
Time bar (total: 7.0s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 100% | 0% | 0% | 0% | 0% | 0 |
| 0% | 0% | 100% | 0% | 0% | 0% | 0% | 1 |
| 50% | 50% | 50% | 0% | 0% | 0% | 0% | 2 |
| 66.7% | 50% | 25% | 0% | 0% | 25% | 0% | 3 |
| 83.3% | 62.5% | 12.5% | 0% | 0% | 25% | 0% | 4 |
| 91.7% | 68.7% | 6.2% | 0% | 0% | 25% | 0% | 5 |
| 95.8% | 71.8% | 3.1% | 0% | 0% | 25% | 0% | 6 |
| 97.9% | 73.4% | 1.6% | 0% | 0% | 25% | 0% | 7 |
| 99% | 74.2% | 0.8% | 0% | 0% | 25% | 0% | 8 |
| 99.5% | 74.6% | 0.4% | 0% | 0% | 25% | 0% | 9 |
| 99.7% | 74.8% | 0.2% | 0% | 0% | 25% | 0% | 10 |
| 99.9% | 74.9% | 0.1% | 0% | 0% | 25% | 0% | 11 |
| 99.9% | 74.9% | 0% | 0% | 0% | 25% | 0% | 12 |
Compiled 10 to 8 computations (20% saved)
| 531.0ms | 8 253× | 0 | valid |
| 0.0ms | 3× | 2 | valid |
| 0.0ms | 2× | 0 | invalid |
ival-add: 147.0ms (38.6% of total)ival-div: 120.0ms (31.5% of total)ival-sqrt: 101.0ms (26.5% of total)ival-true: 6.0ms (1.6% of total)exact: 4.0ms (1.1% of total)ival-assert: 3.0ms (0.8% of total)adjust: 0.0ms (0% of total)| 1× | egg-herbie |
| 44× | associate-*l* |
| 42× | distribute-lft-neg-in |
| 42× | times-frac |
| 38× | unsub-neg |
| 36× | sub-neg |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 21 |
| 1 | 23 | 17 |
| 2 | 51 | 16 |
| 3 | 110 | 16 |
| 4 | 221 | 16 |
| 5 | 333 | 16 |
| 6 | 361 | 16 |
| 7 | 377 | 16 |
| 8 | 390 | 16 |
| 0 | 6 | 8 |
| 0 | 10 | 8 |
| 1 | 14 | 8 |
| 0 | 14 | 8 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Outputs |
|---|
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 0 | 0 | - | 0 | - | (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
| 0 | 0 | - | 0 | - | (+.f64 x #s(literal 1 binary64)) |
| 0 | 0 | - | 0 | - | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
| 0 | 0 | - | 0 | - | x |
| Predicted + | Predicted - | |
|---|---|---|
| + | 0 | 0 |
| - | 0 | 256 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 0 | 0 | 0 |
| - | 0 | 0 | 256 |
| number | freq |
|---|---|
| 0 | 256 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 0 | 0 | 0 |
| - | 0 | 0 | 1 |
| 33.0ms | 512× | 0 | valid |
Compiled 68 to 28 computations (58.8% saved)
ival-add: 5.0ms (36.8% of total)ival-div: 4.0ms (29.5% of total)ival-sqrt: 4.0ms (29.5% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)Compiled 1 to 1 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.7% | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 9 to 6 computations (33.3% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (+.f64 x #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
| ✓ | cost-diff | 0 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 8× | lower-+.f32 |
| 4× | lift-+.f64 |
| 4× | lower-+.f64 |
| 4× | +-commutative |
| 2× | lift-sqrt.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 23 |
| 0 | 10 | 23 |
| 1 | 14 | 23 |
| 0 | 14 | 23 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
x |
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 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 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
x |
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
#s(literal 1 binary64) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (+.f64 x #s(literal 1 binary64)) |
| ✓ | accuracy | 100.0% | (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
| ✓ | accuracy | 99.7% | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 14.0ms | 256× | 0 | valid |
Compiled 25 to 8 computations (68% saved)
ival-add: 3.0ms (43.1% of total)ival-div: 2.0ms (28.8% of total)ival-sqrt: 2.0ms (28.8% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#<alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))> |
#<alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))> |
#<alt (sqrt.f64 (+.f64 x #s(literal 1 binary64)))> |
#<alt (+.f64 x #s(literal 1 binary64))> |
| Outputs |
|---|
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))> |
#<alt (sqrt x)> |
#<alt (- (sqrt x) 1)> |
#<alt (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)> |
#<alt (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))> |
#<alt (* -1 (sqrt x))> |
#<alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))> |
#<alt 2> |
#<alt (+ 2 (* 1/2 x))> |
#<alt (+ 2 (* x (+ 1/2 (* -1/8 x))))> |
#<alt (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))> |
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))> |
#<alt 1> |
#<alt (+ 1 x)> |
#<alt (+ 1 x)> |
#<alt (+ 1 x)> |
#<alt x> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt x> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (/ x (+ 1 (sqrt (+ x 1)))) |
| 1.0ms | x | @ | inf | (/ x (+ 1 (sqrt (+ x 1)))) |
| 0.0ms | x | @ | -inf | (sqrt (+ x 1)) |
| 0.0ms | x | @ | -inf | (+ 1 (sqrt (+ x 1))) |
| 0.0ms | x | @ | inf | (sqrt (+ x 1)) |
| 1× | egg-herbie |
| 18 662× | lower-fma.f64 |
| 18 662× | lower-fma.f32 |
| 3 776× | lower-*.f64 |
| 3 776× | lower-*.f32 |
| 2 642× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 161 | 600 |
| 1 | 485 | 505 |
| 2 | 1633 | 483 |
| 3 | 5433 | 474 |
| 0 | 8374 | 430 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(- (sqrt x) 1) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(* -1 (sqrt x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
2 |
(+ 2 (* 1/2 x)) |
(+ 2 (* x (+ 1/2 (* -1/8 x)))) |
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (/ 1 x))) |
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
1 |
(+ 1 x) |
(+ 1 x) |
(+ 1 x) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
| Outputs |
|---|
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(- (sqrt x) 1) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(+.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(+.f64 (sqrt.f64 x) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))))) |
(* -1 (sqrt x)) |
(neg.f64 (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(-.f64 #s(literal -1 binary64) (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(-.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(-.f64 (neg.f64 (sqrt.f64 x)) (+.f64 (/.f64 (/.f64 (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) x) x) #s(literal 1 binary64))) |
2 |
#s(literal 2 binary64) |
(+ 2 (* 1/2 x)) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 2 binary64)) |
(+ 2 (* x (+ 1/2 (* -1/8 x)))) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) |
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (/ 1 x))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(-.f64 (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))) |
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (/.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))) |
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 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 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 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
1 |
#s(literal 1 binary64) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
| 1× | batch-egg-rewrite |
| 3 950× | lower-fma.f64 |
| 3 950× | lower-fma.f32 |
| 3 308× | lower-/.f32 |
| 3 306× | lower-/.f64 |
| 2 908× | lower-*.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 21 |
| 0 | 10 | 21 |
| 1 | 46 | 21 |
| 2 | 315 | 20 |
| 3 | 3400 | 20 |
| 0 | 8278 | 20 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
| Outputs |
|---|
(+.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(+.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))))) |
(+.f64 (/.f64 x (neg.f64 x)) (*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (neg.f64 x)))) |
(+.f64 (*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(+.f64 (*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64))) |
(+.f64 (*.f64 (/.f64 x (neg.f64 x)) #s(literal 1 binary64)) (*.f64 (/.f64 x (neg.f64 x)) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(+.f64 (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))) |
(exp.f64 (*.f64 (neg.f64 (log.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(fma.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))))) |
(fma.f64 x (/.f64 #s(literal -1 binary64) x) (*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (neg.f64 x)))) |
(fma.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))))) |
(fma.f64 #s(literal 1 binary64) (/.f64 x (neg.f64 x)) (*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (neg.f64 x)))) |
(fma.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))) |
(fma.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64) (*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(fma.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64))) |
(fma.f64 (/.f64 x (neg.f64 x)) #s(literal 1 binary64) (*.f64 (/.f64 x (neg.f64 x)) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(fma.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))))) |
(fma.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (fma.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) (*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (neg.f64 x)))) |
(fma.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))) (+.f64 #s(literal 2 binary64) x) (*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (neg.f64 x)))) |
(fma.f64 (/.f64 x (fma.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))))) |
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x))) |
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x)) |
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) x)) |
(/.f64 (neg.f64 x) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(/.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(/.f64 (/.f64 x (neg.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(/.f64 (*.f64 x (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) |
(/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 x)) |
(/.f64 (*.f64 x (fma.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 1 binary64))) (*.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) (*.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (+.f64 (neg.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(/.f64 (*.f64 x (neg.f64 x)) (*.f64 (neg.f64 x) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (*.f64 (neg.f64 x) (+.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (+.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(/.f64 (*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (fma.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 1 binary64))) (fma.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64)) #s(literal 1 binary64))) |
