
Time bar (total: 7.8s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 25% | 75% | 0% | 0% | 0% | 0 |
| 0% | 0% | 25% | 75% | 0% | 0% | 0% | 1 |
| 50% | 12.5% | 12.5% | 75% | 0% | 0% | 0% | 2 |
| 75% | 18.7% | 6.2% | 75% | 0% | 0% | 0% | 3 |
| 87.5% | 21.9% | 3.1% | 75% | 0% | 0% | 0% | 4 |
| 93.8% | 23.4% | 1.6% | 75% | 0% | 0% | 0% | 5 |
| 96.9% | 24.2% | 0.8% | 75% | 0% | 0% | 0% | 6 |
| 98.4% | 24.6% | 0.4% | 75% | 0% | 0% | 0% | 7 |
| 99.2% | 24.8% | 0.2% | 75% | 0% | 0% | 0% | 8 |
| 99.6% | 24.9% | 0.1% | 75% | 0% | 0% | 0% | 9 |
| 99.8% | 24.9% | 0% | 75% | 0% | 0% | 0% | 10 |
| 99.9% | 25% | 0% | 75% | 0% | 0% | 0% | 11 |
| 100% | 25% | 0% | 75% | 0% | 0% | 0% | 12 |
Compiled 15 to 11 computations (26.7% saved)
| 1.2s | 8 037× | 1 | valid |
| 15.0ms | 219× | 0 | valid |
ival-sqrt: 273.0ms (28% of total)adjust: 188.0ms (19.3% of total)ival-add: 156.0ms (16% of total)ival-sub: 138.0ms (14.2% of total)const: 123.0ms (12.6% of total)ival->: 58.0ms (5.9% of total)ival-<: 18.0ms (1.8% of total)ival-and: 11.0ms (1.1% of total)exact: 7.0ms (0.7% of total)ival-assert: 3.0ms (0.3% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 254 | 0 | - | 0 | - | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 0 | 0 | - | 0 | - | (+.f64 x #s(literal 1 binary64)) |
| 0 | 0 | - | 0 | - | (sqrt.f64 x) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) | cancellation | 254 | 1 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 254 | 0 |
| - | 0 | 2 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 254 | 0 | 0 |
| - | 0 | 1 | 1 |
| number | freq |
|---|---|
| 0 | 2 |
| 1 | 254 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 234.0ms | 502× | 1 | valid |
| 0.0ms | 10× | 0 | valid |
Compiled 65 to 28 computations (56.9% saved)
ival-sub: 189.0ms (87% of total)ival-sqrt: 14.0ms (6.4% of total)adjust: 8.0ms (3.7% of total)ival-add: 5.0ms (2.3% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 19 |
| 1 | 18 | 17 |
| 2 | 41 | 16 |
| 3 | 73 | 16 |
| 4 | 121 | 16 |
| 5 | 178 | 16 |
| 6 | 201 | 16 |
| 7 | 212 | 16 |
| 0 | 6 | 7 |
| 0 | 10 | 7 |
| 1 | 15 | 7 |
| 2 | 19 | 7 |
| 3 | 25 | 7 |
| 4 | 33 | 7 |
| 5 | 48 | 7 |
| 6 | 80 | 7 |
| 7 | 106 | 7 |
| 8 | 150 | 7 |
| 9 | 165 | 7 |
| 10 | 173 | 7 |
| 0 | 173 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Outputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
Compiled 7 to 6 computations (14.3% saved)
Compiled 0 to 1 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 6.1% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
Compiled 7 to 6 computations (14.3% 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)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 0 | 10 | 18 |
| 1 | 15 | 18 |
| 2 | 19 | 18 |
| 3 | 25 | 18 |
| 4 | 33 | 18 |
| 5 | 48 | 18 |
| 6 | 80 | 18 |
| 7 | 106 | 18 |
| 8 | 150 | 18 |
| 9 | 165 | 18 |
| 10 | 173 | 18 |
| 0 | 173 | 18 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
x |
#s(literal 1 binary64) |
(sqrt.f64 x) |
| Outputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 x #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) x) |
x |
#s(literal 1 binary64) |
(sqrt.f64 x) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (+.f64 x #s(literal 1 binary64)) | |
| accuracy | 0 | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 60.10205181898116 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 32.0ms | 251× | 1 | valid |
| 0.0ms | 5× | 0 | valid |
Compiled 38 to 14 computations (63.2% saved)
ival-sqrt: 7.0ms (42.5% of total)adjust: 4.0ms (24.3% of total)ival-add: 3.0ms (18.2% of total)ival-sub: 3.0ms (18.2% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
(sqrt.f64 x) |
| Outputs |
|---|
(- 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 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(+ 1 x) |
(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) |
(* 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)))))))) |
x |
(* x (+ 1 (/ 1 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 (* (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))))))) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | x | @ | -inf | ((- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ x 1) (sqrt x)) |
| 1.0ms | x | @ | inf | ((- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ x 1) (sqrt x)) |
| 1.0ms | x | @ | 0 | ((- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ x 1) (sqrt x)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 113 | 451 |
| 1 | 299 | 399 |
| 2 | 804 | 395 |
| 3 | 2258 | 387 |
| 4 | 4622 | 387 |
| 0 | 8210 | 351 |
| 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 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(+ 1 x) |
(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) |
(* 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)))))))) |
x |
(* x (+ 1 (/ 1 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 (* (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))))))) |
| Outputs |
|---|
(- 1 (sqrt x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) |
(+ 1 x) |
(+.f64 #s(literal 1 binary64) x) |
(sqrt x) |
(sqrt.f64 x) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -5/128 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) x) |
(* -1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 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)) |
(/.f64 (fma.f64 (/.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) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 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)) |
(/.f64 (fma.f64 (/.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) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) x) |
(* -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 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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 (fma.f64 (/.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) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 43 | 16 |
| 2 | 290 | 16 |
| 3 | 3385 | 16 |
| 0 | 8686 | 16 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
(sqrt.f64 x) |
| Outputs |
|---|
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (pow.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 2 binary64)))) (-.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x))) |
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (pow.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 3 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)))) (fma.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) (-.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) |
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
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(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) |
(/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (-.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) #s(literal 2 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -2 binary64))) (fma.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))) |
(/.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -3 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -3 binary64))) (+.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -2 binary64)) (*.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal 1 binary64) x))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (-.f64 #s(literal 1 binary64) x))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) |
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 1 binary64)))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) |
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))) (*.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 2 binary64))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) |
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (neg.f64 (log1p.f64 x))))) |
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 x #s(literal 1 binary64)) (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))))) |
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) |
(/.f64 (+.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))))) |
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) x)) |
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (exp.f64 (neg.f64 (log1p.f64 x)))))) |
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) |
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 x #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) |
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (exp.f64 (neg.f64 (log1p.f64 x))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (exp.f64 (neg.f64 (log1p.f64 x))) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (log1p.f64 x)))) |
(neg.f64 (/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (-.f64 x #s(literal 1 binary64)))) |
(neg.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) |
(neg.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x))) |
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) |
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) |
(fma.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))) |
(fma.f64 (/.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) x) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))) |
(fma.f64 (*.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64)) (sqrt.f64 x) #s(literal 1 binary64)) |
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64)) |
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1 binary64)) |
(fma.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) |
(fma.f64 #s(literal -1 binary64) (neg.f64 x) #s(literal 1 binary64)) |
(fma.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64)) |
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))) |
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1 binary64) x #s(literal 1 binary64)) |
(fma.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64))) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))) |
(fma.f64 x #s(literal 1 binary64) #s(literal 1 binary64)) |
(sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))) |
(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x))) |
(-.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))) |
(fabs.f64 (+.f64 #s(literal 1 binary64) x)) |
(hypot.f64 (neg.f64 (hypot.f64 (sqrt.f64 x) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(hypot.f64 (hypot.f64 (sqrt.f64 x) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(hypot.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (hypot.f64 (sqrt.f64 x) x))) |
(hypot.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (hypot.f64 (sqrt.f64 x) x)) |
(+.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))) |
(+.f64 #s(literal 1 binary64) x) |
(+.f64 x #s(literal 1 binary64)) |
(exp.f64 (*.f64 (neg.f64 (log1p.f64 x)) #s(literal -1 binary64))) |
(exp.f64 (log1p.f64 x)) |
(*.f64 (sqrt.f64 (*.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64))) (pow.f64 x #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 x #s(literal 1/4 binary64)))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 x))) |
(*.f64 (sqrt.f64 (neg.f64 (sqrt.f64 x))) (sqrt.f64 (neg.f64 (sqrt.f64 x)))) |
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3/4 binary64)))) |
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x)) |
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/8 binary64)) |
(pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64)) |
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(pow.f64 x #s(literal 1/2 binary64)) |
(sqrt.f64 x) |
(fabs.f64 (sqrt.f64 x)) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 x)) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 1 binary64))) |
(exp.f64 (log.f64 (sqrt.f64 x))) |
Compiled 7 540 to 1 409 computations (81.3% saved)
11 alts after pruning (10 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 372 | 10 | 382 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 372 | 11 | 383 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 4.7% | (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
| 5.8% | (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) | |
| 3.1% | (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (*.f64 (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x) (+.f64 (+.f64 (pow.f64 (fma.f64 x x x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3 binary64))))) | |
| ▶ | 7.6% | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
| ✓ | 6.1% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 4.4% | (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) | |
| ▶ | 3.8% | (-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) |
| ▶ | 1.6% | (-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
