 binary64) |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 100.0% | (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
| ✓ | accuracy | 99.6% | (/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
| ✓ | accuracy | 100.0% | (*.f64 x #s(literal -1/8 binary64)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 100.0% | (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) |
| ✓ | accuracy | 100.0% | (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x)) |
| ✓ | accuracy | 100.0% | (*.f64 x #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 100.0% | (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ✓ | accuracy | 100.0% | (+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 100.0% | (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ✓ | accuracy | 100.0% | (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
| ✓ | accuracy | 99.8% | (/.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 | 59.9% | (+.f64 x (-.f64 #s(literal 1 binary64) x)) |
| 147.0ms | 104× | 1 | valid |
| 45.0ms | 152× | 0 | valid |
Compiled 163 to 26 computations (84% saved)
ival-mult: 70.0ms (51.2% of total)ival-add: 29.0ms (21.2% of total)ival-pow: 11.0ms (8% of total)ival-div: 7.0ms (5.1% of total)backward-pass: 7.0ms (5.1% of total)ival-sub: 6.0ms (4.4% of total)ival-sqrt: 6.0ms (4.4% of total)const: 1.0ms (0.7% of total)| Inputs |
|---|
#<alt (/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x)))> |
#<alt (+ x (- 1 x))> |
#<alt (- 1 x)> |
#<alt (+ (pow (+ x 1) 1/2) (sqrt x))> |
#<alt (- 1 (sqrt x))> |
#<alt (sqrt x)> |
#<alt (+ (- 1 (sqrt x)) (* x 1/2))> |
#<alt (* x 1/2)> |
#<alt (+ 1 (- (* x (+ 1/2 (* x -1/8))) (sqrt x)))> |
#<alt (- (* x (+ 1/2 (* x -1/8))) (sqrt x))> |
#<alt (* x (+ 1/2 (* x -1/8)))> |
#<alt (+ 1/2 (* x -1/8))> |
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)> |
#<alt (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2))> |
#<alt (* -1/8 (sqrt (/ 1 x)))> |
#<alt (sqrt (/ 1 x))> |
#<alt (pow (+ x 1) 1/2)> |
#<alt (* x -1/8)> |
| 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> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt (+ 1 (* -1 x))> |
#<alt (+ 1 (* -1 x))> |
#<alt (+ 1 (* -1 x))> |
#<alt (* -1 x)> |
#<alt (* x (- (/ 1 x) 1))> |
#<alt (* x (- (/ 1 x) 1))> |
#<alt (* x (- (/ 1 x) 1))> |
#<alt (* -1 x)> |
#<alt (* -1 (* x (- 1 (/ 1 x))))> |
#<alt (* -1 (* x (- 1 (/ 1 x))))> |
#<alt (* -1 (* x (- 1 (/ 1 x))))> |
#<alt (+ 1 (sqrt x))> |
#<alt (+ 1 (+ (sqrt x) (* 1/2 x)))> |
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))> |
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))> |
#<alt (* 2 (sqrt x))> |
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))> |
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))> |
#<alt (- 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 (* 1/2 x)) (sqrt x))> |
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))> |
#<alt (* x (- 1/2 (sqrt (/ 1 x))))> |
#<alt (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))> |
#<alt (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))> |
#<alt (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))> |
#<alt (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))> |
#<alt (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<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 (* -1/8 x)))) (sqrt x))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))> |
#<alt (* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))> |
#<alt (* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))> |
#<alt (* -1 (sqrt x))> |
#<alt (- (* 1/2 x) (sqrt x))> |
#<alt (- (* x (+ 1/2 (* -1/8 x))) (sqrt x))> |
#<alt (- (* x (+ 1/2 (* -1/8 x))) (sqrt x))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))> |
#<alt (* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))> |
#<alt (* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt 1/2> |
#<alt (+ 1/2 (* -1/8 x))> |
#<alt (+ 1/2 (* -1/8 x))> |
#<alt (+ 1/2 (* -1/8 x))> |
#<alt (* -1/8 x)> |
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* -1/8 x)> |
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))> |
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))> |
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))> |
#<alt (* -1/8 (sqrt (/ 1 (pow x 3))))> |
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))> |
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))> |
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))> |
#<alt (* 1/2 (sqrt (/ 1 x)))> |
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))> |
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))> |
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))> |
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))> |
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))> |
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))> |
#<alt (* -1/8 (sqrt (/ 1 x)))> |
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)> |
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)> |
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))> |
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))> |
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1/8 (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> |
#<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 (* -1/8 x)> |
#<alt (* -1/8 x)> |
#<alt (* -1/8 x)> |
#<alt (* -1/8 x)> |
#<alt (* -1/8 x)> |
#<alt (* -1/8 x)> |
#<alt (* -1/8 x)> |
#<alt (* -1/8 x)> |
#<alt (* -1/8 x)> |
#<alt (* -1/8 x)> |
#<alt (* -1/8 x)> |
#<alt (* -1/8 x)> |
54 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (+ 1 (- (* x (+ 1/2 (* x -1/8))) (sqrt x))) |
| 1.0ms | x | @ | 0 | (/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt 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)) x) |
| 1.0ms | x | @ | inf | (/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x))) |
| 1× | batch-egg-rewrite |
| 3464× | *-lowering-*.f32 |
| 3464× | *-lowering-*.f64 |
| 2230× | /-lowering-/.f32 |
| 2230× | /-lowering-/.f64 |
| 2184× | fma-lowering-fma.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 112 |
| 1 | 198 | 97 |
| 2 | 1913 | 97 |
| 0 | 8634 | 97 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x))) |
(+ x (- 1 x)) |
(- 1 x) |
(+ (pow (+ x 1) 1/2) (sqrt x)) |
(- 1 (sqrt x)) |
(sqrt x) |
(+ (- 1 (sqrt x)) (* x 1/2)) |
(* x 1/2) |
(+ 1 (- (* x (+ 1/2 (* x -1/8))) (sqrt x))) |
(- (* x (+ 1/2 (* x -1/8))) (sqrt x)) |
(* x (+ 1/2 (* x -1/8))) |
(+ 1/2 (* x -1/8)) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) |
(+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) |
(* -1/8 (sqrt (/ 1 x))) |
(sqrt (/ 1 x)) |
(pow (+ x 1) 1/2) |
(* x -1/8) |
| 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)) (fma.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) #s(literal 1 binary64) (sqrt.f64 x))) |
(+.f64 (-.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) (sqrt.f64 x))) |
(+.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) #s(literal -1 binary64))) |
(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
(-.f64 (/.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)))) |
(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))) |
(neg.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))) |
(neg.f64 (/.f64 (-.f64 #s(literal 0 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)))) |
(/.f64 #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)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) #s(literal 1 binary64))) |
(/.f64 (+.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 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) |
(/.f64 (+.f64 (*.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 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) (+.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) x))))) |
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) (+.f64 (+.f64 x #s(literal -1 binary64)) x))) |
(/.f64 (*.f64 (+.f64 (*.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)))) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) x))) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) |
(/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 x #s(literal -1 binary64)) x) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x)))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))) |
(/.f64 (*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
(/.f64 (*.f64 (+.f64 (*.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 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) (+.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) x)))) |
(/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) |
(/.f64 (-.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 #s(literal 1 binary64)) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))))) |
(/.f64 (-.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 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) x)) (*.f64 (+.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)))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) #s(literal 1 binary64)) #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))) |
(*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) |
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))) |
(*.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 (+.f64 x #s(literal 1 binary64)) x) (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))) |
(*.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.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 (pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) (+.f64 (*.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))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) x))))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) x))) |
(+.f64 x (-.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) (-.f64 x x)) |
(+.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) x) x)) |
(+.f64 (-.f64 #s(literal 1 binary64) x) x) |
(+.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (sqrt.f64 x)) x)) |
(+.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (-.f64 #s(literal 0 binary64) x) x)) |
(+.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64) x)) |
(+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) x)) |
(+.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (sqrt.f64 x))) |
(-.f64 #s(literal 1 binary64) (-.f64 x x)) |
(-.f64 (+.f64 x #s(literal 1 binary64)) x) |
(-.f64 (/.f64 (*.f64 x x) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 x #s(literal -1 binary64)) x))) |
(fma.f64 x #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) |
(fma.f64 #s(literal 1 binary64) x (-.f64 #s(literal 1 binary64) x)) |
(fma.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 #s(literal 0 binary64) x)) |
(fma.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 0 binary64) (sqrt.f64 x)) (sqrt.f64 x))) |
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x)) |
(fma.f64 (+.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 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (sqrt.f64 x)) x)) |
(fma.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x)) |
(fma.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x))) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (sqrt.f64 x))) |
(fma.f64 (+.f64 (*.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 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) x)))) (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (sqrt.f64 x)) x)) |
(fma.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))))) x) |
(fma.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) x)) |
(fma.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) (sqrt.f64 x)) (sqrt.f64 x))) |
(fma.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (sqrt.f64 x)) x)) |
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) x) |
(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 3/4 binary64)) (-.f64 #s(literal 0 binary64) x)) |
(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 3/4 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (sqrt.f64 x))) |
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/4 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) x)) |