(/.f64 (*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) (+.f64 (neg.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(/.f64 (*.f64 (/.f64 x (neg.f64 x)) (neg.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(/.f64 (*.f64 (/.f64 x (neg.f64 x)) (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (+.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(/.f64 (/.f64 (neg.f64 x) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x) #s(literal -1 binary64)) |
(pow.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 1 binary64)) |
(pow.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x)) #s(literal -1/2 binary64)) |
(pow.f64 (pow.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (exp.f64 (neg.f64 (log.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))) #s(literal -1 binary64)) |
(*.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(*.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(*.f64 (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) x) |
(*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (neg.f64 x))) |
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 1 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 x)) |
(*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) |
(*.f64 (/.f64 x (neg.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 x (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) |
(*.f64 (/.f64 #s(literal -1 binary64) x) (*.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) |
(*.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
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(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)) (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (fma.f64 (*.f64 x x) (neg.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) |
(*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (fabs.f64 (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) |
(*.f64 (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) (fma.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x x)))) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x))) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x)) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))) |
(*.f64 (exp.f64 (log1p.f64 (*.f64 x (*.f64 x x)))) (exp.f64 (neg.f64 (log1p.f64 (-.f64 (*.f64 x x) x))))) |
(*.f64 (exp.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64)))) (exp.f64 (neg.f64 (log.f64 (+.f64 x #s(literal -1 binary64)))))) |
(*.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (fabs.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (fabs.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) (fabs.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) |
(*.f64 (fabs.f64 (fma.f64 x x #s(literal -1 binary64))) (fabs.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (fabs.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))) (fabs.f64 (fma.f64 x x #s(literal -1 binary64)))) |
(*.f64 (fabs.f64 (fma.f64 (*.f64 x x) (neg.f64 x) #s(literal -1 binary64))) (fabs.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))) |
(*.f64 (fabs.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (fabs.f64 (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (fabs.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))) (fabs.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (fabs.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (fabs.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (fabs.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (fabs.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))) (fabs.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x x))))) |
(*.f64 (fabs.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x)))) (fabs.f64 (+.f64 (fma.f64 x x #s(literal -1 binary64)) x))) |
(*.f64 (fabs.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1 binary64)))) (fabs.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (fabs.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 045 to 2 091 computations (81.1% saved)
11 alts after pruning (10 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 510 | 10 | 520 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 510 | 11 | 521 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.7% | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 64.6% | (/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 2 binary64)))) | |
| 38.3% | (/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x))) | |
| ▶ | 99.5% | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x)) |
| ▶ | 43.2% | (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 38.0% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) | |
| 62.7% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) | |
| ▶ | 64.0% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| ▶ | 62.3% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
| ▶ | 63.8% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
| 38.6% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
Compiled 155 to 108 computations (30.3% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (+.f64 x #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
| ✓ | cost-diff | 0 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
| ✓ | cost-diff | 128 | (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| ✓ | cost-diff | 0 | (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
| ✓ | cost-diff | 0 | (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 0 | (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) x) |
| ✓ | cost-diff | 0 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
| ✓ | cost-diff | 0 | (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x) |
| ✓ | cost-diff | 704 | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x)) |
| 1 792× | lower-fma.f32 |
| 1 786× | lower-fma.f64 |
| 816× | lower-*.f32 |
| 810× | lower-*.f64 |
| 570× | div-sub |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 142 |
| 0 | 41 | 142 |
| 1 | 76 | 141 |
| 2 | 124 | 139 |
| 3 | 173 | 139 |
| 4 | 278 | 139 |
| 5 | 313 | 139 |
| 6 | 392 | 139 |
| 7 | 533 | 139 |
| 8 | 790 | 139 |
| 9 | 959 | 139 |
| 10 | 1209 | 139 |
| 11 | 2331 | 139 |
| 12 | 2896 | 139 |
| 13 | 3209 | 139 |
| 14 | 3245 | 139 |
| 15 | 3245 | 139 |
| 0 | 3245 | 139 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x)) |
#s(literal 1 binary64) |
(/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x) |
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
x |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
x |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
#s(literal -1/8 binary64) |
#s(literal 1/2 binary64) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
x |
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
#s(literal 1/16 binary64) |
#s(literal -1/8 binary64) |
#s(literal 1/2 binary64) |
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
#s(literal 1 binary64) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
x |
| Outputs |
|---|
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x)) |
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
#s(literal 1 binary64) |
(/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x) |
(/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x) |
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) 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(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) x) |
(*.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
x |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
x |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
#s(literal -1/8 binary64) |
#s(literal 1/2 binary64) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
x |
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
#s(literal 1/16 binary64) |
#s(literal -1/8 binary64) |
#s(literal 1/2 binary64) |
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
#s(literal 1 binary64) |
(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 |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (+.f64 x #s(literal 1 binary64)) |
| ✓ | accuracy | 100.0% | (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
| ✓ | accuracy | 43.2% | (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
| ✓ | accuracy | 100.0% | (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
| ✓ | accuracy | 99.9% | (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 64.1% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 100.0% | (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 62.3% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal 1/2 binary64) x) |
| ✓ | accuracy | 63.8% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
| ✓ | accuracy | 100.0% | (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
| ✓ | accuracy | 99.8% | (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x) |
| ✓ | accuracy | 99.7% | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x)) |
| 31.0ms | 87× | 1 | valid |
| 28.0ms | 64× | 2 | valid |
| 16.0ms | 105× | 0 | valid |
Compiled 130 to 24 computations (81.5% saved)
adjust: 14.0ms (26.5% of total)ival-add: 12.0ms (22.7% of total)ival-div: 9.0ms (17% of total)ival-mult: 9.0ms (17% of total)ival-sqrt: 4.0ms (7.6% of total)ival-sub: 2.0ms (3.8% of total)ival-neg: 2.0ms (3.8% of total)exact: 1.0ms (1.9% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x))> |
#<alt (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x)> |
#<alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))> |
#<alt (sqrt.f64 (+.f64 x #s(literal 1 binary64)))> |
#<alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))> |
#<alt (*.f64 #s(literal 1/2 binary64) x)> |
#<alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))> |
#<alt (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))> |
#<alt (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))> |
#<alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))))> |
#<alt (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))> |
#<alt (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))> |
#<alt (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))> |