| 7.6% | (*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x))) | |
| ▶ | 98.5% | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
| 98.3% | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
Compiled 399 to 246 computations (38.3% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) | |
| cost-diff | 0 | (/.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) | |
| cost-diff | 0 | (fma.f64 x x #s(literal -1 binary64)) | |
| cost-diff | 9920 | (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) | |
| cost-diff | 0 | (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) | |
| cost-diff | 0 | (+.f64 #s(literal 1 binary64) x) | |
| cost-diff | 0 | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) | |
| cost-diff | 384 | (-.f64 (+.f64 #s(literal 1 binary64) x) x) | |
| cost-diff | 0 | (sqrt.f64 x) | |
| cost-diff | 0 | #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) | |
| cost-diff | 0 | (-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) | |
| cost-diff | 0 | (sqrt.f64 x) | |
| cost-diff | 0 | #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) | |
| cost-diff | 0 | (-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) | |
| cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) | |
| cost-diff | 0 | (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) | |
| cost-diff | 0 | (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) | |
| cost-diff | 0 | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 32 | 225 |
| 0 | 55 | 206 |
| 1 | 90 | 198 |
| 2 | 147 | 198 |
| 3 | 385 | 198 |
| 4 | 1232 | 198 |
| 5 | 4575 | 198 |
| 0 | 8733 | 198 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
#s(literal -1/8 binary64) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
#s(literal 1/2 binary64) |
(sqrt.f64 x) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(sqrt.f64 x) |
x |
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) (sqrt.f64 x)) |
(sqrt.f64 x) |
x |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) x) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 x) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(fma.f64 x x #s(literal -1 binary64)) |
x |
#s(literal -1 binary64) |
(/.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) |
(-.f64 x #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 x) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
(neg.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
| Outputs |
|---|
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) |
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
#s(literal -1/8 binary64) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(sqrt.f64 x) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(sqrt.f64 x) |
x |
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) (sqrt.f64 x)) |
(sqrt.f64 x) |
x |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) x) |
#s(literal 1 binary64) |
(+.f64 #s(literal 1 binary64) x) |
(-.f64 x #s(literal -1 binary64)) |
#s(literal 1 binary64) |
x |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) |
(sqrt.f64 x) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(sqrt.f64 (-.f64 x #s(literal -1 binary64))) |
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))) |
(fma.f64 x x #s(literal -1 binary64)) |
x |
#s(literal -1 binary64) |
(/.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))) |
(pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) |
(-.f64 x #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) |
(sqrt.f64 x) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(sqrt.f64 (-.f64 x #s(literal -1 binary64))) |
(+.f64 #s(literal 1 binary64) x) |
(-.f64 x #s(literal -1 binary64)) |
(neg.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (neg.f64 x) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))) |
(/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))) |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.015625 | (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) | |
| accuracy | 0.22265625 | (/.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) | |
| accuracy | 0.5390625 | (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) | |
| accuracy | 60.36294204843444 | (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 0.015625 | (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) | |
| accuracy | 0.1875 | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) | |
| accuracy | 59.57677049108313 | (-.f64 (+.f64 #s(literal 1 binary64) x) x) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 1.0033222035160128 | #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) | |
| accuracy | 60.10205181898116 | (-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 59.60731944015121 | #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) | |
| accuracy | 60.10205181898116 | (-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) | |
| accuracy | 0.015625 | (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) | |
| accuracy | 0.1171875 | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) | |
| accuracy | 0.30859375 | (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) | |
| accuracy | 0.6492388453732133 | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
| 178.0ms | 251× | 1 | valid |
| 1.0ms | 5× | 0 | valid |
Compiled 434 to 64 computations (85.3% saved)
ival-sqrt: 49.0ms (37.4% of total)ival-neg: 19.0ms (14.5% of total)adjust: 16.0ms (12.2% of total)ival-add: 13.0ms (9.9% of total)ival-div: 13.0ms (9.9% of total)ival-mult: 10.0ms (7.6% of total)ival-sub: 6.0ms (4.6% of total)ival-pow: 5.0ms (3.8% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) |
(sqrt.f64 x) |
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) (sqrt.f64 x)) |
(-.f64 (+.f64 #s(literal 1 binary64) x) x) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(+.f64 #s(literal 1 binary64) x) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(fma.f64 x x #s(literal -1 binary64)) |
(/.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) |
(/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
| Outputs |
|---|
(- 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)) |
(* -1/8 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(* -1/8 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(sqrt (/ 1 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) |
(/ 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 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)))))) |
(+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (/ 1 (+ 1 (sqrt x))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x))))) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* x (- (+ (* 5/8 (/ (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2)))) (+ 1 (sqrt x)))) (/ (* (+ 1/2 (sqrt x)) (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x))))) (+ 1 (sqrt x)))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 3/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))) (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))))))))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x)))))) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))) (/ 1 (+ 1 (sqrt x)))) |
-1 |
(- (pow x 2) 1) |
(/ -1 (+ 1 (sqrt x))) |
(- (* -1 (* x (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))))) (/ 1 (+ 1 (sqrt x)))) |
(- (* x (- (* -1 (* x (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x)))))) (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))))) (/ 1 (+ 1 (sqrt x)))) |
(- (* x (- (* x (- (* x (- (* 3/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 5/8 (/ (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2)))) (+ 1 (sqrt x)))) (/ (* (+ 1/2 (sqrt x)) (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x))))) (+ 1 (sqrt x)))))) (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x)))))) (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))))) (/ 1 (+ 1 (sqrt x)))) |
(- (* -1 x) 1) |
(- (* x (- (* -1 x) 1)) 1) |
(- (* x (- (* x (- (* -1 x) 1)) 1)) 1) |
(/ x (+ 1 (sqrt x))) |
(* x (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))) |
(* 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 (- (* 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) |
(/ (+ (* -1/8 (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) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(* 1/2 (sqrt x)) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 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)))))))) |
(/ (- (+ (* 1/16 (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) |
x |
(* x (+ 1 (/ 1 x))) |
(* 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))))))) |
(/ (- (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) x) |
(/ (- (* -1 (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))) (pow x 2))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 x)))))) x) |
(/ (- (+ (* -1/16 (sqrt (/ 1 x))) (* 1/8 (sqrt (/ 1 (pow x 3))))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (sqrt (/ 1 x))) (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/4 (/ (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt (pow x 3)))) (pow x 2))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -1/32 (sqrt (/ 1 x))) (+ (* 1/4 (sqrt (/ 1 x))) (+ (* 1/4 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))))))))) x) |
(pow x 2) |
(* (pow x 2) (- 1 (/ 1 (pow x 2)))) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* 1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))) (pow x 2)) |
(/ (- (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt (pow x 3)))) (pow x 2))) (* 1/2 (sqrt x))) (* -1/2 (sqrt (/ 1 x)))) (pow x 2)) |
(/ (- (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3))))) (pow x 3))) (* 1/2 (sqrt x))) (+ (* -1/2 (sqrt (/ 1 x))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x)))))) (pow x 2)) |
(/ 1 x) |
(/ (+ 1 (/ 1 x)) x) |
(/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x) |
(/ (+ 1 (+ (/ 1 x) (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))))) x) |
(+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) |
(- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 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))))) |
(* -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)) |
(* -1/2 (* (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 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)))))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* -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 (/ (- (+ (* 1/16 (* (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)) |
(* -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)))))))) |
(+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x))) |
(+ (* -1/2 (sqrt x)) (+ (* -1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) |
(+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x)))) x)) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x)))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))))) x)) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x)))) |
(* -1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/2 (sqrt x)) (* -1/2 (sqrt (/ 1 x)))) (pow x 2)) |
(/ (+ (* -1 (/ (- (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt (/ 1 x)))) (* -1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2)) |
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* 1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))))) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x)))) x)) (* -1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2)) |
(* -1 (/ (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1) x)) |
(* -1/2 (sqrt x)) |
(+ (* -1/2 (sqrt x)) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) |
(- (+ (* -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))))) |
(- (+ (* -1 (/ (+ (* -1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* -1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* -1/2 (sqrt x))) (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))))) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 28.0ms | x | @ | -inf | ((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (sqrt (/ 1 x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (- (+ 1 x) x) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (+ 1 x) (+ (sqrt x) (sqrt (+ 1 x))) (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x)))) (pow (- x 1) -1) (/ x (+ (sqrt x) (sqrt (+ 1 x))))) |
| 6.0ms | x | @ | inf | ((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (sqrt (/ 1 x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (- (+ 1 x) x) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (+ 1 x) (+ (sqrt x) (sqrt (+ 1 x))) (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x)))) (pow (- x 1) -1) (/ x (+ (sqrt x) (sqrt (+ 1 x))))) |