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/4 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (sqrt.f64 x))) |
(fma.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)) x) |
(fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) (+.f64 x #s(literal -1 binary64)) x) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) x))) (+.f64 (*.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 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x #s(literal -1 binary64)) x) (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) |
(/.f64 (+.f64 (*.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 x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) x)))) |
(/.f64 (+.f64 (*.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 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (-.f64 (*.f64 x x) (*.f64 x (-.f64 #s(literal 1 binary64) x))))) |
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) |
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(/.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(literal 1 binary64)) x) |
(/.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #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 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (-.f64 (*.f64 x #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))))) |
(/.f64 (*.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (*.f64 x #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) |
(pow.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) #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 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) |
(*.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 #s(literal 1/2 binary64) (sqrt.f64 x)))) #s(literal -1 binary64))) |
(*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))) |
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (pow.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (-.f64 (*.f64 x #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))))) |
(*.f64 (pow.f64 (/.f64 x (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (*.f64 x #s(literal 1/4 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) |
(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) |
(-.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) |
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) |
(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) |
(fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (-.f64 (*.f64 x #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))) (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (*.f64 x #s(literal 1/4 binary64))))) |
(/.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64))) (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (-.f64 (*.f64 x #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))))) |
(/.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64))) (+.f64 (*.f64 x #s(literal 1/4 binary64)) (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))))) |
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (*.f64 x #s(literal 1/4 binary64))) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) |
(/.f64 (neg.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (-.f64 (*.f64 x #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (*.f64 x #s(literal 1/4 binary64)))) (neg.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) |
(/.f64 (-.f64 (*.f64 x #s(literal 1/4 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (*.f64 x #s(literal 1/4 binary64)))) (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) |
(pow.f64 (/.f64 (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (-.f64 (*.f64 x #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))) (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (*.f64 x #s(literal 1/4 binary64)))) #s(literal -1 binary64)) |
(*.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (-.f64 (*.f64 x #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))))) |
(*.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (*.f64 x #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) |
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) |
(*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1/8 binary64)) |
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal -1 binary64))) |
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))) |
(fabs.f64 (pow.f64 x #s(literal -1/2 binary64))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)))) |
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) |
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64))) |
(pow.f64 x #s(literal -1/2 binary64)) |
(pow.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64)) |
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) |
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) 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) x)))) |
(*.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)) (pow.f64 x #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (pow.f64 x #s(literal -1/2 binary64))) (sqrt.f64 (pow.f64 x #s(literal -1/2 binary64)))) |
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 (*.f64 (log1p.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
(exp.f64 (+.f64 (*.f64 (log1p.f64 x) #s(literal 1/4 binary64)) (*.f64 (log1p.f64 x) #s(literal 1/4 binary64)))) |
(hypot.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(fabs.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))))) |
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)))) |
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x)))) |
(/.f64 (pow.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(/.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 #s(literal 1 binary64) x) (*.f64 x x))))) |
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)))) (sqrt.f64 (neg.f64 (+.f64 x #s(literal -1 binary64))))) |
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/4 binary64)) |
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 x)) |
(*.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 (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x))) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x))))) |
(*.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 (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 (pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/4 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) |
(*.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 (sqrt.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (sqrt.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/4 binary64)))) |
(*.f64 (sqrt.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)))) |
(*.f64 x #s(literal -1/8 binary64)) |
(*.f64 #s(literal -1/8 binary64) x) |
| 1× | egg-herbie |
| 3978× | *-lowering-*.f32 |
| 3978× | *-lowering-*.f64 |
| 2738× | +-lowering-+.f64 |
| 2738× | +-lowering-+.f32 |
| 1048× | sum5-define |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 251 | 1886 |
| 1 | 781 | 1630 |
| 2 | 2751 | 1611 |
| 3 | 7835 | 1611 |
| 0 | 8360 | 1611 |
| 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 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
(+ 1 (* -1 x)) |
(+ 1 (* -1 x)) |
(+ 1 (* -1 x)) |
(* -1 x) |
(* x (- (/ 1 x) 1)) |
(* x (- (/ 1 x) 1)) |
(* x (- (/ 1 x) 1)) |
(* -1 x) |
(* -1 (* x (- 1 (/ 1 x)))) |
(* -1 (* x (- 1 (/ 1 x)))) |
(* -1 (* x (- 1 (/ 1 x)))) |
(+ 1 (sqrt x)) |
(+ 1 (+ (sqrt x) (* 1/2 x))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))) |
(* 2 (sqrt x)) |
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
(- 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 (* 1/2 x)) (sqrt x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(* x (- 1/2 (sqrt (/ 1 x)))) |
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x)))) |
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x)))) |
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x)))) |
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(- 1 (sqrt x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3)))))) |
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3)))))) |
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3)))))) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8)) |
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8)) |
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8)) |
(* -1 (sqrt x)) |
(- (* 1/2 x) (sqrt x)) |
(- (* x (+ 1/2 (* -1/8 x))) (sqrt x)) |
(- (* x (+ 1/2 (* -1/8 x))) (sqrt x)) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3)))))) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3)))))) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3)))))) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8)) |
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8)) |
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8)) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* -1/8 x))) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
1/2 |
(+ 1/2 (* -1/8 x)) |
(+ 1/2 (* -1/8 x)) |
(+ 1/2 (* -1/8 x)) |
(* -1/8 x) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(* -1/8 x) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(* -1/8 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(* 1/2 (sqrt (/ 1 x))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(* -1/8 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(* 1/2 (sqrt x)) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1/8 (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 |
(+ 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))))))) |
(* -1/8 x) |
(* -1/8 x) |
(* -1/8 x) |
(* -1/8 x) |
(* -1/8 x) |
(* -1/8 x) |
(* -1/8 x) |
(* -1/8 x) |
(* -1/8 x) |
(* -1/8 x) |
(* -1/8 x) |
(* -1/8 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 x (/.f64 #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 #s(literal 1/16 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 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 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))))) x) |
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x) |
(/.f64 (+.f64 (-.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))))) x) |
(* -1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x) |
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (+.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) x) |
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x)) |
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))))) (-.f64 #s(literal 0 binary64) x)) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1 x)) |
(-.f64 #s(literal 1 binary64) x) |
(+ 1 (* -1 x)) |
(-.f64 #s(literal 1 binary64) x) |
(+ 1 (* -1 x)) |
(-.f64 #s(literal 1 binary64) x) |
(* -1 x) |
(-.f64 #s(literal 0 binary64) x) |
(* x (- (/ 1 x) 1)) |
(-.f64 #s(literal 1 binary64) x) |
(* x (- (/ 1 x) 1)) |
(-.f64 #s(literal 1 binary64) x) |
(* x (- (/ 1 x) 1)) |
(-.f64 #s(literal 1 binary64) x) |
(* -1 x) |
(-.f64 #s(literal 0 binary64) x) |
(* -1 (* x (- 1 (/ 1 x)))) |
(-.f64 #s(literal 1 binary64) x) |
(* -1 (* x (- 1 (/ 1 x)))) |
(-.f64 #s(literal 1 binary64) x) |
(* -1 (* x (- 1 (/ 1 x)))) |
(-.f64 #s(literal 1 binary64) x) |
(+ 1 (sqrt x)) |
(+.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(+ 1 (+ (sqrt x) (* 1/2 x))) |
(+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 x #s(literal 1/2 binary64)))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))) |
(+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))) |
(+.f64 (+.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))))))) |
(* 2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 2 binary64)) |
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))) |
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))) |
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (+.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))) |
(*.f64 x (+.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 x) #s(literal 2 binary64)) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (+.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 (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 (sqrt x)) |