#<alt (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))> |
#<alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))> |
#<alt (+.f64 x #s(literal 1 binary64))> |
| Outputs |
|---|
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))> |
#<alt (sqrt x)> |
#<alt (- (sqrt x) 1)> |
#<alt (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)> |
#<alt (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))> |
#<alt (* -1 (sqrt x))> |
#<alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))> |
#<alt (/ 2 x)> |
#<alt (/ (+ 2 (* 1/2 x)) x)> |
#<alt (/ (+ 2 (* x (+ 1/2 (* -1/8 x)))) x)> |
#<alt (/ (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) x)> |
#<alt (sqrt (/ 1 x))> |
#<alt (+ (sqrt (/ 1 x)) (/ 1 x))> |
#<alt (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))> |
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))> |
#<alt (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (/ 1 x))> |
#<alt (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* 1/2 (sqrt (/ 1 x))) 1) x)))> |
#<alt (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) 1) x)))> |
#<alt 2> |
#<alt (+ 2 (* 1/2 x))> |
#<alt (+ 2 (* x (+ 1/2 (* -1/8 x))))> |
#<alt (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))> |
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))> |
#<alt (sqrt x)> |
#<alt (- (sqrt x) 1)> |
#<alt (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)> |
#<alt (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))> |
#<alt (* -1 (sqrt x))> |
#<alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))> |
#<alt (sqrt x)> |
#<alt (- (sqrt x) 1)> |
#<alt (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)> |
#<alt (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))> |
#<alt (* -1 (sqrt x))> |
#<alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt 1/2> |
#<alt (+ 1/2 (* -1/8 x))> |
#<alt (+ 1/2 (* -1/8 x))> |
#<alt (+ 1/2 (* -1/8 x))> |
#<alt (* -1/8 x)> |
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* -1/8 x)> |
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))> |
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))> |
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))> |
#<alt (sqrt x)> |
#<alt (- (sqrt x) 1)> |
#<alt (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)> |
#<alt (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))> |
#<alt (* -1 (sqrt x))> |
#<alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* 1/16 (pow x 3))> |
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))> |
#<alt (* 1/16 (pow x 3))> |
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))> |
#<alt 1/2> |
#<alt (+ 1/2 (* -1/8 x))> |
#<alt (+ 1/2 (* x (- (* 1/16 x) 1/8)))> |
#<alt (+ 1/2 (* x (- (* 1/16 x) 1/8)))> |
#<alt (* 1/16 (pow x 2))> |
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))> |
#<alt (* 1/16 (pow x 2))> |
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))))> |
#<alt (* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))))> |
#<alt -1/8> |
#<alt (- (* 1/16 x) 1/8)> |
#<alt (- (* 1/16 x) 1/8)> |
#<alt (- (* 1/16 x) 1/8)> |
#<alt (* 1/16 x)> |
#<alt (* x (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* x (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* x (- 1/16 (* 1/8 (/ 1 x))))> |
#<alt (* 1/16 x)> |
#<alt (* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))> |
#<alt (* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))> |
#<alt (* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))> |
#<alt (sqrt x)> |
#<alt (* x (- (sqrt (/ 1 x)) (/ 1 x)))> |
#<alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x)))> |
#<alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1/2 x)> |
#<alt (* x (- (* 1/8 x) 1/2))> |
#<alt (* x (- (* x (+ 1/8 (* -1/16 x))) 1/2))> |
#<alt (* x (- (* x (+ 1/8 (* x (- (* 5/128 x) 1/16)))) 1/2))> |
#<alt (* -1 (sqrt x))> |
#<alt (* x (- (/ 1 x) (sqrt (/ 1 x))))> |
#<alt (* x (- (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)) (sqrt (/ 1 x))))> |
#<alt (* x (- (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (/ 1 x)) (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))))> |
#<alt (* (sqrt x) (pow (sqrt -1) 2))> |
#<alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))> |
#<alt (* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (- (* -1 (/ (+ 1 (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt 1> |
#<alt (+ 1 x)> |
#<alt (+ 1 x)> |
#<alt (+ 1 x)> |
#<alt x> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt x> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
48 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | 0 | (+ (* x 1/16) -1/8) |
| 1.0ms | x | @ | -inf | (/ (+ 1 (sqrt (+ x 1))) x) |
| 0.0ms | x | @ | -inf | (- 1 (sqrt (+ x 1))) |
| 0.0ms | x | @ | -inf | (* x (+ (* x -1/8) 1/2)) |
| 0.0ms | x | @ | inf | (* x (+ (* x -1/8) 1/2)) |
| 1× | egg-herbie |
| 11 946× | lower-fma.f64 |
| 11 946× | lower-fma.f32 |
| 3 270× | lower-*.f64 |
| 3 270× | lower-*.f32 |
| 3 086× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 277 | 2167 |
| 1 | 829 | 1862 |
| 2 | 2756 | 1777 |
| 3 | 7522 | 1777 |
| 0 | 8423 | 1647 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(- (sqrt x) 1) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(* -1 (sqrt x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(/ 2 x) |
(/ (+ 2 (* 1/2 x)) x) |
(/ (+ 2 (* x (+ 1/2 (* -1/8 x)))) x) |
(/ (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) x) |
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (/ 1 x)) |
(+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))) |
(+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))) |
(* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (/ 1 x)) |
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* 1/2 (sqrt (/ 1 x))) 1) x))) |
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) 1) x))) |
2 |
(+ 2 (* 1/2 x)) |
(+ 2 (* x (+ 1/2 (* -1/8 x)))) |
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (/ 1 x))) |
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(- (sqrt x) 1) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(* -1 (sqrt x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(- (sqrt x) 1) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(* -1 (sqrt x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* -1/8 x))) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
1/2 |
(+ 1/2 (* -1/8 x)) |
(+ 1/2 (* -1/8 x)) |
(+ 1/2 (* -1/8 x)) |
(* -1/8 x) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(* -1/8 x) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(- (sqrt x) 1) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(* -1 (sqrt x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* 1/16 (pow x 3)) |
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x)))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(* 1/16 (pow x 3)) |
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) |
1/2 |
(+ 1/2 (* -1/8 x)) |
(+ 1/2 (* x (- (* 1/16 x) 1/8))) |
(+ 1/2 (* x (- (* 1/16 x) 1/8))) |
(* 1/16 (pow x 2)) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(* 1/16 (pow x 2)) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x)))) |
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x)))) |
-1/8 |
(- (* 1/16 x) 1/8) |
(- (* 1/16 x) 1/8) |
(- (* 1/16 x) 1/8) |
(* 1/16 x) |
(* x (- 1/16 (* 1/8 (/ 1 x)))) |
(* x (- 1/16 (* 1/8 (/ 1 x)))) |
(* x (- 1/16 (* 1/8 (/ 1 x)))) |
(* 1/16 x) |
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16))) |
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16))) |
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x))) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1/2 x) |
(* x (- (* 1/8 x) 1/2)) |
(* x (- (* x (+ 1/8 (* -1/16 x))) 1/2)) |
(* x (- (* x (+ 1/8 (* x (- (* 5/128 x) 1/16)))) 1/2)) |
(* -1 (sqrt x)) |
(* x (- (/ 1 x) (sqrt (/ 1 x)))) |
(* x (- (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)) (sqrt (/ 1 x)))) |
(* x (- (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (/ 1 x)) (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* (sqrt x) (pow (sqrt -1) 2)) |
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))) |
(* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (- (* -1 (/ (+ 1 (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
1 |
(+ 1 x) |
(+ 1 x) |
(+ 1 x) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
| Outputs |
|---|
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(- (sqrt x) 1) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(-.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(-.f64 (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64)))) |
(* -1 (sqrt x)) |
(neg.f64 (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(-.f64 #s(literal -1 binary64) (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(-.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(-.f64 (neg.f64 (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (*.f64 (neg.f64 (sqrt.f64 (*.f64 x (*.f64 x x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))) x) x))) |
(/ 2 x) |
(/.f64 #s(literal 2 binary64) x) |
(/ (+ 2 (* 1/2 x)) x) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 2 binary64)) x) |
(/ (+ 2 (* x (+ 1/2 (* -1/8 x)))) x) |
(/.f64 (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) x) |
(/ (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) x) |
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) x) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(+ (sqrt (/ 1 x)) (/ 1 x)) |
(+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))) |
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x))) |
(+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))) |
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1 binary64) x)))) |
(* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (/ 1 x)) |
(+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* 1/2 (sqrt (/ 1 x))) 1) x))) |
(neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x))) |
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) 1) x))) |
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.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)) x)) |
2 |
#s(literal 2 binary64) |
(+ 2 (* 1/2 x)) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 2 binary64)) |
(+ 2 (* x (+ 1/2 (* -1/8 x)))) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) |