| 5.0ms | x | @ | 0 | ((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (sqrt (/ 1 x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (- (+ 1 x) x) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (+ 1 x) (+ (sqrt x) (sqrt (+ 1 x))) (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x)))) (pow (- x 1) -1) (/ x (+ (sqrt x) (sqrt (+ 1 x))))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 424 | 2519 |
| 1 | 1300 | 2238 |
| 2 | 4456 | 2185 |
| 0 | 8713 | 2053 |
| 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)) |
(* -1/8 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(* -1/8 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(sqrt (/ 1 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) |
(/ 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 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)))))) |
(+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (/ 1 (+ 1 (sqrt x))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x))))) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* x (- (+ (* 5/8 (/ (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2)))) (+ 1 (sqrt x)))) (/ (* (+ 1/2 (sqrt x)) (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x))))) (+ 1 (sqrt x)))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 3/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))) (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))))))))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x)))))) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))) (/ 1 (+ 1 (sqrt x)))) |
-1 |
(- (pow x 2) 1) |
(/ -1 (+ 1 (sqrt x))) |
(- (* -1 (* x (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))))) (/ 1 (+ 1 (sqrt x)))) |
(- (* x (- (* -1 (* x (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x)))))) (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))))) (/ 1 (+ 1 (sqrt x)))) |
(- (* x (- (* x (- (* x (- (* 3/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 5/8 (/ (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2)))) (+ 1 (sqrt x)))) (/ (* (+ 1/2 (sqrt x)) (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x))))) (+ 1 (sqrt x)))))) (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x)))))) (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))))) (/ 1 (+ 1 (sqrt x)))) |
(- (* -1 x) 1) |
(- (* x (- (* -1 x) 1)) 1) |
(- (* x (- (* x (- (* -1 x) 1)) 1)) 1) |
(/ x (+ 1 (sqrt x))) |
(* x (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))) |
(* 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 (- (* 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) |
(/ (+ (* -1/8 (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) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(* 1/2 (sqrt x)) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 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)))))))) |
(/ (- (+ (* 1/16 (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) |
x |
(* x (+ 1 (/ 1 x))) |
(* 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))))))) |
(/ (- (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) x) |
(/ (- (* -1 (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))) (pow x 2))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 x)))))) x) |
(/ (- (+ (* -1/16 (sqrt (/ 1 x))) (* 1/8 (sqrt (/ 1 (pow x 3))))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (sqrt (/ 1 x))) (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/4 (/ (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt (pow x 3)))) (pow x 2))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -1/32 (sqrt (/ 1 x))) (+ (* 1/4 (sqrt (/ 1 x))) (+ (* 1/4 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))))))))) x) |
(pow x 2) |
(* (pow x 2) (- 1 (/ 1 (pow x 2)))) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* 1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))) (pow x 2)) |
(/ (- (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt (pow x 3)))) (pow x 2))) (* 1/2 (sqrt x))) (* -1/2 (sqrt (/ 1 x)))) (pow x 2)) |
(/ (- (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3))))) (pow x 3))) (* 1/2 (sqrt x))) (+ (* -1/2 (sqrt (/ 1 x))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x)))))) (pow x 2)) |
(/ 1 x) |
(/ (+ 1 (/ 1 x)) x) |
(/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x) |
(/ (+ 1 (+ (/ 1 x) (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))))) x) |
(+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) |
(- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 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))))) |
(* -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)) |
(* -1/2 (* (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 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)))))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* -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 (/ (- (+ (* 1/16 (* (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)) |
(* -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)))))))) |
(+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x))) |
(+ (* -1/2 (sqrt x)) (+ (* -1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) |
(+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x)))) x)) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x)))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))))) x)) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x)))) |
(* -1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/2 (sqrt x)) (* -1/2 (sqrt (/ 1 x)))) (pow x 2)) |
(/ (+ (* -1 (/ (- (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt (/ 1 x)))) (* -1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2)) |
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* 1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))))) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x)))) x)) (* -1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2)) |
(* -1 (/ (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1) x)) |
(* -1/2 (sqrt x)) |
(+ (* -1/2 (sqrt x)) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) |
(- (+ (* -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))))) |
(- (+ (* -1 (/ (+ (* -1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* -1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* -1/2 (sqrt x))) (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))))) |
| Outputs |
|---|
(- 1 (sqrt x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(* -1/8 (sqrt (/ 1 (pow x 3)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64)) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x)) |
(* -1/8 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(/ 1 (+ 1 (sqrt x))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(fma.f64 (/.f64 x (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 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)))) |
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
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(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x) |
(/ (- (* -1 (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))) (pow x 2))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 x)))))) x) |
(/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) |
(/ (- (+ (* -1/16 (sqrt (/ 1 x))) (* 1/8 (sqrt (/ 1 (pow x 3))))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (sqrt (/ 1 x))) (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/4 (/ (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt (pow x 3)))) (pow x 2))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -1/32 (sqrt (/ 1 x))) (+ (* 1/4 (sqrt (/ 1 x))) (+ (* 1/4 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))))))))) x) |
(/.f64 (-.f64 (fma.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/8 binary64))) (fma.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64) (fma.f64 #s(literal -1/4 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (*.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -5/32 binary64) (fma.f64 #s(literal 1/4 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))))) x) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (- 1 (/ 1 (pow x 2)))) |
(*.f64 x (fma.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) x x)) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) |
(/ (+ (* 1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))) (pow x 2)) |
(*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x))) |
(/ (- (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt (pow x 3)))) (pow x 2))) (* 1/2 (sqrt x))) (* -1/2 (sqrt (/ 1 x)))) (pow x 2)) |
(/.f64 (fma.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1/2 binary64) (/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (*.f64 x x))) (*.f64 x x)) |
(/ (- (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3))))) (pow x 3))) (* 1/2 (sqrt x))) (+ (* -1/2 (sqrt (/ 1 x))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x)))))) (pow x 2)) |
(/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64)))) (*.f64 x x)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ (+ 1 (/ 1 x)) x) |
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) |
(/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x) |
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 #s(literal 1 binary64) x)) x) |
(/ (+ 1 (+ (/ 1 x) (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))))) x) |
(/.f64 (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) x) |
(+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 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))))) |
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (neg.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 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)) |
(/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 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)) |
(/.f64 (fma.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) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) (neg.f64 x)) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/8 binary64))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/8 binary64))) x) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -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 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 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 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) 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 (fma.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) x) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 x)) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) (neg.f64 x)) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))) (neg.f64 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 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))))) (neg.f64 x)) |
(+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x))) |
#s(literal 0 binary64) |
(+ (* -1/2 (sqrt x)) (+ (* -1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x)))) x)) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x)))) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))))) x)) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x)))) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x) |
(* -1/2 (sqrt (/ 1 (pow x 3)))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) |
(/ (+ (* -1/2 (sqrt x)) (* -1/2 (sqrt (/ 1 x)))) (pow x 2)) |
(*.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x))) |
(/ (+ (* -1 (/ (- (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt (/ 1 x)))) (* -1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2)) |
(/.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 (fma.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)) (*.f64 x x)) |
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* 1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))))) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x)))) x)) (* -1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2)) |
(/.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) x) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)) (*.f64 x x)) |
(* -1 (/ (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) x)) |
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)) (neg.f64 x)) |
(* -1 (/ (- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1) x)) |
(/.f64 (fma.f64 (/.f64 (-.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) x) #s(literal -1 binary64) #s(literal 1 binary64)) x) |
(* -1/2 (sqrt x)) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) |
(+ (* -1/2 (sqrt x)) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) |
(- (+ (* -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))))) |
(fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) |