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(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) |
(* -1/8 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) |
(* -1/8 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) |
(* -1/8 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) |
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
1 |
#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 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 x (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)))))) |
(* 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 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (+.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* -1/8 x) |
(*.f64 x #s(literal -1/8 binary64)) |
(* -1/8 x) |
(*.f64 x #s(literal -1/8 binary64)) |
(* -1/8 x) |
(*.f64 x #s(literal -1/8 binary64)) |
(* -1/8 x) |
(*.f64 x #s(literal -1/8 binary64)) |
(* -1/8 x) |
(*.f64 x #s(literal -1/8 binary64)) |
(* -1/8 x) |
(*.f64 x #s(literal -1/8 binary64)) |
(* -1/8 x) |
(*.f64 x #s(literal -1/8 binary64)) |
(* -1/8 x) |
(*.f64 x #s(literal -1/8 binary64)) |
(* -1/8 x) |
(*.f64 x #s(literal -1/8 binary64)) |
(* -1/8 x) |
(*.f64 x #s(literal -1/8 binary64)) |
(* -1/8 x) |
(*.f64 x #s(literal -1/8 binary64)) |
(* -1/8 x) |
(*.f64 x #s(literal -1/8 binary64)) |
Compiled 19451 to 2172 computations (88.8% saved)
17 alts after pruning (14 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 863 | 12 | 875 |
| Fresh | 3 | 2 | 5 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 1 | 1 |
| Total | 869 | 17 | 886 |
| Status | Accuracy | Program |
|---|---|---|
| 43.9% | (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) | |
| 59.2% | (/.f64 (+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) | |
| ▶ | 58.0% | (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.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.f64 x))) |
| 7.4% | (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 47.0% | (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) | |
| ▶ | 99.7% | (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
| ▶ | 62.9% | (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
| ▶ | 57.8% | (-.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 x)) |
| 57.6% | (-.f64 (+.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.f64 x)) | |
| ✓ | 58.8% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 57.8% | (-.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x))) | |
| ✓ | 55.4% | (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ✓ | 56.6% | (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x))) |
| 53.4% | (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) | |
| 43.9% | (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) | |
| 47.1% | (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) | |
| ▶ | 2.0% | (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) |
Compiled 354 to 252 computations (28.8% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (+.f64 (+.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.f64 x)) |
| ✓ | cost-diff | 0 | (-.f64 #s(literal 1 binary64) x) |
| ✓ | cost-diff | 256 | (+.f64 x (-.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 256 | (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.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.f64 x))) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | (*.f64 x #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (-.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
| ✓ | cost-diff | 0 | (*.f64 x x) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) |
| ✓ | cost-diff | 0 | (+.f64 x #s(literal 1 binary64)) |
| ✓ | 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 | 64 | (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
| 1948× | sum3-define |
| 1762× | +-lowering-+.f64 |
| 1762× | +-lowering-+.f32 |
| 1704× | fnmadd-define |
| 1592× | fnmsub-define |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 27 | 162 |
| 1 | 70 | 149 |
| 2 | 170 | 145 |
| 3 | 366 | 144 |
| 4 | 796 | 144 |
| 5 | 1995 | 144 |
| 6 | 3462 | 144 |
| 7 | 5536 | 144 |
| 0 | 8162 | 144 |
| 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) |
(* -1/8 (* x x)) |
-1/8 |
(* x x) |
x |
(/ 1 (+ 1 (sqrt x))) |
1 |
(+ 1 (sqrt x)) |
(sqrt x) |
x |
(- (+ (* x 1/2) 1) (sqrt x)) |
(+ (* x 1/2) 1) |
(* x 1/2) |
x |
1/2 |
1 |
(sqrt x) |
(/ (+ x (- 1 x)) (+ (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (sqrt x))) |
(+ x (- 1 x)) |
x |
(- 1 x) |
1 |
(+ (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (sqrt x)) |
(+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) |
(* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))) |
(+ 1/2 (* x (+ -1/8 (* x 1/16)))) |
1/2 |
(* x (+ -1/8 (* x 1/16))) |
(+ -1/8 (* x 1/16)) |
-1/8 |
(* x 1/16) |
1/16 |
(sqrt x) |
| Outputs |
|---|
(/ 1 (+ (pow (+ x 1) 1/2) (sqrt x))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
1 |
#s(literal 1 binary64) |
(+ (pow (+ x 1) 1/2) (sqrt x)) |
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(pow (+ x 1) 1/2) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+ x 1) |
(+.f64 #s(literal 1 binary64) x) |
x |
1/2 |
#s(literal 1/2 binary64) |
(sqrt x) |
(sqrt.f64 x) |
(* -1/8 (* x x)) |
(*.f64 x (*.f64 x #s(literal -1/8 binary64))) |
-1/8 |
#s(literal -1/8 binary64) |
(* x x) |
(*.f64 x x) |
x |
(/ 1 (+ 1 (sqrt x))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
1 |
#s(literal 1 binary64) |
(+ 1 (sqrt x)) |
(+.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(sqrt x) |
(sqrt.f64 x) |
x |
(- (+ (* x 1/2) 1) (sqrt x)) |
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(+ (* x 1/2) 1) |
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) |
(* x 1/2) |
(*.f64 x #s(literal 1/2 binary64)) |
x |
1/2 |
#s(literal 1/2 binary64) |
1 |
#s(literal 1 binary64) |
(sqrt x) |
(sqrt.f64 x) |
(/ (+ x (- 1 x)) (+ (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (sqrt x))) |
(/.f64 #s(literal 1 binary64) (+.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)))))))) |
(+ x (- 1 x)) |
#s(literal 1 binary64) |
x |
(- 1 x) |
(-.f64 #s(literal 1 binary64) x) |
1 |
#s(literal 1 binary64) |
(+ (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (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 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) |
(+.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))))))) |
(* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))) |
(*.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 (* x (+ -1/8 (* x 1/16)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) |
1/2 |
#s(literal 1/2 binary64) |
(* x (+ -1/8 (* x 1/16))) |
(*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) |
(+ -1/8 (* x 1/16)) |
(+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) |
-1/8 |
#s(literal -1/8 binary64) |
(* x 1/16) |
(*.f64 x #s(literal 1/16 binary64)) |
1/16 |
#s(literal 1/16 binary64) |
(sqrt x) |
(sqrt.f64 x) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (+.f64 (+.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.f64 x)) |
| ✓ | accuracy | 99.9% | (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) |
| ✓ | accuracy | 99.7% | (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.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.f64 x))) |
| ✓ | accuracy | 59.9% | (+.f64 x (-.f64 #s(literal 1 binary64) x)) |
| ✓ | accuracy | 100.0% | (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 x #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 99.9% | (-.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 x)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 100.0% | (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ✓ | accuracy | 99.8% | (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
| ✓ | accuracy | 100.0% | (*.f64 x x) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 100.0% | (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
| ✓ | accuracy | 99.8% | (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
| 1.1s | 152× | 0 | valid |
| 81.0ms | 104× | 1 | valid |
Compiled 179 to 28 computations (84.4% saved)
ival-add: 36.0ms (44.2% of total)ival-mult: 14.0ms (17.2% of total)ival-pow: 11.0ms (13.5% of total)ival-div: 7.0ms (8.6% of total)backward-pass: 7.0ms (8.6% of total)ival-sub: 3.0ms (3.7% of total)ival-sqrt: 3.0ms (3.7% of total)const: 1.0ms (1.2% 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 (* -1/8 (* x x))> |
#<alt (* x x)> |
#<alt (/ 1 (+ 1 (sqrt x)))> |
#<alt (+ 1 (sqrt x))> |
#<alt (sqrt x)> |
#<alt (- (+ (* x 1/2) 1) (sqrt x))> |
#<alt (+ (* x 1/2) 1)> |
#<alt (* x 1/2)> |
#<alt (/ (+ x (- 1 x)) (+ (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (sqrt x)))> |
#<alt (+ x (- 1 x))> |
#<alt (- 1 x)> |
#<alt (+ (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (sqrt x))> |
#<alt (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))> |
| 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 (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (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 (pow x 2)> |
#<alt (/ 1 (+ 1 (sqrt x)))> |
#<alt (/ 1 (+ 1 (sqrt x)))> |
#<alt (/ 1 (+ 1 (sqrt x)))> |
#<alt (/ 1 (+ 1 (sqrt x)))> |
#<alt (sqrt (/ 1 x))> |
#<alt (/ (- (sqrt x) 1) x)> |
#<alt (/ (- (+ (sqrt x) (sqrt (/ 1 x))) 1) x)> |
#<alt (/ (- (sqrt x) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (/ 1 x)))) x)> |
#<alt (* -1 (sqrt (/ 1 x)))> |
#<alt (* -1 (/ (- (sqrt x) (/ 1 (pow (sqrt -1) 2))) x))> |
#<alt (* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))> |
#<alt (* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (/ (- (/ x (pow (sqrt -1) 4)) (* -1 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))> |
#<alt (+ 1 (sqrt x))> |
#<alt (+ 1 (sqrt x))> |
#<alt (+ 1 (sqrt x))> |
#<alt (+ 1 (sqrt x))> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))> |
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))> |
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* -1 (* 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 (* 1/2 x)) (sqrt x))> |
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))> |
#<alt (* x (- 1/2 (sqrt (/ 1 x))))> |
#<alt (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))> |
#<alt (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))> |
#<alt (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))> |
#<alt (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))> |
#<alt (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 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 (/ 16 (pow x 3))> |
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 3))> |
#<alt (/ (- (+ 16 (+ (* 32 (/ 1 x)) (/ 64 (pow x 2)))) (* 256 (/ (+ 1/2 (sqrt (/ 1 x))) (pow x 2)))) (pow x 3))> |
#<alt (/ (- (+ 16 (+ (* -1 (/ (+ 256 (+ (* -2 (- 64 (* 256 (+ 1/2 (sqrt (/ 1 x)))))) (* 512 (+ 1/2 (sqrt (/ 1 x)))))) (pow x 3))) (+ (* 32 (/ 1 x)) (/ 64 (pow x 2))))) (* 256 (/ (+ 1/2 (sqrt (/ 1 x))) (pow x 2)))) (pow x 3))> |
#<alt (/ 16 (pow x 3))> |
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 3))> |
#<alt (* -1 (/ (- (* -1 (/ (+ 32 (+ (* 256 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) (* 64 (/ 1 x)))) x)) 16) (pow x 3)))> |
#<alt (* -1 (/ (- (* -1 (/ (+ 32 (* -1 (/ (- (+ (* -512 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) (+ (* -2 (/ (+ 64 (* 256 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2))) x)) (* 256 (/ 1 x)))) (+ 64 (* 256 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))) x))) x)) 16) (pow x 3)))> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt 1> |
#<alt (+ 1 (* -1 x))> |
#<alt (+ 1 (* -1 x))> |
#<alt (+ 1 (* -1 x))> |
#<alt (* -1 x)> |
#<alt (* x (- (/ 1 x) 1))> |
#<alt (* x (- (/ 1 x) 1))> |
#<alt (* x (- (/ 1 x) 1))> |
#<alt (* -1 x)> |
#<alt (* -1 (* x (- 1 (/ 1 x))))> |
#<alt (* -1 (* x (- 1 (/ 1 x))))> |
#<alt (* -1 (* x (- 1 (/ 1 x))))> |
#<alt (+ 1 (sqrt x))> |
#<alt (+ 1 (+ (sqrt x) (* 1/2 x)))> |
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))> |
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))> |
#<alt (* 1/16 (pow x 3))> |