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (/ 1 x))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(-.f64 (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (/.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))) |
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 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(*.f64 x (fma.f64 #s(literal 1/16 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) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(neg.f64 (*.f64 x (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 x (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (-.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
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(-.f64 (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1 binary64))) #s(literal 1 binary64))) |
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (/.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))) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* x (- (* 1/8 x) 1/2)) |
(*.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))) |
(* x (- (* x (+ 1/8 (* -1/16 x))) 1/2)) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal -1/16 binary64) #s(literal 1/8 binary64)) #s(literal -1/2 binary64))) |
(* x (- (* x (+ 1/8 (* x (- (* 5/128 x) 1/16)))) 1/2)) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 5/128 binary64) #s(literal -1/16 binary64)) #s(literal 1/8 binary64)) #s(literal -1/2 binary64))) |
(* -1 (sqrt x)) |
(neg.f64 (sqrt.f64 x)) |
(* x (- (/ 1 x) (sqrt (/ 1 x)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 x) #s(literal 1 binary64)) |
(* x (- (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)) (sqrt (/ 1 x)))) |
(fma.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) |
(* x (- (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (/ 1 x)) (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* (sqrt x) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 x)) |
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 x) #s(literal 1 binary64)) |
(* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 x (-.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* -1 (* x (- (* -1 (/ (+ 1 (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(-.f64 (+.f64 #s(literal 1 binary64) (/.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)) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
1 |
#s(literal 1 binary64) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
| 1× | batch-egg-rewrite |
| 4 426× | lower-fma.f32 |
| 4 420× | lower-fma.f64 |
| 4 268× | lower-*.f32 |
| 4 262× | lower-*.f64 |
| 4 126× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 122 |
| 0 | 41 | 120 |
| 1 | 157 | 119 |
| 2 | 1045 | 119 |
| 0 | 8467 | 118 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x)) |
(/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x) |
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(+.f64 x #s(literal 1 binary64)) |
| Outputs |
|---|
(+.f64 (*.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(+.f64 (*.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (*.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 1 binary64))) |
(+.f64 (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(+.f64 (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) |
(+.f64 (*.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))) |
(+.f64 (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (*.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))) |
(+.f64 (*.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))) |
(+.f64 (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) (*.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x)) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (/.f64 x (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 x (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(fma.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))) |
(fma.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))) |
(fma.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (*.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))) |
(fma.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))) |
(fma.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 1 binary64) (*.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(fma.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 1 binary64))) |
(fma.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(fma.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) |
(neg.f64 (/.f64 x (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(neg.f64 (/.f64 (/.f64 x (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x)) |
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x)) |
(/.f64 (neg.f64 x) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) x)) |
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal -1 binary64) x)) |
(/.f64 (/.f64 x (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) |
(/.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))) (*.f64 (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))) |
(/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) (*.f64 (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (*.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (*.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(/.f64 (*.f64 x (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) (*.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (neg.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))) |
(/.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x))) (*.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x) #s(literal -1 binary64)) |
(pow.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) |
(pow.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x)) #s(literal -1/2 binary64)) |
(pow.f64 (exp.f64 (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(*.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(*.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (/.f64 x (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) x) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 x)) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (fma.f64 x (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) x)) |
(*.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(*.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
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(*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x)))) |
(*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) |
(*.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 x) #s(literal 1 binary64)))) |
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (pow.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))) |
Compiled 21 480 to 2 918 computations (86.4% saved)
10 alts after pruning (6 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 049 | 2 | 1 051 |
| Fresh | 1 | 4 | 5 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 052 | 10 | 1 062 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.7% | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 38.3% | (/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x))) | |
| ▶ | 43.2% | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
| ▶ | 62.3% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
| ▶ | 38.0% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
| ▶ | 62.7% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| ✓ | 64.0% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| ✓ | 62.3% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
| ✓ | 63.8% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
| ▶ | 38.6% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
Compiled 114 to 79 computations (30.7% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) x) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
| ✓ | cost-diff | 0 | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x x) |
| ✓ | cost-diff | 0 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 320 | (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | (+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
| ✓ | cost-diff | 0 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) |
| ✓ | cost-diff | 0 | (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| 684× | lower-fma.f32 |
| 676× | lower-fma.f64 |
| 244× | lower-+.f32 |
| 240× | lower-+.f64 |
| 180× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 27 | 143 |
| 0 | 43 | 143 |
| 1 | 79 | 141 |
| 2 | 147 | 141 |
| 3 | 248 | 141 |
| 4 | 404 | 141 |
| 5 | 481 | 141 |
| 6 | 483 | 141 |
| 0 | 483 | 139 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
x |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) |
(fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) |
#s(literal -5/128 binary64) |
#s(literal 1/16 binary64) |
#s(literal -1/8 binary64) |
#s(literal 1/2 binary64) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
(sqrt.f64 x) |
x |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(sqrt.f64 x) |
x |
#s(literal -1 binary64) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
(fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64))) |
(*.f64 x x) |
x |
#s(literal -1/8 binary64) |
(*.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
x |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) |
(fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) |
#s(literal -5/128 binary64) |
#s(literal 1/16 binary64) |
#s(literal -1/8 binary64) |
#s(literal 1/2 binary64) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
(sqrt.f64 x) |
x |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(sqrt.f64 x) |
x |
#s(literal -1 binary64) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
(fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(*.f64 x x) |
x |
#s(literal -1/8 binary64) |
(*.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(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(literal 1 binary64) |
x |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (+.f64 #s(literal 1 binary64) x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
| ✓ | accuracy | 71.9% | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
| ✓ | accuracy | 100.0% | (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64))) |
| ✓ | accuracy | 100.0% | (*.f64 x x) |