(- (+ (* -1 (/ (+ (* -1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* -1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* -1/2 (sqrt x))) (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))))) |
(fma.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 32 | 167 |
| 0 | 55 | 152 |
| 1 | 248 | 130 |
| 2 | 2102 | 130 |
| 0 | 8735 | 127 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) |
(sqrt.f64 x) |
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) (sqrt.f64 x)) |
(-.f64 (+.f64 #s(literal 1 binary64) x) x) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(+.f64 #s(literal 1 binary64) x) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(fma.f64 x x #s(literal -1 binary64)) |
(/.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) |
(/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
| Outputs |
|---|
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)) |
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x)) |
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (sqrt.f64 x)) (pow.f64 x #s(literal -1/2 binary64))) |
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal 1 binary64)) (pow.f64 x #s(literal -1 binary64))) |
(*.f64 (/.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) x) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))))) |
(*.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1/4 binary64) x)) (sqrt.f64 x)) (/.f64 (pow.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) #s(literal -1 binary64)) (sqrt.f64 x))) |
(*.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1/4 binary64) x)) #s(literal 1 binary64)) (/.f64 (pow.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) #s(literal -1 binary64)) x)) |
(*.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1/4 binary64) x)) x) (/.f64 (pow.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) #s(literal -1 binary64)) #s(literal 1 binary64))) |
(*.f64 (/.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (sqrt.f64 x)) (/.f64 (pow.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) #s(literal -1 binary64)) (sqrt.f64 x))) |
(*.f64 (/.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 1 binary64)) (/.f64 (pow.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) #s(literal -1 binary64)) x)) |
(*.f64 (/.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) x) (/.f64 (pow.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) #s(literal -1 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (/.f64 x (-.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1/4 binary64) x))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 x (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) #s(literal -1 binary64))) |
(*.f64 (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal 1 binary64)) (pow.f64 x #s(literal -1 binary64))) |
(*.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x)) |
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x) (/.f64 (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 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) |
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x) #s(literal 1 binary64)) |
(*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal -1 binary64))) |
(*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) |
(*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)) |
(pow.f64 (/.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1/4 binary64) x)) (pow.f64 x #s(literal -1 binary64)))) (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (pow.f64 x #s(literal -1 binary64)))) (neg.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal -1 binary64))) (neg.f64 (neg.f64 x))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal 1 binary64))) (neg.f64 x)) |
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))) (neg.f64 (neg.f64 (neg.f64 x)))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64))) (neg.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (neg.f64 x)))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1/4 binary64) x)) #s(literal 1 binary64))) (neg.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal -1 binary64))) (neg.f64 (*.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) (neg.f64 x)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 1 binary64))) (neg.f64 (*.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) x))) |
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1/4 binary64) x)) (pow.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) |
(/.f64 (*.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (pow.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))))) |
(/.f64 (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal -1 binary64)) (neg.f64 x)) |
(/.f64 (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal 1 binary64)) x) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) (neg.f64 (neg.f64 x))) |
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1/4 binary64) x))) (neg.f64 (*.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)))))) |
(/.f64 (neg.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))) (neg.f64 (*.f64 x (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))))))) |
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64)) (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (neg.f64 x))) |
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1/4 binary64) x)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)) |
(/.f64 (*.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal -1 binary64)) (*.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) (neg.f64 x))) |
(/.f64 (*.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) x)) |
(/.f64 (-.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1/4 binary64) x)) (*.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))))) |
(/.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (*.f64 x (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))))) |
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (neg.f64 x)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal 1 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))) |
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) |
(neg.f64 (/.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) |
(neg.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (neg.f64 x))) |
(-.f64 (/.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.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))))) (/.f64 (*.f64 #s(literal 1/4 binary64) x) (*.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)))))) |
(-.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x) (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) 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)))) x)) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (neg.f64 x))) |
(exp.f64 (*.f64 (log.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) #s(literal -1 binary64))) |
(*.f64 (-.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1/4 binary64) x)) (pow.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) #s(literal -1 binary64))) |
(*.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (pow.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (-.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1/4 binary64) x))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))) #s(literal -1 binary64)) |
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(*.f64 #s(literal 1 binary64) (*.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) x)) |
(*.f64 x (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(pow.f64 (/.f64 (/.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))) |
(/.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (neg.f64 x) (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x) #s(literal 1 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x)) |
(/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(neg.f64 (/.f64 (neg.f64 x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (/.f64 (neg.f64 x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x)) #s(literal -1 binary64))) |
Compiled 54 180 to 4 827 computations (91.1% saved)
12 alts after pruning (11 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 577 | 9 | 1 586 |
| Fresh | 3 | 2 | 5 |
| Picked | 5 | 0 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 585 | 12 | 1 597 |
| Status | Accuracy | Program |
|---|---|---|
| 7.6% | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))) | |
| 7.6% | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) | |
| 7.6% | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) | |
| 6.1% | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))) | |
| ▶ | 68.6% | (/.f64 (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) x))) |
| ▶ | 99.7% | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
| ✓ | 6.1% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 4.4% | (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) | |
| ▶ | 18.8% | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
| ▶ | 98.0% | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
| 98.3% | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) | |
| ▶ | 3.8% | #s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) |
Compiled 415 to 268 computations (35.4% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (+.f64 #s(literal 1 binary64) x) | |
| cost-diff | 0 | (+.f64 (+.f64 #s(literal 1 binary64) x) x) | |
| cost-diff | 320 | (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) | |
| cost-diff | 1088 | (/.f64 (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) x))) | |
| cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) | |
| cost-diff | 0 | #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) | |
| cost-diff | 0 | (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) | |
| cost-diff | 0 | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) | |
| cost-diff | 0 | (sqrt.f64 x) | |
| cost-diff | 0 | (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) | |
| cost-diff | 0 | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) | |
| cost-diff | 0 | #s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) | |
| cost-diff | 0 | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) | |
| cost-diff | 0 | (sqrt.f64 x) | |
| cost-diff | 0 | (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 46 | 226 |
| 0 | 64 | 211 |
| 1 | 115 | 207 |
| 2 | 249 | 187 |
| 3 | 714 | 187 |
| 4 | 3149 | 187 |
| 5 | 7224 | 187 |
| 0 | 8369 | 181 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
#s(literal 1 binary64) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 x) |
x |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
#s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) |
#s(literal 0 binary64) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) |
#s(literal 1 binary64) |
(+.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(sqrt.f64 x) |
x |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
(/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) |
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
#s(literal 1/2 binary64) |
(sqrt.f64 x) |
x |
(/.f64 (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) x))) |
(*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) |
(+.f64 (+.f64 #s(literal 1 binary64) x) x) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) x)) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 x) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
| Outputs |
|---|
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) |
#s(literal 1 binary64) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)) |
(sqrt.f64 x) |
x |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(sqrt.f64 (-.f64 x #s(literal -1 binary64))) |
(+.f64 #s(literal 1 binary64) x) |
(-.f64 x #s(literal -1 binary64)) |
#s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) |
#s(literal 0 binary64) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
#s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) |
#s(literal 1 binary64) |
(+.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(sqrt.f64 x) |
x |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
(/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) |
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
#s(literal 1/2 binary64) |
(sqrt.f64 x) |
x |
(/.f64 (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) x))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) |
(*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) |
(fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) |
(+.f64 (+.f64 #s(literal 1 binary64) x) x) |
(fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) x) |
(-.f64 x #s(literal -1 binary64)) |