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ 1/16 (+ (sqrt (/ 1 (pow x 5))) (/ 1/2 (pow x 2)))) (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ 1/16 (+ (sqrt (/ 1 (pow x 5))) (+ (/ 1/2 (pow x 2)) (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))> |
#<alt (* 1/16 (pow x 3))> |
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) 1/8) x)) 1/16)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x))) x)) 1/8) x)) 1/16)))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* 1/16 (pow x 3))> |
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))> |
#<alt (* 1/16 (pow x 3))> |
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))> |
51 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (/ (+ x (- 1 x)) (+ (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (sqrt x))) |
| 1.0ms | x | @ | -inf | (/ 1 (+ 1 (sqrt x))) |
| 1.0ms | x | @ | inf | (/ (+ x (- 1 x)) (+ (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (sqrt x))) |
| 0.0ms | x | @ | 0 | (/ 1 (+ 1 (sqrt x))) |
| 0.0ms | x | @ | inf | (/ 1 (+ 1 (sqrt x))) |
| 1× | batch-egg-rewrite |
| 3162× | *-lowering-*.f32 |
| 3162× | *-lowering-*.f64 |
| 2554× | /-lowering-/.f32 |
| 2554× | /-lowering-/.f64 |
| 1974× | fma-lowering-fma.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 27 | 108 |
| 1 | 217 | 102 |
| 2 | 2058 | 102 |
| 0 | 8712 | 102 |
| 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) |
(* -1/8 (* x x)) |
(* x x) |
(/ 1 (+ 1 (sqrt x))) |
(+ 1 (sqrt x)) |
(sqrt x) |
(- (+ (* x 1/2) 1) (sqrt x)) |
(+ (* x 1/2) 1) |
(* x 1/2) |
(/ (+ x (- 1 x)) (+ (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (sqrt x))) |
(+ x (- 1 x)) |
(- 1 x) |
(+ (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (sqrt x)) |
(* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))) |
| 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 #s(literal 1 binary64) x) (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))) #s(literal -1 binary64))) |
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(exp.f64 (neg.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64)))) |
(-.f64 (/.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)))) |
(fma.f64 #s(literal 1 binary64) (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 (sqrt.f64 x) #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (sqrt.f64 x)) |
(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)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 x (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1 binary64)) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) 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 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 x (-.f64 #s(literal 1 binary64) x))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (neg.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (neg.f64 (*.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))) |
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(*.f64 (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 (+.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))))))) (*.f64 (+.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))))))) (+.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)))))))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.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))))))) (+.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)))))))) (-.f64 x (*.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))))))) |
(*.f64 (-.f64 (*.f64 (+.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))))))) (+.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)))))))) x) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))) |
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) |
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) |
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) #s(literal 1 binary64))) |
(+.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) |
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) |
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) #s(literal 1 binary64))) |
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) |
(fma.f64 x #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) |
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 #s(literal 1/2 binary64) x (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) |
(fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) |
(fma.f64 #s(literal 1/2 binary64) x (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) |
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) |
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) #s(literal 1 binary64))) |
(fma.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) (*.f64 x x) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) x (*.f64 x #s(literal 1/2 binary64))) |
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) (*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (-.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) |
(/.f64 (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) (*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) (-.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) #s(literal 1/2 binary64))))) |
(/.f64 (*.f64 x (-.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (-.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) |
(/.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) (*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) x) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) (-.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) #s(literal 1/2 binary64))))) |
(/.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) x) (-.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) |
(/.f64 (neg.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) (*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))))) (neg.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (neg.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) |
(/.f64 (neg.f64 (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) (*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) (-.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) #s(literal 1/2 binary64)))))) |
(/.f64 (neg.f64 (*.f64 x (-.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) (*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) x)) (neg.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) (-.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) #s(literal 1/2 binary64)))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) x)) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) |
(*.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))))))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) x) |
(*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64)) |
(*.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) x) |
| 1× | egg-herbie |
| 4120× | *-lowering-*.f32 |
| 4120× | *-lowering-*.f64 |
| 2068× | +-lowering-+.f64 |
| 2068× | +-lowering-+.f32 |
| 1488× | times-frac |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 350 | 1906 |
| 1 | 1151 | 1653 |
| 2 | 4057 | 1628 |
| 0 | 8329 | 1628 |
| 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))) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (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) |
(pow x 2) |
(/ 1 (+ 1 (sqrt x))) |
(/ 1 (+ 1 (sqrt x))) |
(/ 1 (+ 1 (sqrt x))) |
(/ 1 (+ 1 (sqrt x))) |
(sqrt (/ 1 x)) |
(/ (- (sqrt x) 1) x) |
(/ (- (+ (sqrt x) (sqrt (/ 1 x))) 1) x) |
(/ (- (sqrt x) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (/ 1 x)))) x) |
(* -1 (sqrt (/ 1 x))) |
(* -1 (/ (- (sqrt x) (/ 1 (pow (sqrt -1) 2))) x)) |
(* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x)) |
(* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (/ (- (/ x (pow (sqrt -1) 4)) (* -1 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x)) |
(+ 1 (sqrt x)) |
(+ 1 (sqrt x)) |
(+ 1 (sqrt x)) |
(+ 1 (sqrt x)) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (/ 1 x))) |
(* x (+ (sqrt (/ 1 x)) (/ 1 x))) |
(* x (+ (sqrt (/ 1 x)) (/ 1 x))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* -1 (* 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 (* 1/2 x)) (sqrt x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(* x (- 1/2 (sqrt (/ 1 x)))) |
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x)))) |
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x)))) |
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x)))) |
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* 1/2 x)) |
(+ 1 (* 1/2 x)) |
(* 1/2 x) |
(* x (+ 1/2 (/ 1 x))) |
(* x (+ 1/2 (/ 1 x))) |
(* x (+ 1/2 (/ 1 x))) |
(* 1/2 x) |
(* x (+ 1/2 (/ 1 x))) |
(* x (+ 1/2 (/ 1 x))) |
(* x (+ 1/2 (/ 1 x))) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 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)))) |
(/ 16 (pow x 3)) |
(/ (+ 16 (* 32 (/ 1 x))) (pow x 3)) |
(/ (- (+ 16 (+ (* 32 (/ 1 x)) (/ 64 (pow x 2)))) (* 256 (/ (+ 1/2 (sqrt (/ 1 x))) (pow x 2)))) (pow x 3)) |
(/ (- (+ 16 (+ (* -1 (/ (+ 256 (+ (* -2 (- 64 (* 256 (+ 1/2 (sqrt (/ 1 x)))))) (* 512 (+ 1/2 (sqrt (/ 1 x)))))) (pow x 3))) (+ (* 32 (/ 1 x)) (/ 64 (pow x 2))))) (* 256 (/ (+ 1/2 (sqrt (/ 1 x))) (pow x 2)))) (pow x 3)) |
(/ 16 (pow x 3)) |
(/ (+ 16 (* 32 (/ 1 x))) (pow x 3)) |
(* -1 (/ (- (* -1 (/ (+ 32 (+ (* 256 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) (* 64 (/ 1 x)))) x)) 16) (pow x 3))) |
(* -1 (/ (- (* -1 (/ (+ 32 (* -1 (/ (- (+ (* -512 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) (+ (* -2 (/ (+ 64 (* 256 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2))) x)) (* 256 (/ 1 x)))) (+ 64 (* 256 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))) x))) x)) 16) (pow x 3))) |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
(+ 1 (* -1 x)) |
(+ 1 (* -1 x)) |
(+ 1 (* -1 x)) |
(* -1 x) |
(* x (- (/ 1 x) 1)) |
(* x (- (/ 1 x) 1)) |
(* x (- (/ 1 x) 1)) |
(* -1 x) |
(* -1 (* x (- 1 (/ 1 x)))) |
(* -1 (* x (- 1 (/ 1 x)))) |
(* -1 (* x (- 1 (/ 1 x)))) |
(+ 1 (sqrt x)) |
(+ 1 (+ (sqrt x) (* 1/2 x))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))) |
(* 1/16 (pow x 3)) |
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x)))) |
(* (pow x 3) (- (+ 1/16 (+ (sqrt (/ 1 (pow x 5))) (/ 1/2 (pow x 2)))) (* 1/8 (/ 1 x)))) |
(* (pow x 3) (- (+ 1/16 (+ (sqrt (/ 1 (pow x 5))) (+ (/ 1/2 (pow x 2)) (/ 1 (pow x 3))))) (* 1/8 (/ 1 x)))) |
(* 1/16 (pow x 3)) |
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) 1/8) x)) 1/16))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x))) x)) 1/8) x)) 1/16))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* 1/16 (pow x 3)) |
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x)))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(* 1/16 (pow x 3)) |
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) |
| 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 #s(literal -1/2 binary64) (/.f64 x (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 (/.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)))) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)))))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (+.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 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x) |
(/.f64 (+.f64 (-.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))))) (+.f64 (*.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) |
(* -1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x)) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 (*.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) #s(literal -5/128 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))))) (-.f64 #s(literal 0 binary64) x)) |
(+ 1 (sqrt x)) |
(+.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(+ 1 (+ (sqrt x) (* 1/2 x))) |
(+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 x #s(literal 1/2 binary64)))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))) |
(+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))) |
(+.f64 (+.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))))))) |
(* 2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 2 binary64)) |