| ✓ | accuracy | 100.0% | (*.f64 x #s(literal 1/2 binary64)) |
| ✓ | accuracy | 62.7% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 100.0% | (+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
| ✓ | accuracy | 69.6% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 70.2% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
| ✓ | accuracy | 100.0% | (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 99.9% | (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 99.9% | (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) |
| ✓ | accuracy | 62.7% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| 17.0ms | 91× | 0 | valid |
| 15.0ms | 53× | 1 | valid |
| 14.0ms | 81× | 0 | invalid |
| 12.0ms | 31× | 2 | valid |
Compiled 125 to 29 computations (76.8% saved)
ival-mult: 11.0ms (28.3% of total)ival-add: 10.0ms (25.8% of total)ival-sqrt: 7.0ms (18% of total)adjust: 6.0ms (15.5% of total)ival-div: 2.0ms (5.2% of total)ival-sub: 2.0ms (5.2% of total)exact: 1.0ms (2.6% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))))> |
#<alt (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))> |
#<alt (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))> |
#<alt (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))> |
#<alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))> |
#<alt (sqrt.f64 x)> |
#<alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))> |
#<alt (+.f64 (sqrt.f64 x) #s(literal -1 binary64))> |
#<alt (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))> |
#<alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64))))> |
#<alt (*.f64 x x)> |
#<alt (*.f64 x #s(literal 1/2 binary64))> |
#<alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))> |
#<alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x))> |
#<alt (+.f64 #s(literal 1 binary64) x)> |
| Outputs |
|---|
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))> |
#<alt (sqrt x)> |
#<alt (- (sqrt x) 1)> |
#<alt (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)> |
#<alt (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))> |
#<alt (* -1 (sqrt x))> |
#<alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))> |
#<alt (* -5/128 (pow x 4))> |
#<alt (* (pow x 4) (- (* 1/16 (/ 1 x)) 5/128))> |
#<alt (* (pow x 4) (- (* 1/16 (/ 1 x)) (+ 5/128 (/ 1/8 (pow x 2)))))> |
#<alt (* (pow x 4) (- (+ (* 1/16 (/ 1 x)) (* 1/2 (/ 1 (pow x 3)))) (+ 5/128 (/ 1/8 (pow x 2)))))> |
#<alt (* -5/128 (pow x 4))> |
#<alt (* (pow x 4) (- (* 1/16 (/ 1 x)) 5/128))> |
#<alt (* (pow x 4) (- (* -1 (/ (- (* 1/8 (/ 1 x)) 1/16) x)) 5/128))> |
#<alt (* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16) x)) 5/128))> |
#<alt 1/2> |
#<alt (+ 1/2 (* -1/8 x))> |
#<alt (+ 1/2 (* x (- (* 1/16 x) 1/8)))> |
#<alt (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))> |
#<alt (* -5/128 (pow x 3))> |
#<alt (* (pow x 3) (- (* 1/16 (/ 1 x)) 5/128))> |
#<alt (* (pow x 3) (- (* 1/16 (/ 1 x)) (+ 5/128 (/ 1/8 (pow x 2)))))> |
#<alt (* (pow x 3) (- (+ (* 1/16 (/ 1 x)) (* 1/2 (/ 1 (pow x 3)))) (+ 5/128 (/ 1/8 (pow x 2)))))> |
#<alt (* -5/128 (pow x 3))> |
#<alt (* -1 (* (pow x 3) (- 5/128 (* 1/16 (/ 1 x)))))> |
#<alt (* -1 (* (pow x 3) (+ 5/128 (* -1 (/ (- 1/16 (* 1/8 (/ 1 x))) x)))))> |
#<alt (* -1 (* (pow x 3) (+ 5/128 (* -1 (/ (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))) x)))))> |
#<alt -1/8> |
#<alt (- (* 1/16 x) 1/8)> |
#<alt (- (* x (+ 1/16 (* -5/128 x))) 1/8)> |
#<alt (- (* x (+ 1/16 (* -5/128 x))) 1/8)> |
#<alt (* -5/128 (pow x 2))> |
#<alt (* (pow x 2) (- (* 1/16 (/ 1 x)) 5/128))> |
#<alt (* (pow x 2) (- (* 1/16 (/ 1 x)) (+ 5/128 (/ 1/8 (pow x 2)))))> |
#<alt (* (pow x 2) (- (* 1/16 (/ 1 x)) (+ 5/128 (/ 1/8 (pow x 2)))))> |
#<alt (* -5/128 (pow x 2))> |
#<alt (* (pow x 2) (- (* 1/16 (/ 1 x)) 5/128))> |
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/8 (/ 1 x)) 1/16) x)) 5/128))> |
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/8 (/ 1 x)) 1/16) x)) 5/128))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))> |
#<alt (sqrt x)> |
#<alt (- (sqrt x) 1)> |
#<alt (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)> |
#<alt (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))> |
#<alt (* -1 (sqrt x))> |
#<alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))> |
#<alt (sqrt x)> |
#<alt (- (sqrt x) 1)> |
#<alt (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)> |
#<alt (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))> |
#<alt (* -1 (sqrt x))> |
#<alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))> |
#<alt (- (sqrt x) 1)> |
#<alt (- (sqrt x) 1)> |
#<alt (- (sqrt x) 1)> |
#<alt (- (sqrt x) 1)> |
#<alt (sqrt x)> |
#<alt (* x (- (sqrt (/ 1 x)) (/ 1 x)))> |
#<alt (* x (- (sqrt (/ 1 x)) (/ 1 x)))> |
#<alt (* x (- (sqrt (/ 1 x)) (/ 1 x)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))> |
#<alt (sqrt x)> |
#<alt (- (sqrt x) 1)> |
#<alt (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)> |
#<alt (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))> |
#<alt (* -1 (sqrt x))> |
#<alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))> |
#<alt (sqrt x)> |
#<alt (* x (- (sqrt (/ 1 x)) (/ 1 x)))> |
#<alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x)))> |
#<alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))> |
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))> |
#<alt 1> |
#<alt (+ 1 x)> |
#<alt (+ 1 x)> |
#<alt (+ 1 x)> |
#<alt x> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt x> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
#<alt (* x (+ 1 (/ 1 x)))> |
45 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | -inf | (sqrt x) |
| 0.0ms | x | @ | inf | (+ (* (* x x) -1/8) (* x 1/2)) |
| 0.0ms | x | @ | inf | (* x (+ (* x (+ (* x (+ (* x -5/128) 1/16)) -1/8)) 1/2)) |
| 0.0ms | x | @ | -inf | (* x (+ (* x (+ (* x (+ (* x -5/128) 1/16)) -1/8)) 1/2)) |
| 0.0ms | x | @ | 0 | (+ (* (* x x) -1/8) (* x 1/2)) |
| 1× | egg-herbie |
| 10 958× | lower-fma.f64 |
| 10 958× | lower-fma.f32 |
| 3 478× | lower-+.f64 |
| 3 478× | lower-+.f32 |
| 2 994× | lower-*.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 212 | 1825 |
| 1 | 647 | 1584 |
| 2 | 2218 | 1505 |
| 3 | 6411 | 1494 |
| 0 | 8111 | 1400 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(- (sqrt x) 1) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(* -1 (sqrt x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(* -5/128 (pow x 4)) |
(* (pow x 4) (- (* 1/16 (/ 1 x)) 5/128)) |
(* (pow x 4) (- (* 1/16 (/ 1 x)) (+ 5/128 (/ 1/8 (pow x 2))))) |
(* (pow x 4) (- (+ (* 1/16 (/ 1 x)) (* 1/2 (/ 1 (pow x 3)))) (+ 5/128 (/ 1/8 (pow x 2))))) |
(* -5/128 (pow x 4)) |
(* (pow x 4) (- (* 1/16 (/ 1 x)) 5/128)) |
(* (pow x 4) (- (* -1 (/ (- (* 1/8 (/ 1 x)) 1/16) x)) 5/128)) |
(* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16) x)) 5/128)) |
1/2 |
(+ 1/2 (* -1/8 x)) |
(+ 1/2 (* x (- (* 1/16 x) 1/8))) |
(+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))) |
(* -5/128 (pow x 3)) |
(* (pow x 3) (- (* 1/16 (/ 1 x)) 5/128)) |
(* (pow x 3) (- (* 1/16 (/ 1 x)) (+ 5/128 (/ 1/8 (pow x 2))))) |
(* (pow x 3) (- (+ (* 1/16 (/ 1 x)) (* 1/2 (/ 1 (pow x 3)))) (+ 5/128 (/ 1/8 (pow x 2))))) |
(* -5/128 (pow x 3)) |
(* -1 (* (pow x 3) (- 5/128 (* 1/16 (/ 1 x))))) |
(* -1 (* (pow x 3) (+ 5/128 (* -1 (/ (- 1/16 (* 1/8 (/ 1 x))) x))))) |
(* -1 (* (pow x 3) (+ 5/128 (* -1 (/ (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))) x))))) |
-1/8 |
(- (* 1/16 x) 1/8) |
(- (* x (+ 1/16 (* -5/128 x))) 1/8) |
(- (* x (+ 1/16 (* -5/128 x))) 1/8) |
(* -5/128 (pow x 2)) |
(* (pow x 2) (- (* 1/16 (/ 1 x)) 5/128)) |
(* (pow x 2) (- (* 1/16 (/ 1 x)) (+ 5/128 (/ 1/8 (pow x 2))))) |
(* (pow x 2) (- (* 1/16 (/ 1 x)) (+ 5/128 (/ 1/8 (pow x 2))))) |
(* -5/128 (pow x 2)) |
(* (pow x 2) (- (* 1/16 (/ 1 x)) 5/128)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/8 (/ 1 x)) 1/16) x)) 5/128)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/8 (/ 1 x)) 1/16) x)) 5/128)) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(- (sqrt x) 1) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(* -1 (sqrt x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(- (sqrt x) 1) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(* -1 (sqrt x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(- (sqrt x) 1) |
(- (sqrt x) 1) |
(- (sqrt x) 1) |
(- (sqrt x) 1) |
(sqrt x) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* -1/8 x))) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(- (sqrt x) 1) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(* -1 (sqrt x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x))) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
1 |
(+ 1 x) |
(+ 1 x) |
(+ 1 x) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
| Outputs |
|---|
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(- (sqrt x) 1) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(+.f64 (sqrt.f64 x) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 x x)) #s(literal -1 binary64))) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(-.f64 (/.f64 #s(literal 1/2 binary64) x) (-.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (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 -1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 x))) |
(* -1 (sqrt x)) |
(neg.f64 (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(-.f64 #s(literal -1 binary64) (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(-.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x)) |
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(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(-.f64 (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal 1 binary64))) |
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(-.f64 (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.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))) (neg.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 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* -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))))) |
(neg.f64 (*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(neg.f64 (*.f64 x (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (neg.f64 x)) |
1 |
#s(literal 1 binary64) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
| 1× | batch-egg-rewrite |