#s(literal 1 binary64) |
x |
(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) x)) |
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)) |
(sqrt.f64 x) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(sqrt.f64 (-.f64 x #s(literal -1 binary64))) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 0.015625 | (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) | |
| accuracy | 0.17578125 | (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) x)) | |
| accuracy | 20.01468797922405 | (/.f64 (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) x))) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 0.30859375 | (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) | |
| accuracy | 0.6492388453732133 | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) | |
| accuracy | 0.9674733052204768 | #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) | |
| accuracy | 0 | (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 0.2109375 | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) | |
| accuracy | 51.99194561974797 | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) | |
| accuracy | 61.54891021730242 | #s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) | |
| accuracy | 0 | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 0.015625 | (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) | |
| accuracy | 0.1875 | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
| 177.0ms | 251× | 1 | valid |
| 1.0ms | 5× | 0 | valid |
Compiled 416 to 87 computations (79.1% saved)
ival-div: 48.0ms (32.2% of total)ival-mult: 34.0ms (22.8% of total)ival-add: 20.0ms (13.4% of total)adjust: 19.0ms (12.7% of total)ival-sqrt: 12.0ms (8% of total)ival-sub: 7.0ms (4.7% of total)ival-pow: 5.0ms (3.4% of total)ival-neg: 2.0ms (1.3% of total)exact: 1.0ms (0.7% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 x) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
#s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) |
(+.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
(/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) |
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(/.f64 (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) x))) |
(*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) |
(+.f64 (+.f64 #s(literal 1 binary64) x) x) |
(+.f64 #s(literal 1 binary64) x) |
(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) x)) |
| Outputs |
|---|
(/ 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 (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)))))) |
(sqrt x) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (/ 1 (+ 1 (sqrt x))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x))))) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* x (- (+ (* 5/8 (/ (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2)))) (+ 1 (sqrt x)))) (/ (* (+ 1/2 (sqrt x)) (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x))))) (+ 1 (sqrt x)))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 3/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))) (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))))))))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x)))))) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))) (/ 1 (+ 1 (sqrt x)))) |
(- 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)) |
(* -1/8 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(* -1/8 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(* 1/2 (sqrt x)) |
(+ 1 (* 2 x)) |
(+ 1 x) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* 2 (+ 1 (sqrt x))))))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (+ (* 7/8 x) (* 2 (+ 1 (sqrt x)))))))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (+ (* 2 (+ 1 (sqrt x))) (* x (+ 7/8 (* -3/16 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) |
(* 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))))))) |
(* 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 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) x) |
(/ (- (* -1 (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))) (pow x 2))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 x)))))) x) |
(/ (- (+ (* -1/16 (sqrt (/ 1 x))) (* 1/8 (sqrt (/ 1 (pow x 3))))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (sqrt (/ 1 x))) (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/4 (/ (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt (pow x 3)))) (pow x 2))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -1/32 (sqrt (/ 1 x))) (+ (* 1/4 (sqrt (/ 1 x))) (+ (* 1/4 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))))))))) 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) |
(* x (+ (sqrt (/ 1 x)) (/ 1 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) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* 2 x) |
(* x (+ 2 (/ 1 x))) |
x |
(* x (+ 1 (/ 1 x))) |
(* 4 (sqrt (pow x 3))) |
(* (pow x 2) (+ (* 2 (sqrt (/ 1 (pow x 3)))) (* 4 (sqrt (/ 1 x))))) |
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* 2 (sqrt (/ 1 (pow x 3)))) (* 4 (sqrt (/ 1 x)))))) |
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (+ (* 2 (sqrt (/ 1 (pow x 3)))) (* 4 (sqrt (/ 1 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)) |
(* -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) (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))))))) |
(+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x))) |
(+ (* -1/2 (sqrt x)) (+ (* -1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) |
(+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x)))) x)) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x)))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))))) x)) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt 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 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 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)) |
(* -1/2 (* (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 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)))))) |
(* -4 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) |
(* (pow x 2) (+ (* -4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))) |
(* (pow x 2) (+ (* -4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (sqrt (/ 1 x)) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))) |
(* (pow x 2) (+ (* -4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (sqrt x)) (* -1/2 (sqrt (/ 1 x)))) x)) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 26.0ms | x | @ | 0 | ((/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (+ (sqrt x) (sqrt (+ 1 x))) (sqrt x) (sqrt (+ 1 x)) (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/ 1 (+ (sqrt x) 1)) (+ (sqrt x) 1) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (* 1/2 (sqrt x)) (/ (* (+ (+ 1 x) x) 1) (* (+ (sqrt x) (sqrt (+ 1 x))) (+ (+ 1 x) x))) (* (+ (+ 1 x) x) 1) (+ (+ 1 x) x) (+ 1 x) (* (+ (sqrt x) (sqrt (+ 1 x))) (+ (+ 1 x) x))) |
| 3.0ms | x | @ | -inf | ((/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (+ (sqrt x) (sqrt (+ 1 x))) (sqrt x) (sqrt (+ 1 x)) (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/ 1 (+ (sqrt x) 1)) (+ (sqrt x) 1) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (* 1/2 (sqrt x)) (/ (* (+ (+ 1 x) x) 1) (* (+ (sqrt x) (sqrt (+ 1 x))) (+ (+ 1 x) x))) (* (+ (+ 1 x) x) 1) (+ (+ 1 x) x) (+ 1 x) (* (+ (sqrt x) (sqrt (+ 1 x))) (+ (+ 1 x) x))) |
| 2.0ms | x | @ | inf | ((/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (+ (sqrt x) (sqrt (+ 1 x))) (sqrt x) (sqrt (+ 1 x)) (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/ 1 (+ (sqrt x) 1)) (+ (sqrt x) 1) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (* 1/2 (sqrt x)) (/ (* (+ (+ 1 x) x) 1) (* (+ (sqrt x) (sqrt (+ 1 x))) (+ (+ 1 x) x))) (* (+ (+ 1 x) x) 1) (+ (+ 1 x) x) (+ 1 x) (* (+ (sqrt x) (sqrt (+ 1 x))) (+ (+ 1 x) x))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 423 | 2021 |
| 1 | 1310 | 1734 |
| 2 | 4324 | 1683 |
| 0 | 8237 | 1573 |
| 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 (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)))))) |
(sqrt x) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (/ 1 (+ 1 (sqrt x))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x))))) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* x (- (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* x (- (+ (* 5/8 (/ (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2)))) (+ 1 (sqrt x)))) (/ (* (+ 1/2 (sqrt x)) (+ (* 5/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x))))) (+ 1 (sqrt x)))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 3/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))) (+ (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))))))))) (/ (* (+ 1/2 (sqrt x)) (+ (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x)))))) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))) (/ 1 (+ 1 (sqrt x)))) |
(- 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)) |
(* -1/8 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(* -1/8 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(* 1/2 (sqrt x)) |
(+ 1 (* 2 x)) |
(+ 1 x) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* 2 (+ 1 (sqrt x))))))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (+ (* 7/8 x) (* 2 (+ 1 (sqrt x)))))))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (+ (* 2 (+ 1 (sqrt x))) (* x (+ 7/8 (* -3/16 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) |
(* 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))))))) |
(* 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 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) x) |
(/ (- (* -1 (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))) (pow x 2))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 x)))))) x) |
(/ (- (+ (* -1/16 (sqrt (/ 1 x))) (* 1/8 (sqrt (/ 1 (pow x 3))))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (sqrt (/ 1 x))) (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/4 (/ (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt (pow x 3)))) (pow x 2))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -1/32 (sqrt (/ 1 x))) (+ (* 1/4 (sqrt (/ 1 x))) (+ (* 1/4 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))))))))) 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) |
(* x (+ (sqrt (/ 1 x)) (/ 1 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) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* 2 x) |
(* x (+ 2 (/ 1 x))) |
x |
(* x (+ 1 (/ 1 x))) |
(* 4 (sqrt (pow x 3))) |
(* (pow x 2) (+ (* 2 (sqrt (/ 1 (pow x 3)))) (* 4 (sqrt (/ 1 x))))) |
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* 2 (sqrt (/ 1 (pow x 3)))) (* 4 (sqrt (/ 1 x)))))) |
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (+ (* 2 (sqrt (/ 1 (pow x 3)))) (* 4 (sqrt (/ 1 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)) |
(* -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) (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))))))) |
(+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x))) |
(+ (* -1/2 (sqrt x)) (+ (* -1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) |
(+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x)))) x)) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x)))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))))) x)) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt 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 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 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)) |
(* -1/2 (* (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 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)))))) |
(* -4 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) |
(* (pow x 2) (+ (* -4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))) |
(* (pow x 2) (+ (* -4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (sqrt (/ 1 x)) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))) |
(* (pow x 2) (+ (* -4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (sqrt x)) (* -1/2 (sqrt (/ 1 x)))) x)) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))) |
| Outputs |
|---|
(/ 1 (+ 1 (sqrt x))) |
(/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(fma.f64 (/.f64 x (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) |
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(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 3 binary64) (*.f64 #s(literal 4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x)) |