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))) |
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))) |
(*.f64 x (+.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))) |
(*.f64 x (+.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 x) #s(literal 2 binary64)) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 x (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
(*.f64 (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (/.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (-.f64 #s(literal 0 binary64) x)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #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 (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 (*.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 (-.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))) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (-.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (-.f64 #s(literal 0 binary64) x)) |
1 |
#s(literal 1 binary64) |
(+ 1 x) |
(+.f64 #s(literal 1 binary64) x) |
(+ 1 x) |
(+.f64 #s(literal 1 binary64) x) |
(+ 1 x) |
(+.f64 #s(literal 1 binary64) x) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* -1/8 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/8 binary64))) |
(* -1/8 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/8 binary64))) |
(* -1/8 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/8 binary64))) |
(* -1/8 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/8 binary64))) |
(* -1/8 (pow x 2)) |
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(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))) |
(* 1/16 (pow x 3)) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/16 binary64))) |
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) |
(*.f64 (-.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)) (*.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) |
(*.f64 (-.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)) (*.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x)))) |
Compiled 30735 to 2771 computations (91% saved)
26 alts after pruning (20 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 920 | 13 | 933 |
| Fresh | 2 | 7 | 9 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 3 | 3 |
| Total | 924 | 26 | 950 |
| Status | Accuracy | Program |
|---|---|---|
| 56.8% | (/.f64 (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 x x) (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (+.f64 (+.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.f64 x))) | |
| 43.9% | (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) | |
| 57.0% | (/.f64 (+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (+.f64 (+.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.f64 x))) | |
| 2.3% | (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))) | |
| 4.1% | (/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (*.f64 x (*.f64 x x))) | |
| 57.9% | (/.f64 (*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (*.f64 (+.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))) (+.f64 (+.f64 x #s(literal -1 binary64)) x))) | |
| ▶ | 47.0% | (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
| 4.2% | (/.f64 #s(literal 16 binary64) (*.f64 x (*.f64 x x))) | |
| 58.1% | (/.f64 #s(literal 1 binary64) (+.f64 (+.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.f64 x))) | |
| 57.5% | (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x))) | |
| ▶ | 99.7% | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
| 58.9% | (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 x #s(literal 1/2 binary64))))) | |
| ✓ | 62.9% | (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
| 47.1% | (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) | |
| 12.2% | (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) | |
| ✓ | 57.8% | (-.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 x)) |
| ▶ | 57.6% | (-.f64 (+.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.f64 x)) |
| ✓ | 58.8% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 57.8% | (-.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x))) | |
| ✓ | 55.4% | (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| ✓ | 56.6% | (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x))) |
| ▶ | 53.4% | (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) |
| 43.9% | (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) | |
| 47.1% | (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) | |
| ✓ | 2.0% | (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) |
| ▶ | 12.2% | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
Compiled 654 to 434 computations (33.6% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) |
| ✓ | cost-diff | 0 | (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) |
| ✓ | cost-diff | 0 | (+.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))))))) |
| ✓ | cost-diff | 0 | (-.f64 (+.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.f64 x)) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) x) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 0 | (*.f64 x x) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.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 (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))) |
| 1538× | fma-define |
| 1534× | fma-lowering-fma.f32 |
| 1534× | fma-lowering-fma.f64 |
| 1140× | +-lowering-+.f64 |
| 1140× | +-lowering-+.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 133 |
| 1 | 59 | 120 |
| 2 | 150 | 120 |
| 3 | 308 | 120 |
| 4 | 840 | 120 |
| 5 | 2481 | 120 |
| 6 | 3493 | 120 |
| 7 | 6207 | 120 |
| 8 | 7126 | 120 |
| 9 | 7608 | 120 |
| 0 | 8002 | 120 |
| 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 (* -1/8 (* x x))) |
1 |
(* -1/8 (* x x)) |
-1/8 |
(* x x) |
x |
(sqrt (/ 1 x)) |
(/ 1 x) |
1 |
x |
(/ (* (sqrt x) 1/2) x) |
(* (sqrt x) 1/2) |
(sqrt x) |
x |
1/2 |
(- (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (sqrt x)) |
(+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) |
1 |
(* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))) |
x |
(+ 1/2 (* x (+ -1/8 (* x 1/16)))) |
1/2 |
(* x (+ -1/8 (* x 1/16))) |
(+ -1/8 (* x 1/16)) |
-1/8 |
(* x 1/16) |
1/16 |
(sqrt x) |
| 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 (* -1/8 (* x x))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/8 binary64)))) |
1 |
#s(literal 1 binary64) |
(* -1/8 (* x x)) |
(*.f64 x (*.f64 x #s(literal -1/8 binary64))) |
-1/8 |
#s(literal -1/8 binary64) |
(* x x) |
(*.f64 x x) |
x |
(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) x) |
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
(* (sqrt x) 1/2) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
x |
1/2 |
#s(literal 1/2 binary64) |
(- (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (sqrt x)) |
(+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))))) (sqrt.f64 x))) |
(+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) |
(+.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))))))) |
1 |
#s(literal 1 binary64) |
(* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))))) |
x |
(+ 1/2 (* x (+ -1/8 (* x 1/16)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64))))) |
1/2 |
#s(literal 1/2 binary64) |
(* x (+ -1/8 (* x 1/16))) |
(*.f64 x (-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))) |
(+ -1/8 (* x 1/16)) |
(-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64))) |
-1/8 |
#s(literal -1/8 binary64) |
(* x 1/16) |
(*.f64 x #s(literal 1/16 binary64)) |
1/16 |
#s(literal 1/16 binary64) |
(sqrt x) |
(sqrt.f64 x) |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 100.0% | (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) |
| ✓ | accuracy | 99.9% | (-.f64 (+.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.f64 x)) |
| ✓ | accuracy | 99.9% | (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) |
| ✓ | accuracy | 100.0% | (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 99.5% | (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 1 binary64) x) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
| ✓ | accuracy | 100.0% | (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) |
| ✓ | accuracy | 100.0% | (*.f64 x x) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
| ✓ | accuracy | 100.0% | (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
| ✓ | accuracy | 99.8% | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
| 217.0ms | 256× | 0 | valid |
Compiled 141 to 25 computations (82.3% saved)
ival-mult: 10.0ms (33% of total)ival-add: 8.0ms (26.4% of total)ival-sqrt: 6.0ms (19.8% of total)ival-div: 5.0ms (16.5% of total)ival-sub: 1.0ms (3.3% of total)const: 1.0ms (3.3% of total)backward-pass: 0.0ms (0% of total)| Inputs |
|---|
#<alt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))> |
#<alt (+ (sqrt (+ 1 x)) (sqrt x))> |
#<alt (sqrt (+ 1 x))> |
#<alt (+ 1 x)> |
#<alt (+ 1 (* -1/8 (* x x)))> |
#<alt (* -1/8 (* x x))> |
#<alt (* x x)> |
#<alt (sqrt (/ 1 x))> |
#<alt (/ 1 x)> |
#<alt (/ (* (sqrt x) 1/2) x)> |
#<alt (* (sqrt x) 1/2)> |
#<alt (sqrt x)> |
#<alt (- (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (sqrt x))> |
#<alt (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))))> |
#<alt (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))> |
#<alt (+ 1/2 (* x (+ -1/8 (* x 1/16))))> |
#<alt (* x (+ -1/8 (* x 1/16)))> |
| 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> |
#<alt (+ 1 (* -1/8 (pow x 2)))> |
#<alt (+ 1 (* -1/8 (pow x 2)))> |
#<alt (+ 1 (* -1/8 (pow x 2)))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/8))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/8))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/8))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/8))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/8))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/8))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* -1/8 (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 (pow x 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)) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* 1/2 (sqrt x))> |
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (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 (* 1/16 (pow x 3))> |
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (+ (sqrt (/ 1 (pow x 5))) (* 1/8 (/ 1 x)))))> |
#<alt (* (pow x 3) (- (+ 1/16 (+ (/ 1/2 (pow x 2)) (/ 1 (pow x 3)))) (+ (sqrt (/ 1 (pow x 5))) (* 1/8 (/ 1 x)))))> |
#<alt (* 1/16 (pow x 3))> |
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8) x)) 1/16)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8) x)) 1/16)))> |
#<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 (* 1/16 (pow x 3))> |
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ 1/16 (+ (/ 1/2 (pow x 2)) (/ 1 (pow x 3)))) (* 1/8 (/ 1 x))))> |
#<alt (* 1/16 (pow x 3))> |
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8) x)) 1/16)))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* 1/16 (pow x 3))> |
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))> |
#<alt (* 1/16 (pow x 3))> |
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))> |
#<alt 1/2> |
#<alt (+ 1/2 (* -1/8 x))> |
#<alt (+ 1/2 (* x (- (* 1/16 x) 1/8)))> |
#<alt (+ 1/2 (* x (- (* 1/16 x) 1/8)))> |
#<alt (* 1/16 (pow x 2))> |
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))> |
#<alt (* 1/16 (pow x 2))> |
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))))> |
#<alt (* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))))> |
#<alt (* -1/8 x)> |
#<alt (* x (- (* 1/16 x) 1/8))> |
#<alt (* x (- (* 1/16 x) 1/8))> |
#<alt (* x (- (* 1/16 x) 1/8))> |
#<alt (* 1/16 (pow x 2))> |
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* 1/16 (pow x 2))> |
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))> |
51 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | x | @ | -inf | (/ (* (sqrt x) 1/2) x) |
| 0.0ms | x | @ | inf | (* x (+ -1/8 (* x 1/16))) |
| 0.0ms | x | @ | -inf | (/ 1 x) |
| 0.0ms | x | @ | -inf | (* x (+ -1/8 (* x 1/16))) |
| 0.0ms | x | @ | 0 | (* x (+ -1/8 (* x 1/16))) |
| 1× | batch-egg-rewrite |