| 4 254× | lower-fma.f32 |
| 4 246× | lower-fma.f64 |
| 4 130× | lower-/.f64 |
| 4 130× | lower-/.f32 |
| 3 778× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 27 | 124 |
| 0 | 43 | 124 |
| 1 | 202 | 122 |
| 2 | 1419 | 122 |
| 0 | 8546 | 119 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
(sqrt.f64 x) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
(*.f64 x x) |
(*.f64 x #s(literal 1/2 binary64)) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) |
(+.f64 (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (*.f64 x #s(literal 1/2 binary64))) |
(-.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) (-.f64 (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (*.f64 x #s(literal 1/2 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (-.f64 (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (*.f64 x #s(literal 1/2 binary64))))) |
(fma.f64 x #s(literal 1/2 binary64) (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) |
(fma.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) (*.f64 x x) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 #s(literal 1/2 binary64) x (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) |
(fma.f64 (*.f64 x x) (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) x (*.f64 x #s(literal 1/2 binary64))) |
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (*.f64 x #s(literal 1/2 binary64))))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (*.f64 x #s(literal 1/2 binary64))) (-.f64 (*.f64 (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) (*.f64 (*.f64 x x) #s(literal 1/4 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) #s(literal 1/4 binary64)) (*.f64 x (*.f64 (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (*.f64 x (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) #s(literal 1/8 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) (*.f64 x (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) #s(literal -1/4 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) #s(literal 1/4 binary64)) (*.f64 x (*.f64 (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (*.f64 (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) #s(literal 1/8 binary64)) x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) (*.f64 (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) #s(literal -1/4 binary64)) x))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (fma.f64 (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (*.f64 x #s(literal 1/2 binary64)))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) (-.f64 (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (*.f64 x #s(literal 1/2 binary64)))) |
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(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) |
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))) |
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(+.f64 x #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) x) |
(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))) |
(+.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) |
(exp.f64 (log1p.f64 x)) |
(exp.f64 (*.f64 (log1p.f64 x) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) #s(literal 1/2 binary64))) |
(fabs.f64 (+.f64 x #s(literal 1 binary64))) |
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x))) |
(-.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) |
(sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) |
(fma.f64 x #s(literal 1 binary64) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1 binary64) x #s(literal 1 binary64)) |
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal 1 binary64)) |
(fma.f64 #s(literal -1 binary64) (neg.f64 x) #s(literal 1 binary64)) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) |
(fma.f64 (/.f64 x (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) (/.f64 x (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))) |
(/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) |
(/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) |
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x)) |
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) |
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (neg.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal 1 binary64) x))) |
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (+.f64 x #s(literal -1 binary64)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x))) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (*.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (neg.f64 (+.f64 x #s(literal -1 binary64))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (fma.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (*.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))))) |
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) |
(pow.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))) |
(*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) |
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) |
(*.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))) |
(*.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) |
(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 x #s(literal -1 binary64))))) |
(*.f64 (pow.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) |
Compiled 12 650 to 1 460 computations (88.5% saved)
13 alts after pruning (4 fresh and 9 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 625 | 3 | 628 |
| Fresh | 0 | 1 | 1 |
| Picked | 0 | 5 | 5 |
| Done | 0 | 4 | 4 |
| Total | 625 | 13 | 638 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.7% | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| ▶ | 38.3% | (/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x))) |
| ✓ | 43.2% | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
| ▶ | 5.7% | (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
| ▶ | 7.7% | (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)) |
| ▶ | 4.5% | (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
| ✓ | 62.3% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
| ✓ | 38.0% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
| ✓ | 62.7% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| ✓ | 64.0% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| ✓ | 62.3% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
| ✓ | 63.8% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
| ✓ | 38.6% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
Compiled 93 to 65 computations (30.1% saved)
| 1× | egg-herbie |
Found 12 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)) |
| ✓ | cost-diff | 0 | (/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x))) |
| ✓ | cost-diff | 0 | (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
| ✓ | cost-diff | 0 | (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) |
| ✓ | cost-diff | 0 | (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
| 48× | lower-+.f64 |
| 48× | lower-+.f32 |
| 44× | lower-fma.f32 |
| 38× | lower-fma.f64 |
| 22× | lower-*.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 106 |
| 0 | 32 | 106 |
| 1 | 53 | 106 |
| 2 | 67 | 106 |
| 3 | 72 | 106 |
| 0 | 72 | 106 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (sqrt (+ 1 x)) (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) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
x |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
#s(literal -1/8 binary64) |
#s(literal 1/2 binary64) |
#s(literal 1 binary64) |
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x))) |
x |
#s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)) |
(sqrt.f64 x) |
| Outputs |
|---|
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(+.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)) |
(+.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(literal -1 binary64)) |
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) |
#s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) |
#s(literal 1/2 binary64) |
x |
#s(literal 1 binary64) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
(+.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) |
#s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
x |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
#s(literal -1/8 binary64) |
#s(literal 1/2 binary64) |
#s(literal 1 binary64) |
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x))) |
x |
#s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)) |
(sqrt.f64 x) |
Found 12 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 99.7% | (/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x))) |
| ✓ | accuracy | 70.2% | #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)) |
| ✓ | accuracy | 100.0% | (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
| ✓ | accuracy | 100.0% | (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 71.9% | (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
| ✓ | accuracy | 62.7% | #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
| ✓ | accuracy | 100.0% | (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
| ✓ | accuracy | 71.9% | (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)) |
| ✓ | accuracy | 65.0% | #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) |
| ✓ | accuracy | 71.9% | (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
| ✓ | accuracy | 64.4% | #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) |
| 77.0ms | 81× | 0 | invalid |
| 13.0ms | 30× | 2 | valid |
| 12.0ms | 98× | 0 | valid |
| 10.0ms | 47× | 1 | valid |
Compiled 76 to 20 computations (73.7% saved)
ival-add: 74.0ms (78.8% of total)ival-sqrt: 6.0ms (6.4% of total)ival-mult: 5.0ms (5.3% of total)adjust: 4.0ms (4.3% of total)ival-div: 2.0ms (2.1% of total)ival-sub: 2.0ms (2.1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#<alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64))> |
#<alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))> |
#<alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64))> |
#<alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))> |
#<alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))> |
#<alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))> |
#<alt #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))> |
#<alt (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))> |