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (+ (* 2 (sqrt (/ 1 (pow x 3)))) (* 4 (sqrt (/ 1 x))))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 3 binary64) (*.f64 #s(literal 4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (*.f64 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 (fma.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 (/ (- (+ (* 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 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (neg.f64 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 (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64)))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) (neg.f64 x)) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 x)) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (neg.f64 x) (fma.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #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)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #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)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 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 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (neg.f64 x) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))) |
(+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x))) |
#s(literal 0 binary64) |
(+ (* -1/2 (sqrt x)) (+ (* -1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x)))) x)) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x)))) |
(/.f64 (fma.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 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))))) x)) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x)))) |
(/.f64 (fma.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 (sqrt (/ 1 x))) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1 (/ (- (sqrt x) (/ 1 (pow (sqrt -1) 2))) x)) |
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1 binary64) #s(literal -1 binary64)) x) |
(* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x)) |
(/.f64 (-.f64 (/.f64 (-.f64 (sqrt.f64 x) x) x) (sqrt.f64 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)) |
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (-.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (neg.f64 x)) x) x) (sqrt.f64 x)) x) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal 1 binary64)) |
(* -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 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (neg.f64 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 (fma.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) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) (neg.f64 x)) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x) |
(* -4 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 4 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) |
(* (pow x 2) (+ (* -4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 #s(literal 4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 2 binary64))) (*.f64 x x)) |
(* (pow x 2) (+ (* -4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (sqrt (/ 1 x)) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))) |
(*.f64 (fma.f64 #s(literal 4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x)) (*.f64 x x)) |
(* (pow x 2) (+ (* -4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (sqrt x)) (* -1/2 (sqrt (/ 1 x)))) x)) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))) |
(*.f64 (-.f64 (*.f64 #s(literal 4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (fma.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) x)) x)) (*.f64 x x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 46 | 197 |
| 0 | 64 | 182 |
| 1 | 283 | 144 |
| 2 | 2487 | 144 |
| 0 | 8233 | 138 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 x) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
#s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) |
(+.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
(/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) |
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(/.f64 (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) x))) |
(*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) |
(+.f64 (+.f64 #s(literal 1 binary64) x) x) |
(+.f64 #s(literal 1 binary64) x) |
(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) x)) |
| Outputs |
|---|
(*.f64 (pow.f64 (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x (-.f64 x (+.f64 x #s(literal 1 binary64))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (-.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (-.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (pow.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x))) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))) #s(literal -1 binary64)) (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)))) |
(*.f64 (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (+.f64 x #s(literal 1 binary64))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (pow.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 2 binary64))) (pow.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) #s(literal -1 binary64))) |
(*.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) |
(*.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (+.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x))) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (pow.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) x) #s(literal -3 binary64)) #s(literal -1 binary64) (pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) #s(literal 3 binary64))) (pow.f64 (+.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 x))) (pow.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 2 binary64))) (pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) #s(literal 2 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) |
(*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (pow.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal -1 binary64))) |
(*.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (pow.f64 (*.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) #s(literal -1 binary64))) |
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) |
(*.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) |
(pow.f64 (exp.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) #s(literal -1 binary64)) |
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(+.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x))) |
(+.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x)) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(+.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x #s(literal 1 binary64))) (*.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) x)) |
(+.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) x) (*.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x #s(literal 1 binary64)))) |
(+.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (*.f64 (*.f64 #s(literal 2 binary64) x) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) |
(+.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (*.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (*.f64 #s(literal 2 binary64) x))) |
Compiled 36 440 to 3 777 computations (89.6% saved)
14 alts after pruning (9 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 251 | 8 | 1 259 |
| Fresh | 5 | 1 | 6 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 257 | 14 | 1 271 |
| Status | Accuracy | Program |
|---|---|---|
| 68.6% | (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) | |
| ▶ | 99.6% | (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| ▶ | 50.0% | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))))) |
| 50.1% | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))))) | |
| ✓ | 99.7% | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
| ▶ | 98.2% | (/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))) |
| ✓ | 6.1% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| ▶ | 4.4% | (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
| ✓ | 18.8% | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
| ▶ | 18.8% | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x))) |
| 18.7% | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) | |
| 98.3% | #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) | |
| ✓ | 98.0% | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
| ✓ | 3.8% | #s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) |
Compiled 404 to 275 computations (31.9% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) | |
| cost-diff | 0 | (sqrt.f64 x) | |
| cost-diff | 0 | (+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))))) | |
| cost-diff | 0 | (sqrt.f64 x) | |
| cost-diff | 0 | (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) | |
| cost-diff | 0 | #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x))) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))) | |
| cost-diff | 0 | (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) | |
| cost-diff | 0 | (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x) | |
| cost-diff | 0 | #s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x)) | |
| cost-diff | 0 | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x))) | |
| cost-diff | 0 | (sqrt.f64 x) | |
| cost-diff | 0 | (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) | |
| cost-diff | 0 | (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) | |
| cost-diff | 0 | (sqrt.f64 x) | |
| cost-diff | 0 | (sqrt.f64 (sqrt.f64 x)) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) | |
| cost-diff | 2112 | (fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 38 | 216 |
| 0 | 61 | 208 |
| 1 | 93 | 204 |
| 2 | 133 | 204 |
| 3 | 185 | 204 |
| 4 | 273 | 204 |
| 5 | 533 | 204 |
| 6 | 1124 | 204 |
| 7 | 3681 | 204 |
| 8 | 5857 | 204 |
| 0 | 8223 | 204 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
#s(literal 1 binary64) |
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(sqrt.f64 (sqrt.f64 x)) |
(sqrt.f64 x) |
x |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
#s(literal 1/2 binary64) |
x |
#s(literal 1 binary64) |
(sqrt.f64 x) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x))) |
#s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x)) |
(/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x) |
(-.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(sqrt.f64 x) |
x |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))) |
#s(literal 1 binary64) |
#s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 x)) |
#s(literal 2 binary64) |
(sqrt.f64 x) |
x |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))))) |
#s(literal 1 binary64) |
(+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))) |
(sqrt.f64 x) |
x |
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) |
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) |
(fma.f64 x x #s(literal -1 binary64)) |
#s(literal -1 binary64) |
(sqrt.f64 (-.f64 x #s(literal 1 binary64))) |
(-.f64 x #s(literal 1 binary64)) |
| Outputs |
|---|
(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) |
#s(literal 1 binary64) |
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)) |
(sqrt.f64 (sqrt.f64 x)) |
(sqrt.f64 x) |
x |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(sqrt.f64 (-.f64 x #s(literal -1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
(-.f64 x #s(literal -1 binary64)) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
#s(literal 1/2 binary64) |
x |
#s(literal 1 binary64) |
(sqrt.f64 x) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x))) |
#s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x)) |
(/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x) |
(-.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(sqrt.f64 x) |
x |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))) |
#s(literal 1 binary64) |
#s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 x)) |
#s(literal 2 binary64) |
(sqrt.f64 x) |
x |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))))) |
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))) |
#s(literal 1 binary64) |
(+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))) |
(+.f64 (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) (sqrt.f64 x)) |
(sqrt.f64 x) |
x |
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) |
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) |
(fma.f64 x x #s(literal -1 binary64)) |
#s(literal -1 binary64) |
(sqrt.f64 (-.f64 x #s(literal 1 binary64))) |
(-.f64 x #s(literal 1 binary64)) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.015625 | (+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))) | |
| accuracy | 0.1875 | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))))) | |
| accuracy | 0.54296875 | (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) | |
| accuracy | 31.043574437256527 | (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) | |