| 3138× | *-lowering-*.f32 |
| 3138× | *-lowering-*.f64 |
| 2644× | /-lowering-/.f32 |
| 2644× | /-lowering-/.f64 |
| 2298× | +-lowering-+.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 107 |
| 1 | 167 | 94 |
| 2 | 1490 | 92 |
| 0 | 8145 | 92 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ 1 (+ (sqrt (+ 1 x)) (sqrt x))) |
(+ (sqrt (+ 1 x)) (sqrt x)) |
(sqrt (+ 1 x)) |
(+ 1 x) |
(+ 1 (* -1/8 (* x x))) |
(* -1/8 (* x x)) |
(* x x) |
(sqrt (/ 1 x)) |
(/ 1 x) |
(/ (* (sqrt x) 1/2) x) |
(* (sqrt x) 1/2) |
(sqrt x) |
(- (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (sqrt x)) |
(+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) |
(* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))) |
(+ 1/2 (* x (+ -1/8 (* x 1/16)))) |
(* x (+ -1/8 (* x 1/16))) |
| 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)))) |
(/.f64 #s(literal -1 binary64) (neg.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)))))) |
(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 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))) |
(*.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) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x)))) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) x) 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 (+.f64 #s(literal 1 binary64) x) 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 #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 #s(literal 0 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 (+.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)))) |
(-.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))) #s(literal 1 binary64)) (/.f64 (/.f64 x (-.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 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))) (/.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 (/.f64 x (-.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) |
(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) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) (-.f64 (+.f64 #s(literal 1 binary64) x) x))) |
(/.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) (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) (neg.f64 (/.f64 (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) (-.f64 (+.f64 #s(literal 1 binary64) x) 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) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x)))) |
(/.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 x (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x))))) |
(/.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal 1 binary64) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x))))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) 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) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) 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 x (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) 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 #s(literal 1 binary64) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x)))))) |
(/.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (neg.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))) |
(/.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (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 (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)) |
(/.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)))) |
(/.f64 (neg.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 (neg.f64 (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x)))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x))) (neg.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))))) |
(/.f64 (neg.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x))) (neg.f64 (-.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) |
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(pow.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) #s(literal -1 binary64)) |
(*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) (*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) (-.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) #s(literal 1/2 binary64)))))) |
(*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) |
(+.f64 (*.f64 x #s(literal -1/8 binary64)) (*.f64 x (*.f64 x #s(literal 1/16 binary64)))) |
(+.f64 (*.f64 x (*.f64 x #s(literal 1/16 binary64))) (*.f64 x #s(literal -1/8 binary64))) |
(-.f64 (/.f64 (*.f64 (*.f64 x #s(literal -1/8 binary64)) (*.f64 x #s(literal -1/8 binary64))) (-.f64 (*.f64 x #s(literal -1/8 binary64)) (*.f64 x (*.f64 x #s(literal 1/16 binary64))))) (/.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/16 binary64))) (*.f64 x (*.f64 x #s(literal 1/16 binary64)))) (-.f64 (*.f64 x #s(literal -1/8 binary64)) (*.f64 x (*.f64 x #s(literal 1/16 binary64)))))) |
(fma.f64 x #s(literal -1/8 binary64) (*.f64 x (*.f64 x #s(literal 1/16 binary64)))) |
(fma.f64 x (*.f64 x #s(literal 1/16 binary64)) (*.f64 x #s(literal -1/8 binary64))) |
(fma.f64 #s(literal -1/8 binary64) x (*.f64 x (*.f64 x #s(literal 1/16 binary64)))) |
(fma.f64 (*.f64 x x) #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) |
(fma.f64 #s(literal 1/16 binary64) (*.f64 x x) (*.f64 x #s(literal -1/8 binary64))) |
(fma.f64 (*.f64 x #s(literal 1/16 binary64)) x (*.f64 x #s(literal -1/8 binary64))) |
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4096 binary64)))) (+.f64 (*.f64 (*.f64 x #s(literal -1/8 binary64)) (*.f64 x #s(literal -1/8 binary64))) (-.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/16 binary64))) (*.f64 x (*.f64 x #s(literal 1/16 binary64)))) (*.f64 (*.f64 x #s(literal -1/8 binary64)) (*.f64 x (*.f64 x #s(literal 1/16 binary64))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x #s(literal -1/8 binary64)) (*.f64 x #s(literal -1/8 binary64))) (*.f64 (*.f64 x (*.f64 x #s(literal 1/16 binary64))) (*.f64 x (*.f64 x #s(literal 1/16 binary64))))) (-.f64 (*.f64 x #s(literal -1/8 binary64)) (*.f64 x (*.f64 x #s(literal 1/16 binary64))))) |
(/.f64 (*.f64 x (+.f64 #s(literal -1/512 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4096 binary64)))) (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x #s(literal 1/16 binary64)) (-.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) |
(/.f64 (*.f64 x (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) #s(literal 1/256 binary64)))) (-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) |
(/.f64 (*.f64 (+.f64 #s(literal -1/512 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4096 binary64))) x) (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x #s(literal 1/16 binary64)) (-.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) |
(/.f64 (*.f64 (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) #s(literal 1/256 binary64))) x) (-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) |
(/.f64 (neg.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4096 binary64))))) (neg.f64 (+.f64 (*.f64 (*.f64 x #s(literal -1/8 binary64)) (*.f64 x #s(literal -1/8 binary64))) (-.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/16 binary64))) (*.f64 x (*.f64 x #s(literal 1/16 binary64)))) (*.f64 (*.f64 x #s(literal -1/8 binary64)) (*.f64 x (*.f64 x #s(literal 1/16 binary64)))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x #s(literal -1/8 binary64)) (*.f64 x #s(literal -1/8 binary64))) (*.f64 (*.f64 x (*.f64 x #s(literal 1/16 binary64))) (*.f64 x (*.f64 x #s(literal 1/16 binary64)))))) (neg.f64 (-.f64 (*.f64 x #s(literal -1/8 binary64)) (*.f64 x (*.f64 x #s(literal 1/16 binary64)))))) |
(/.f64 (neg.f64 (*.f64 x (+.f64 #s(literal -1/512 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4096 binary64))))) (neg.f64 (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x #s(literal 1/16 binary64)) (-.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))))) |
(/.f64 (neg.f64 (*.f64 x (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) #s(literal 1/256 binary64))))) (neg.f64 (-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal -1/512 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4096 binary64))) x)) (neg.f64 (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x #s(literal 1/16 binary64)) (-.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) #s(literal 1/256 binary64))) x)) (neg.f64 (-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) |
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4096 binary64))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64))) (+.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/16 binary64))) (*.f64 x (*.f64 x #s(literal 1/16 binary64)))) (-.f64 (*.f64 (*.f64 x #s(literal -1/8 binary64)) (*.f64 x #s(literal -1/8 binary64))) (*.f64 (*.f64 x (*.f64 x #s(literal 1/16 binary64))) (*.f64 x #s(literal -1/8 binary64)))))) |
(*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) |
(*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))) x) |
| 1× | egg-herbie |
| 3578× | +-lowering-+.f64 |
| 3578× | +-lowering-+.f32 |
| 3264× | *-lowering-*.f32 |
| 3264× | *-lowering-*.f64 |
| 1152× | distribute-lft-in |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 255 | 1717 |
| 1 | 819 | 1501 |
| 2 | 2933 | 1481 |
| 0 | 8284 | 1481 |
| 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 |
(+ 1 (* -1/8 (pow x 2))) |
(+ 1 (* -1/8 (pow x 2))) |
(+ 1 (* -1/8 (pow x 2))) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/8)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/8)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/8)) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/8)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/8)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/8)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (pow x 2)) |
(* -1/8 (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) |
(pow x 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)) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (sqrt x)) |
(* 1/2 (sqrt x)) |
(* 1/2 (sqrt x)) |
(* 1/2 (sqrt x)) |
(* 1/2 (sqrt x)) |
(* 1/2 (sqrt x)) |
(* 1/2 (sqrt x)) |
(* 1/2 (sqrt x)) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(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)) |
(* 1/16 (pow x 3)) |
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x)))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (+ (sqrt (/ 1 (pow x 5))) (* 1/8 (/ 1 x))))) |
(* (pow x 3) (- (+ 1/16 (+ (/ 1/2 (pow x 2)) (/ 1 (pow x 3)))) (+ (sqrt (/ 1 (pow x 5))) (* 1/8 (/ 1 x))))) |
(* 1/16 (pow x 3)) |
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8) x)) 1/16))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8) x)) 1/16))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(* 1/16 (pow x 3)) |
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x)))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(* (pow x 3) (- (+ 1/16 (+ (/ 1/2 (pow x 2)) (/ 1 (pow x 3)))) (* 1/8 (/ 1 x)))) |
(* 1/16 (pow x 3)) |
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8) x)) 1/16))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* 1/16 (pow x 3)) |
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x)))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(* 1/16 (pow x 3)) |
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) |
1/2 |
(+ 1/2 (* -1/8 x)) |
(+ 1/2 (* x (- (* 1/16 x) 1/8))) |
(+ 1/2 (* x (- (* 1/16 x) 1/8))) |
(* 1/16 (pow x 2)) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(* 1/16 (pow x 2)) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x)))) |
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x)))) |
(* -1/8 x) |
(* x (- (* 1/16 x) 1/8)) |
(* x (- (* 1/16 x) 1/8)) |
(* x (- (* 1/16 x) 1/8)) |
(* 1/16 (pow x 2)) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(* 1/16 (pow x 2)) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 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 x (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (*.f64 x (+.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)))))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