#<alt (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))> |
#<alt (/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)))> |
#<alt #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x))> |
#<alt (sqrt.f64 x)> |
| Outputs |
|---|
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))> |
#<alt (sqrt x)> |
#<alt (* x (- (sqrt (/ 1 x)) (/ 1 x)))> |
#<alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x)))> |
#<alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))> |
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))> |
#<alt (sqrt x)> |
#<alt (* x (- (sqrt (/ 1 x)) (/ 1 x)))> |
#<alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x)))> |
#<alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))> |
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))> |
#<alt (sqrt x)> |
#<alt (* x (- (sqrt (/ 1 x)) (/ 1 x)))> |
#<alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x)))> |
#<alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))> |
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))> |
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))> |
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))> |
#<alt (* -1/8 (pow x 2))> |
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))> |
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))> |
#<alt 1/2> |
#<alt (+ 1/2 (* -1/8 x))> |
#<alt (+ 1/2 (* -1/8 x))> |
#<alt (+ 1/2 (* -1/8 x))> |
#<alt (* -1/8 x)> |
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))> |
#<alt (* -1/8 x)> |
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))> |
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))> |
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* -1/8 x)))> |
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))> |
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))> |
#<alt (sqrt x)> |
#<alt (- (sqrt x) 1)> |
#<alt (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)> |
#<alt (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))> |
#<alt (* -1 (sqrt x))> |
#<alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))> |
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))> |
#<alt 2> |
#<alt (+ 2 (* 1/2 x))> |
#<alt (+ 2 (* x (+ 1/2 (* -1/8 x))))> |
#<alt (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))> |
#<alt (* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
36 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | inf | (+ (* x (+ (* x -1/8) 1/2)) 1) |
| 0.0ms | x | @ | inf | (+ (* 1/2 x) 1) |
| 0.0ms | x | @ | -inf | (+ (* x (+ (* x -1/8) 1/2)) 1) |
| 0.0ms | x | @ | -inf | (- (sqrt (+ 1 x)) 1) |
| 0.0ms | x | @ | -inf | (+ (* 1/2 x) 1) |
| 1× | egg-herbie |
| 18 780× | lower-fma.f64 |
| 18 780× | lower-fma.f32 |
| 3 712× | lower-*.f64 |
| 3 712× | lower-*.f32 |
| 2 710× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 192 | 1722 |
| 1 | 581 | 1520 |
| 2 | 1982 | 1447 |
| 3 | 5886 | 1426 |
| 0 | 8466 | 1262 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x))) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x))) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* 1/2 x)) |
(+ 1 (* 1/2 x)) |
(* 1/2 x) |
(* x (+ 1/2 (/ 1 x))) |
(* x (+ 1/2 (/ 1 x))) |
(* x (+ 1/2 (/ 1 x))) |
(* 1/2 x) |
(* x (+ 1/2 (/ 1 x))) |
(* x (+ 1/2 (/ 1 x))) |
(* x (+ 1/2 (/ 1 x))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x))) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8)) |
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8)) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8)) |
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8)) |
1/2 |
(+ 1/2 (* -1/8 x)) |
(+ 1/2 (* -1/8 x)) |
(+ 1/2 (* -1/8 x)) |
(* -1/8 x) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(* -1/8 x) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(- (sqrt x) 1) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(* -1 (sqrt x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
2 |
(+ 2 (* 1/2 x)) |
(+ 2 (* x (+ 1/2 (* -1/8 x)))) |
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (/ 1 x))) |
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
| Outputs |
|---|
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1 binary64))) |
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (/.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))) |
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 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 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 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1 binary64))) |
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (/.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))) |
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 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 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 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (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 (* 1/2 x)) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(+ 1 (* 1/2 x)) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(* x (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(* x (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(* x (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(* x (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1 binary64))) |
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (/.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))) |
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 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 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 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (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 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* -1/8 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/8 binary64))) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8)) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8)) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* -1/8 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/8 binary64))) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8)) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8)) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* -1/8 x)) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(+ 1/2 (* -1/8 x)) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(+ 1/2 (* -1/8 x)) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(* -1/8 x) |
(*.f64 x #s(literal -1/8 binary64)) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(* -1/8 x) |
(*.f64 x #s(literal -1/8 binary64)) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(- (sqrt x) 1) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(+.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(-.f64 (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (*.f64 x (*.f64 x x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64)))) |
(* -1 (sqrt x)) |
(neg.f64 (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(-.f64 #s(literal -1 binary64) (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(-.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(-.f64 (neg.f64 (sqrt.f64 x)) (+.f64 (/.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))) x) x) #s(literal 1 binary64))) |
2 |
#s(literal 2 binary64) |
(+ 2 (* 1/2 x)) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 2 binary64)) |
(+ 2 (* x (+ 1/2 (* -1/8 x)))) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) |
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (/ 1 x))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(-.f64 (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))) |
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (/.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))) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
| 1× | batch-egg-rewrite |
| 4 544× | lower-/.f32 |
| 4 542× | lower-/.f64 |
| 4 152× | lower-*.f64 |
| 4 152× | lower-*.f32 |
| 3 068× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 97 |
| 0 | 32 | 97 |
| 1 | 159 | 97 |
| 2 | 1162 | 97 |
| 0 | 8271 | 97 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x))) |
#s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)) |
(sqrt.f64 x) |
| Outputs |
|---|
(+.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))) |
(+.f64 (/.f64 (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))) (+.f64 (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))))) |
(+.f64 (/.f64 (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))))) |
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(-.f64 (/.f64 (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))) (+.f64 (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))))) |
(-.f64 (/.f64 (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))))) |
(-.f64 (/.f64 (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))) (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal -1 binary64)))))) |
(fma.f64 #s(literal 1 binary64) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64) #s(literal -1 binary64)) |
(fma.f64 (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))))) |
(fma.f64 (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))))) |
(fma.f64 (/.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))) (/.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal -1 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal -1 binary64)))) (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))) #s(literal -1 binary64)))) |
(/.f64 (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))) #s(literal -1 binary64)) (+.f64 (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))) |
(/.f64 (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))) #s(literal -1 binary64)) (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal -1 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal -1 binary64))))) |
(/.f64 (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))) |
(/.f64 (neg.f64 (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))) #s(literal -1 binary64))) (neg.f64 (+.f64 (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))) #s(literal -1 binary64))) (neg.f64 (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal -1 binary64)))))) |
(/.f64 (neg.f64 (fma.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal -1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))))) |