| accuracy | 0 | (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 0.1875 | (/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))) | |
| accuracy | 0.9669215908111927 | #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x))) | |
| accuracy | 0.0078125 | (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) | |
| accuracy | 0.28125 | (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x) | |
| accuracy | 1.0400273004989606 | #s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x)) | |
| accuracy | 51.99194561974797 | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x))) | |
| accuracy | 0 | (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 59.58404267047932 | #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) | |
| accuracy | 60.10205181898116 | (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 0.1328125 | (sqrt.f64 (sqrt.f64 x)) | |
| accuracy | 0.18359375 | (fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) | |
| accuracy | 0.1875 | (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 132.0ms | 250× | 1 | valid |
| 1.0ms | 6× | 0 | valid |
Compiled 401 to 75 computations (81.3% saved)
ival-add: 18.0ms (21.1% of total)adjust: 18.0ms (21.1% of total)ival-div: 17.0ms (20% of total)ival-sqrt: 16.0ms (18.8% of total)ival-mult: 8.0ms (9.4% of total)ival-sub: 7.0ms (8.2% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(sqrt.f64 (sqrt.f64 x)) |
(sqrt.f64 x) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x))) |
#s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x)) |
(/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x) |
(-.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))) |
#s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))))) |
(+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))) |
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) |
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) |
| Outputs |
|---|
(+ 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 (+ 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)))) |
(pow (* 1 x) 1/4) |
(sqrt x) |
(- 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 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(/ (- (sqrt x) 1) x) |
(- (sqrt x) 1) |
(* 2 (sqrt x)) |
(sqrt -1) |
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1)))) |
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))) |
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1)))))) |
(* 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))))))) |
(* 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) |
(/ (+ (* -1/8 (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) |
(* 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)))))))) |
(* 1/2 x) |
(* x (+ 1/2 (/ 1 x))) |
(sqrt (/ 1 x)) |
(/ (- (+ (sqrt x) (sqrt (/ 1 x))) 1) x) |
(/ (- (sqrt x) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (/ 1 x)))) x) |
(- (sqrt (/ 1 x)) (/ 1 x)) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
x |
(* x (- 1 (* 1/2 (/ 1 (pow x 2))))) |
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))) |
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))) |
(* -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)))))))) |
(* -1/2 (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)) |
(* (pow (* -1 x) 1/4) (sqrt (sqrt -1))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -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 (* 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 (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 (/ 1 x)) (pow (sqrt -1) 2))) |
(- (* -1 (* (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)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) |
(* -1 (/ (- (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/4 (/ 1 (* (pow x 3) (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))))))) x)) |
(* -1 (/ (- (+ (/ 1/16 (* (pow x 4) (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 11))) (/ (- (* -1/4 (/ x (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/4 (/ 1 (* (pow x 3) (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))))))))) x)) |
(* -1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/16 (sqrt (/ 1 (pow x 7)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
(* -1 (sqrt x)) |
(* -1 (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))) |
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))) |
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))) |
(* -1 x) |
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))) |
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))) |
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 36.0ms | x | @ | 0 | ((+ (* (sqrt (sqrt x)) (sqrt (sqrt x))) (sqrt (+ x 1))) (/ 1 (+ (* (sqrt (sqrt x)) (sqrt (sqrt x))) (sqrt (+ x 1)))) (sqrt (sqrt x)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/ 1 (+ (sqrt x) 1)) (/ (- (sqrt x) 1) x) (- (sqrt x) 1) (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (+ (sqrt x) (sqrt (+ 1 x))) (* 2 (sqrt x)) (/ 1 (+ (sqrt x) (/ (sqrt (+ (* x x) -1)) (sqrt (- x 1))))) (+ (sqrt x) (/ (sqrt (+ (* x x) -1)) (sqrt (- x 1)))) (/ (sqrt (+ (* x x) -1)) (sqrt (- x 1))) (sqrt (+ (* x x) -1))) |
| 13.0ms | x | @ | inf | ((+ (* (sqrt (sqrt x)) (sqrt (sqrt x))) (sqrt (+ x 1))) (/ 1 (+ (* (sqrt (sqrt x)) (sqrt (sqrt x))) (sqrt (+ x 1)))) (sqrt (sqrt x)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/ 1 (+ (sqrt x) 1)) (/ (- (sqrt x) 1) x) (- (sqrt x) 1) (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (+ (sqrt x) (sqrt (+ 1 x))) (* 2 (sqrt x)) (/ 1 (+ (sqrt x) (/ (sqrt (+ (* x x) -1)) (sqrt (- x 1))))) (+ (sqrt x) (/ (sqrt (+ (* x x) -1)) (sqrt (- x 1)))) (/ (sqrt (+ (* x x) -1)) (sqrt (- x 1))) (sqrt (+ (* x x) -1))) |
| 12.0ms | x | @ | -inf | ((+ (* (sqrt (sqrt x)) (sqrt (sqrt x))) (sqrt (+ x 1))) (/ 1 (+ (* (sqrt (sqrt x)) (sqrt (sqrt x))) (sqrt (+ x 1)))) (sqrt (sqrt x)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/ 1 (+ (sqrt x) 1)) (/ (- (sqrt x) 1) x) (- (sqrt x) 1) (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (+ (sqrt x) (sqrt (+ 1 x))) (* 2 (sqrt x)) (/ 1 (+ (sqrt x) (/ (sqrt (+ (* x x) -1)) (sqrt (- x 1))))) (+ (sqrt x) (/ (sqrt (+ (* x x) -1)) (sqrt (- x 1)))) (/ (sqrt (+ (* x x) -1)) (sqrt (- x 1))) (sqrt (+ (* x x) -1))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 377 | 1933 |
| 1 | 1137 | 1580 |
| 2 | 4484 | 1447 |
| 0 | 8621 | 1356 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ 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 (+ 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)))) |
(pow (* 1 x) 1/4) |
(sqrt x) |
(- 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 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(/ (- (sqrt x) 1) x) |
(- (sqrt x) 1) |
(* 2 (sqrt x)) |
(sqrt -1) |
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1)))) |
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))) |
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1)))))) |
(* 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))))))) |
(* 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) |
(/ (+ (* -1/8 (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) |
(* 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)))))))) |
(* 1/2 x) |
(* x (+ 1/2 (/ 1 x))) |
(sqrt (/ 1 x)) |
(/ (- (+ (sqrt x) (sqrt (/ 1 x))) 1) x) |
(/ (- (sqrt x) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (/ 1 x)))) x) |
(- (sqrt (/ 1 x)) (/ 1 x)) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
x |
(* x (- 1 (* 1/2 (/ 1 (pow x 2))))) |
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))) |
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))) |
(* -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)))))))) |
(* -1/2 (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)) |
(* (pow (* -1 x) 1/4) (sqrt (sqrt -1))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -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 (* 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 (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 (/ 1 x)) (pow (sqrt -1) 2))) |
(- (* -1 (* (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)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) |
(* -1 (/ (- (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/4 (/ 1 (* (pow x 3) (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))))))) x)) |
(* -1 (/ (- (+ (/ 1/16 (* (pow x 4) (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 11))) (/ (- (* -1/4 (/ x (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/4 (/ 1 (* (pow x 3) (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))))))))) x)) |
(* -1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/16 (sqrt (/ 1 (pow x 7)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
(* -1 (sqrt x)) |
(* -1 (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))) |
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))) |
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))) |
(* -1 x) |
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))) |
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))) |
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))) |
| Outputs |
|---|
(+ 1 (sqrt x)) |
(-.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(+ 1 (+ (sqrt x) (* 1/2 x))) |
(fma.f64 #s(literal 1/2 binary64) x (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(/ 1 (+ 1 (sqrt x))) |
(/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(fma.f64 (/.f64 x (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 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)))) |
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal -1/2 binary64) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 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)))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)))) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 3 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64))))) x (/.f64 #s(literal -1/2 binary64) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) |
(pow (* 1 x) 1/4) |
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(* -1 (/ (- (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/4 (/ 1 (* (pow x 3) (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))))))) x)) |
(/.f64 (-.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 0 binary64)) #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) #s(literal 0 binary64))) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 0 binary64)) #s(literal -1/8 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64)))))) x) |
(* -1 (/ (- (+ (/ 1/16 (* (pow x 4) (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 11))) (/ (- (* -1/4 (/ x (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/4 (/ 1 (* (pow x 3) (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))))))))) x)) |
(/.f64 (-.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) #s(literal 0 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) #s(literal 0 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 0 binary64)) (*.f64 (fma.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 0 binary64)) #s(literal 1/8 binary64) (*.f64 (/.f64 x #s(literal 0 binary64)) #s(literal -1/4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64)))))) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 0 binary64)) #s(literal -1/16 binary64) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 0 binary64)) #s(literal -1/8 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64)))))))) (neg.f64 x)) |
(* -1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 #s(literal 0 binary64) x) |
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) #s(literal 0 binary64)) x) |
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) #s(literal 0 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64))) x) |
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/16 (sqrt (/ 1 (pow x 7)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
(*.f64 (fma.f64 #s(literal -1 binary64) (+.f64 (fma.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) |
(* -1 (sqrt x)) |
(neg.f64 (sqrt.f64 x)) |
(* -1 (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (neg.f64 x)) |
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x)) |
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))) |
(*.f64 (+.f64 (fma.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (neg.f64 x)) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)) x) |
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))) |
(neg.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -1 binary64) #s(literal -1/2 binary64)) x) #s(literal 1 binary64) x)) |
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))) |