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(* 1/2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* 1/2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* 1/2 (sqrt x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(- 1 (sqrt x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
(+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(* 1/16 (pow x 3)) |
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/16 binary64)))) |
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x)))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (+ (sqrt (/ 1 (pow x 5))) (* 1/8 (/ 1 x))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (-.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) |
(* (pow x 3) (- (+ 1/16 (+ (/ 1/2 (pow x 2)) (/ 1 (pow x 3)))) (+ (sqrt (/ 1 (pow x 5))) (* 1/8 (/ 1 x))))) |
(*.f64 x (*.f64 (*.f64 x x) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)) (-.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))) |
(* 1/16 (pow x 3)) |
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/16 binary64)))) |
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8) x)) 1/16))) |
(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x (*.f64 x x)) (-.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x))) x)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8) x)) 1/16))) |
(*.f64 (-.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)))) x)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x 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))))))) |
(* 1/16 (pow x 3)) |
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/16 binary64)))) |
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x)))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))) |
(* (pow x 3) (- (+ 1/16 (+ (/ 1/2 (pow x 2)) (/ 1 (pow x 3)))) (* 1/8 (/ 1 x)))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))) |
(* 1/16 (pow x 3)) |
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/16 binary64)))) |
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) |
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8) x)) 1/16))) |
(*.f64 (-.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x))) x)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) |
(* 1/16 (pow x 3)) |
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/16 binary64)))) |
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x)))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))) |
(* 1/16 (pow x 3)) |
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/16 binary64)))) |
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) |
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) |
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* -1/8 x)) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))) |
(+ 1/2 (* x (- (* 1/16 x) 1/8))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) |
(+ 1/2 (* x (- (* 1/16 x) 1/8))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) |
(* 1/16 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/16 binary64))) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) |
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))) |
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))) |
(* 1/16 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/16 binary64))) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) |
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x)))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))) |
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x)))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))) |
(* -1/8 x) |
(*.f64 x #s(literal -1/8 binary64)) |
(* x (- (* 1/16 x) 1/8)) |
(*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) |
(* x (- (* 1/16 x) 1/8)) |
(*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) |
(* x (- (* 1/16 x) 1/8)) |
(*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) |
(* 1/16 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/16 binary64))) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) |
(* 1/16 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/16 binary64))) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) |
Compiled 16498 to 1911 computations (88.4% saved)
26 alts after pruning (18 fresh and 8 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 728 | 9 | 737 |
| Fresh | 6 | 9 | 15 |
| Picked | 2 | 3 | 5 |
| Done | 1 | 5 | 6 |
| Total | 737 | 26 | 763 |
| Status | Accuracy | Program |
|---|---|---|
| 12.2% | (pow.f64 x #s(literal -1/2 binary64)) | |
| 56.8% | (/.f64 (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 x x) (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (+.f64 (+.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.f64 x))) | |
| 43.9% | (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) | |
| 47.0% | (/.f64 (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) x) | |
| 57.9% | (/.f64 (*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (*.f64 (+.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))) (+.f64 (+.f64 x #s(literal -1 binary64)) x))) | |
| 12.2% | (/.f64 (sqrt.f64 x) x) | |
| 53.2% | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) | |
| 47.1% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) | |
| 58.1% | (/.f64 #s(literal 1 binary64) (+.f64 (+.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.f64 x))) | |
| 57.5% | (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x))) | |
| ✓ | 99.7% | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
| 58.9% | (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 x #s(literal 1/2 binary64))))) | |
| ✓ | 62.9% | (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
| 12.2% | (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) | |
| ✓ | 57.8% | (-.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 x)) |
| ✓ | 57.6% | (-.f64 (+.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.f64 x)) |
| ✓ | 58.8% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 57.8% | (-.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x))) | |
| ✓ | 55.4% | (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
| 57.6% | (+.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (sqrt.f64 x)) #s(literal 1 binary64)) | |
| ✓ | 56.6% | (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x))) |
| ✓ | 53.4% | (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) |
| 47.2% | (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) | |
| 43.9% | (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) | |
| 47.0% | (*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) | |
| 55.9% | #s(literal 1 binary64) |
Compiled 901 to 366 computations (59.4% saved)
| Inputs |
|---|
#s(literal 1 binary64) |
(*.f64 #s(literal -1/8 binary64) (*.f64 x x)) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) |
(/.f64 #s(literal 16 binary64) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(pow.f64 x #s(literal -1/2 binary64)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 (sqrt.f64 x) x) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64))) |
(-.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x))) |
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x)) |
(-.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 x)) |
(/.f64 (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) x) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 x #s(literal 1/2 binary64))))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x))) |
(+.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (sqrt.f64 x)) #s(literal 1 binary64)) |
(-.f64 (+.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.f64 x)) |
(/.f64 #s(literal 1 binary64) (+.f64 (+.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.f64 x))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.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.f64 x))) |
(/.f64 (+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (+.f64 (+.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.f64 x))) |
(/.f64 (*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (*.f64 (+.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))) (+.f64 (+.f64 x #s(literal -1 binary64)) x))) |
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 x x) (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (+.f64 (+.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.f64 x))) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (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) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) |
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))) |
(/.f64 (+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 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)))))) |
(/.f64 (-.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 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) x)) (*.f64 (+.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)))) |
| Outputs |
|---|
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
2 calls:
| 12.0ms | x |
| 12.0ms | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | x |
| 99.7% | 1 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
Compiled 10 to 7 computations (30% saved)
| Inputs |
|---|
#s(literal 1 binary64) |
(*.f64 #s(literal -1/8 binary64) (*.f64 x x)) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) |
(/.f64 #s(literal 16 binary64) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(pow.f64 x #s(literal -1/2 binary64)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 (sqrt.f64 x) x) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64))) |
(-.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x))) |
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x)) |
(-.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 x)) |
(/.f64 (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) x) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 x #s(literal 1/2 binary64))))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x))) |
(+.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (sqrt.f64 x)) #s(literal 1 binary64)) |
(-.f64 (+.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.f64 x)) |
(/.f64 #s(literal 1 binary64) (+.f64 (+.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.f64 x))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.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.f64 x))) |
(/.f64 (+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (+.f64 (+.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.f64 x))) |
(/.f64 (*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (*.f64 (+.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))) (+.f64 (+.f64 x #s(literal -1 binary64)) x))) |
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 x x) (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (+.f64 (+.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.f64 x))) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Outputs |
|---|
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
2 calls:
| 10.0ms | x |
| 8.0ms | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 2 | x |
| 99.6% | 2 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
Compiled 10 to 7 computations (30% saved)
| Inputs |
|---|
#s(literal 1 binary64) |
(*.f64 #s(literal -1/8 binary64) (*.f64 x x)) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) |
(/.f64 #s(literal 16 binary64) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(pow.f64 x #s(literal -1/2 binary64)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 (sqrt.f64 x) x) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64))) |
(-.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x))) |
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x)) |
(-.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 x)) |
(/.f64 (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) x) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 x #s(literal 1/2 binary64))))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x))) |
(+.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (sqrt.f64 x)) #s(literal 1 binary64)) |
(-.f64 (+.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.f64 x)) |