(*.f64 (neg.f64 x) (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))) |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 38 | 177 |
| 0 | 61 | 156 |
| 1 | 263 | 147 |
| 2 | 2018 | 147 |
| 0 | 8168 | 147 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(sqrt.f64 (sqrt.f64 x)) |
(sqrt.f64 x) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x))) |
#s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x)) |
(/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x) |
(-.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))) |
#s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))))) |
(+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))) |
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) |
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) |
| Outputs |
|---|
(*.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) x) x)) |
(*.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (+.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) |
(*.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x)) (pow.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (pow.f64 (-.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 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1 binary64)) |
(pow.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (-.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x))) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1 binary64)) |
(/.f64 (neg.f64 (neg.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (neg.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) 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 (-.f64 (*.f64 x (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (*.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) x))) (*.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (neg.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x))) (neg.f64 (*.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (neg.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x))) (neg.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) 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 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x)))))) |
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) 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 (neg.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 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x)) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) 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 (fma.f64 (sqrt.f64 x) x (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 (+.f64 #s(literal 1 binary64) x) x))))) |
(/.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) 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 (neg.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (-.f64 x (+.f64 #s(literal 1 binary64) 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))) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1 binary64)))) |
(/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #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 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (-.f64 x (+.f64 #s(literal 1 binary64) 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))) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1 binary64))) |
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 (sqrt.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(fma.f64 (sqrt.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (hypot.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x) (sqrt.f64 x)) |
(fma.f64 (sqrt.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal -1 binary64))))) (sqrt.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 x)) |
(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (*.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 x)) |
(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) |
(fma.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (hypot.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x) (sqrt.f64 x)) |
(fma.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x 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 1/2 binary64)) (sqrt.f64 x)) |
(fma.f64 (pow.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
(fma.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(fma.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (sqrt.f64 x)) |
(fma.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3/4 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) (sqrt.f64 x)) |
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
(fma.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (sqrt.f64 (pow.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) (sqrt.f64 x)) |
(fma.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (sqrt.f64 (pow.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))) (sqrt.f64 x)) |
(fma.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (pow.f64 (pow.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
(fma.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (pow.f64 (pow.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
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(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (*.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (*.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) |
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 x x) #s(literal -1 binary64)))))) |
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal -1 binary64))))) |
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal -1 binary64))) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))))) |
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) |
(exp.f64 (fma.f64 (log1p.f64 x) #s(literal 1/2 binary64) (*.f64 (log.f64 (-.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal 1/2 binary64))) |
Compiled 18 321 to 2 733 computations (85.1% saved)
15 alts after pruning (5 fresh and 10 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 723 | 2 | 725 |
| Fresh | 1 | 3 | 4 |
| Picked | 0 | 5 | 5 |
| Done | 0 | 5 | 5 |
| Total | 724 | 15 | 739 |
| Status | Accuracy | Program |
|---|---|---|
| 68.6% | (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) | |
| ✓ | 99.6% | (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| ✓ | 50.0% | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))))) |
| 50.1% | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))))) | |
| ✓ | 99.7% | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
| ✓ | 98.2% | (/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))) |
| ✓ | 6.1% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| ✓ | 4.4% | (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 4.3% | (-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x)) | |
| ✓ | 18.8% | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
| ✓ | 18.8% | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x))) |
| 18.7% | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) | |
| 98.3% | #s(approx (/ 1 (+ (* (sqrt (sqrt x)) (sqrt (sqrt x))) (sqrt (+ x 1)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) | |
| ✓ | 98.0% | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
| ✓ | 3.8% | #s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) |
Compiled 833 to 339 computations (59.3% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x)) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x))) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
#s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
#s(approx (/ 1 (+ (* (sqrt (sqrt x)) (sqrt (sqrt x))) (sqrt (+ x 1)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
(/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) |
(/.f64 (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) x))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))))) |
(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))) |
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x))) |
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (*.f64 (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x) (+.f64 (+.f64 (pow.f64 (fma.f64 x x x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3 binary64))))) |
| Outputs |
|---|
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
2 calls:
| 8.0ms | x |
| 7.0ms | (-.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 8 to 7 computations (12.5% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x)) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x))) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
#s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
#s(approx (/ 1 (+ (* (sqrt (sqrt x)) (sqrt (sqrt x))) (sqrt (+ x 1)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))) |
| Outputs |
|---|
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
2 calls:
| 13.0ms | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 5.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.3% | 1 | x |
| 98.3% | 1 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
Compiled 8 to 7 computations (12.5% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x)) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x))) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
| Outputs |
|---|
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x))) |
2 calls:
| 3.0ms | x |
| 2.0ms | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 18.8% | 1 | x |
| 18.8% | 1 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
Compiled 8 to 7 computations (12.5% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x)) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) |
| Outputs |
|---|
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
2 calls:
| 3.0ms | x |
| 2.0ms | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 18.7% | 1 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 18.7% | 1 | x |
Compiled 8 to 7 computations (12.5% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x)) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Outputs |
|---|
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
2 calls:
| 2.0ms | x |
| 2.0ms | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 4.4% | 1 | x |
| 4.4% | 1 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
Compiled 8 to 7 computations (12.5% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x)) |
| Outputs |
|---|
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x)) |
2 calls:
| 6.0ms | x |
| 1.0ms | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 4.3% | 1 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 4.3% | 1 | x |
Compiled 8 to 7 computations (12.5% saved)
Total -1.4b remaining (-2.4%)
Threshold costs -1.4b (-2.4%)
| Inputs |
|---|
#s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
| Outputs |
|---|
#s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) |
2 calls:
| 2.0ms | x |
| 1.0ms | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 3.8% | 1 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 3.8% | 1 | x |
Compiled 8 to 7 computations (12.5% saved)
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 50 | 136 |
| 1 | 61 | 136 |
| 2 | 68 | 136 |
| 3 | 75 | 136 |
| 4 | 76 | 136 |
| 1× | saturated |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x))) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x)) |
#s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) |
| Outputs |
|---|
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (/.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) x))) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) #s(approx (/ 1 (+ (sqrt x) 1)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x)) |
#s(approx (+ (* (+ (* x x) -1) (/ (pow (- x 1) -1) (+ (sqrt x) (sqrt (+ 1 x))))) (neg (/ x (+ (sqrt x) (sqrt (+ 1 x)))))) #s(literal 0 binary64)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 377 | 1933 |
| 1 | 1137 | 1580 |
| 2 | 4484 | 1447 |
| 0 | 8621 | 1356 |
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 43 | 16 |
| 2 | 290 | 16 |
| 3 | 3385 | 16 |
| 0 | 8686 | 16 |
| 0 | 423 | 2021 |
| 1 | 1310 | 1734 |
| 2 | 4324 | 1683 |
| 0 | 8237 | 1573 |
| 0 | 424 | 2519 |
| 1 | 1300 | 2238 |
| 2 | 4456 | 2185 |
| 0 | 8713 | 2053 |
| 0 | 113 | 451 |
| 1 | 299 | 399 |
| 2 | 804 | 395 |
| 3 | 2258 | 387 |
| 4 | 4622 | 387 |
| 0 | 8210 | 351 |
| 0 | 32 | 167 |
| 0 | 55 | 152 |
| 1 | 248 | 130 |
| 2 | 2102 | 130 |
| 0 | 8735 | 127 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter 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× | iter limit |
| 1× | node limit |
Compiled 297 to 139 computations (53.2% saved)
Compiled 296 to 126 computations (57.4% saved)
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