(/.f64 #s(literal 1 binary64) (+.f64 (+.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.f64 x))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.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.f64 x))) |
(/.f64 (+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (+.f64 (+.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.f64 x))) |
(/.f64 (*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (*.f64 (+.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))) (+.f64 (+.f64 x #s(literal -1 binary64)) x))) |
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 x x) (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (+.f64 (+.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.f64 x))) |
| Outputs |
|---|
(+.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (sqrt.f64 x)) #s(literal 1 binary64)) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
1 calls:
| 11.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.4% | 2 | x |
Compiled 2 to 1 computations (50% saved)
| Inputs |
|---|
#s(literal 1 binary64) |
(*.f64 #s(literal -1/8 binary64) (*.f64 x x)) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) |
(/.f64 #s(literal 16 binary64) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(pow.f64 x #s(literal -1/2 binary64)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 (sqrt.f64 x) x) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64))) |
(-.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x))) |
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x)) |
(-.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 x)) |
(/.f64 (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) x) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 x #s(literal 1/2 binary64))))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x))) |
| Outputs |
|---|
(+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x))) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
1 calls:
| 8.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.3% | 2 | x |
Compiled 2 to 1 computations (50% saved)
| Inputs |
|---|
#s(literal 1 binary64) |
(*.f64 #s(literal -1/8 binary64) (*.f64 x x)) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) |
(/.f64 #s(literal 16 binary64) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(pow.f64 x #s(literal -1/2 binary64)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 (sqrt.f64 x) x) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64))) |
(-.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x))) |
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x)) |
(-.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 x)) |
(/.f64 (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) x) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 x #s(literal 1/2 binary64))))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
| Outputs |
|---|
(-.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x))) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
1 calls:
| 34.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.1% | 2 | x |
Compiled 2 to 1 computations (50% saved)
| Inputs |
|---|
#s(literal 1 binary64) |
(*.f64 #s(literal -1/8 binary64) (*.f64 x x)) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) |
(/.f64 #s(literal 16 binary64) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(pow.f64 x #s(literal -1/2 binary64)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 (sqrt.f64 x) x) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64))) |
| Outputs |
|---|
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
1 calls:
| 6.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.1% | 2 | x |
Compiled 2 to 1 computations (50% saved)
| Inputs |
|---|
#s(literal 1 binary64) |
(*.f64 #s(literal -1/8 binary64) (*.f64 x x)) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) |
(/.f64 #s(literal 16 binary64) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(pow.f64 x #s(literal -1/2 binary64)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 (sqrt.f64 x) x) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x) |
| Outputs |
|---|
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) |
1 calls:
| 6.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.9% | 2 | x |
Compiled 2 to 1 computations (50% saved)
| Inputs |
|---|
#s(literal 1 binary64) |
(*.f64 #s(literal -1/8 binary64) (*.f64 x x)) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) |
(/.f64 #s(literal 16 binary64) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(pow.f64 x #s(literal -1/2 binary64)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(/.f64 (sqrt.f64 x) x) |
| Outputs |
|---|
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(pow.f64 x #s(literal -1/2 binary64)) |
1 calls:
| 4.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 62.9% | 2 | x |
Compiled 2 to 1 computations (50% saved)
| Inputs |
|---|
#s(literal 1 binary64) |
(*.f64 #s(literal -1/8 binary64) (*.f64 x x)) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) |
(/.f64 #s(literal 16 binary64) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(pow.f64 x #s(literal -1/2 binary64)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
| Outputs |
|---|
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) |
(pow.f64 x #s(literal -1/2 binary64)) |
1 calls:
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 61.1% | 2 | x |
Compiled 2 to 1 computations (50% saved)
Total -35.3b remaining (-125.3%)
Threshold costs -35.3b (-125.3%)
| Inputs |
|---|
#s(literal 1 binary64) |
(*.f64 #s(literal -1/8 binary64) (*.f64 x x)) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) |
(/.f64 #s(literal 16 binary64) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (*.f64 x (*.f64 x x))) |
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
| Outputs |
|---|
#s(literal 1 binary64) |
1 calls:
| 5.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 55.9% | 1 | x |
Compiled 2 to 1 computations (50% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 4.964833533449564e-5 | 0.006983208953499798 |
Compiled 12 to 9 computations (25% saved)
| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 12.0ms | 0.0005740468287233434 | 5126.105924518911 |
| 7.0ms | 144× | 0 | valid |
Compiled 237 to 189 computations (20.3% saved)
ival-sqrt: 2.0ms (54.9% of total)ival-sub: 1.0ms (27.5% of total)ival-add: 1.0ms (27.5% of total)const: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 13.0ms | 0.0005740468287233434 | 5126.105924518911 |
| 8.0ms | 144× | 0 | valid |
Compiled 201 to 162 computations (19.4% saved)
ival-add: 2.0ms (38.2% of total)ival-sqrt: 2.0ms (38.2% of total)ival-sub: 1.0ms (19.1% of total)const: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 13.0ms | 0.0005740468287233434 | 5126.105924518911 |
| 7.0ms | 144× | 0 | valid |
Compiled 165 to 135 computations (18.2% saved)
ival-sqrt: 2.0ms (54.8% of total)ival-sub: 1.0ms (27.4% of total)ival-add: 1.0ms (27.4% of total)const: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 11.0ms | 0.0005740468287233434 | 5126.105924518911 |
| 7.0ms | 144× | 0 | valid |
Compiled 165 to 135 computations (18.2% saved)
ival-sqrt: 2.0ms (54.8% of total)ival-sub: 1.0ms (27.4% of total)ival-add: 1.0ms (27.4% of total)const: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 29.0ms | 0.0005740468287233434 | 5126.105924518911 |
| 7.0ms | 144× | 0 | valid |
Compiled 129 to 108 computations (16.3% saved)
ival-sqrt: 2.0ms (53.7% of total)ival-sub: 1.0ms (26.8% of total)ival-add: 1.0ms (26.8% of total)const: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 11.0ms | 0.0005740468287233434 | 5126.105924518911 |
| 7.0ms | 144× | 0 | valid |
Compiled 111 to 90 computations (18.9% saved)
ival-sqrt: 2.0ms (55.3% of total)ival-sub: 1.0ms (27.6% of total)ival-add: 1.0ms (27.6% of total)const: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 11.0ms | 0.0005740468287233434 | 5126.105924518911 |
| 7.0ms | 144× | 0 | valid |
Compiled 138 to 108 computations (21.7% saved)
ival-sqrt: 2.0ms (54.6% of total)ival-sub: 1.0ms (27.3% of total)ival-add: 1.0ms (27.3% of total)const: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| 1× | egg-herbie |
| 40× | +-commutative_binary64 |
| 28× | *-commutative_binary64 |
| 20× | sub-neg_binary64 |
| 10× | neg-sub0_binary64 |
| 10× | neg-mul-1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 58 | 150 |
| 1 | 88 | 150 |
| 2 | 101 | 150 |
| 3 | 115 | 150 |
| 4 | 123 | 150 |
| 5 | 128 | 150 |
| 6 | 130 | 150 |
| 1× | saturated |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 7378697629483821/147573952589676412928 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) |
(if (<=.f64 x #s(literal 3039929748475085/2251799813685248 binary64)) (+.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (sqrt.f64 x)) #s(literal 1 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) |
(if (<=.f64 x #s(literal 5/4 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) |
(if (<=.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) |
(if (<=.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) |
(if (<=.f64 x #s(literal 3242591731706757/9007199254740992 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) |
(if (<=.f64 x #s(literal 5854679515581645/9007199254740992 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 x #s(literal -1/2 binary64))) |
(if (<=.f64 x #s(literal 5854679515581645/2251799813685248 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) (pow.f64 x #s(literal -1/2 binary64))) |
#s(literal 1 binary64) |
| Outputs |
|---|
(/.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 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 7378697629483821/147573952589676412928 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) |
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 7378697629483821/147573952589676412928 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(if (<=.f64 x #s(literal 3039929748475085/2251799813685248 binary64)) (+.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (sqrt.f64 x)) #s(literal 1 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) |
(if (<=.f64 x #s(literal 3039929748475085/2251799813685248 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (sqrt.f64 x))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) |
(if (<=.f64 x #s(literal 5/4 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) |
(if (<=.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) |
(if (<=.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 x #s(literal -1/2 binary64)))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) |
(if (<=.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) |
(if (<=.f64 x #s(literal 3242591731706757/9007199254740992 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) |
(if (<=.f64 x #s(literal 5854679515581645/9007199254740992 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 x #s(literal -1/2 binary64))) |
(if (<=.f64 x #s(literal 5854679515581645/2251799813685248 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) (pow.f64 x #s(literal -1/2 binary64))) |
#s(literal 1 binary64) |
| 4120× | *-lowering-*.f32 |
| 4120× | *-lowering-*.f64 |
| 3978× | *-lowering-*.f32 |
| 3978× | *-lowering-*.f64 |
| 3578× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 255 | 1717 |
| 1 | 819 | 1501 |
| 2 | 2933 | 1481 |
| 0 | 8284 | 1481 |
| 0 | 350 | 1906 |
| 1 | 1151 | 1653 |
| 2 | 4057 | 1628 |
| 0 | 8329 | 1628 |
| 0 | 25 | 112 |
| 1 | 198 | 97 |
| 2 | 1913 | 97 |
| 0 | 8634 | 97 |
| 0 | 113 | 434 |
| 1 | 325 | 384 |
| 2 | 1039 | 376 |
| 3 | 3226 | 373 |
| 4 | 7122 | 373 |
| 0 | 8132 | 373 |
| 0 | 27 | 108 |
| 1 | 217 | 102 |
| 2 | 2058 | 102 |
| 0 | 8712 | 102 |
| 0 | 6 | 16 |
| 1 | 39 | 16 |
| 2 | 303 | 16 |
| 3 | 3722 | 16 |
| 0 | 8045 | 16 |
| 0 | 251 | 1886 |
| 1 | 781 | 1630 |
| 2 | 2751 | 1611 |
| 3 | 7835 | 1611 |
| 0 | 8360 | 1611 |
| 0 | 24 | 107 |
| 1 | 167 | 94 |
| 2 | 1490 | 92 |
| 0 | 8145 | 92 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 539 to 350 computations (35.1% saved)
Compiled 338 to 138 computations (59.2% saved)
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