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))) (-.f64 #s(literal -1 binary64) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))) |
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(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x (*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 (*.f64 x (*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (+.f64 (/.f64 (*.f64 x (*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) (*.f64 x (*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x (*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))))) |
(*.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) (*.f64 x (*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))))) |
(*.f64 (fma.f64 (*.f64 x x) (*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) (*.f64 x (*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x (*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))) |
(+.f64 (*.f64 x #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))) |
(-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))) |
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) |
(fma.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (*.f64 x #s(literal -1/16 binary64)))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64)) (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/16 binary64)))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (*.f64 x #s(literal -1/16 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))) |
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal -1/4 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64))) (neg.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/16 binary64))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (*.f64 x #s(literal -1/16 binary64)))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))) |
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) #s(literal -1/134217728 binary64) #s(literal 1/512 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/262144 binary64) (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/4096 binary64)))) (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/16 binary64))))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/262144 binary64) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64) #s(literal -1/8 binary64)) (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/16 binary64))))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/262144 binary64) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal 1/4 binary64)))) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -1/16 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal 1/4 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/16 binary64)))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/16 binary64))))) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) (*.f64 x #s(literal -1/16 binary64)))))) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/16 binary64)))))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))) |
(*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)) x)) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 x) #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)))) (/.f64 (neg.f64 x) #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)))) |
(neg.f64 (/.f64 (neg.f64 x) #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)) x)) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)) x)))) |
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x))) |
(/.f64 (neg.f64 x) (neg.f64 #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)) x))) |
(pow.f64 (/.f64 #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)) x) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)))) |
(*.f64 x (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)))) |
(*.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x))) x) |
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x))) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) |
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 x) #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)))) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)) x)))) |
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)))) |
(neg.f64 (neg.f64 #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)))) |
(/.f64 #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)) #s(literal 1 binary64)) |
(/.f64 (neg.f64 #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x))) #s(literal -1 binary64)) |
#s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)) |
(*.f64 #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (neg.f64 #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x)))) |
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64))) |
(sqrt.f64 x) |
(pow.f64 x #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(*.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 x) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
Compiled 10 949 to 1 137 computations (89.6% saved)
14 alts after pruning (1 fresh and 13 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 458 | 1 | 459 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 4 | 4 |
| Done | 0 | 9 | 9 |
| Total | 458 | 14 | 472 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.7% | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| ✓ | 38.3% | (/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x))) |
| ✓ | 43.2% | (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
| ✓ | 5.7% | (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
| ✓ | 7.7% | (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)) |
| 4.8% | (-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64)) | |
| ✓ | 4.5% | (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
| ✓ | 62.3% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
| ✓ | 38.0% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
| ✓ | 62.7% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| ✓ | 64.0% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| ✓ | 62.3% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
| ✓ | 63.8% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
| ✓ | 38.6% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
Compiled 208 to 113 computations (45.7% saved)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64)) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 2 binary64)))) |
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x)) |
| Outputs |
|---|
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
2 calls:
| 7.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 5.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | x |
| 99.7% | 1 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64)) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 2 binary64)))) |
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
2 calls:
| 7.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 5.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 2 | x |
| 99.9% | 2 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64)) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 2 binary64)))) |
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (sqrt.f64 x))) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
2 calls:
| 10.0ms | x |
| 5.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 2 | x |
| 99.8% | 2 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64)) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
2 calls:
| 4.0ms | x |
| 4.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 2 | x |
| 99.6% | 2 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64)) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
2 calls:
| 3.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.4% | 2 | x |
| 99.4% | 2 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64)) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
2 calls:
| 3.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.4% | 2 | x |
| 99.4% | 2 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64)) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
2 calls:
| 3.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.4% | 2 | x |
| 98.4% | 2 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64)) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
2 calls:
| 68.0ms | x |
| 2.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.6% | 2 | x |
| 97.6% | 2 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
(-.f64 #s(approx (sqrt (+ 1 x)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64)) |
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
2 calls:
| 2.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 63.8% | 1 | x |
| 63.8% | 1 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
Total -0.0b remaining (-0%)
Threshold costs -0b (-0%)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
| Outputs |
|---|
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
2 calls:
| 1.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 1.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 4.5% | 1 | x |
| 4.5% | 1 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.4461738134021545e-6 | 560.8228079976525 |
Compiled 12 to 10 computations (16.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.4461738134021545e-6 | 560.8228079976525 |
Compiled 12 to 10 computations (16.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.4461738134021545e-6 | 560.8228079976525 |
Compiled 12 to 10 computations (16.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.4461738134021545e-6 | 560.8228079976525 |
Compiled 12 to 10 computations (16.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.4461738134021545e-6 | 560.8228079976525 |
Compiled 12 to 10 computations (16.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.4461738134021545e-6 | 560.8228079976525 |
Compiled 12 to 10 computations (16.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.4461738134021545e-6 | 560.8228079976525 |
Compiled 12 to 10 computations (16.7% saved)
| 1× | egg-herbie |
| 12× | +-commutative_binary64 |
| 10× | *-commutative_binary64 |
| 6× | sub-neg_binary64 |
| 2× | mul-1-neg_binary64 |
| 2× | 1-exp_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 53 | 286 |
| 1 | 67 | 286 |
| 2 | 71 | 286 |
| 3 | 76 | 286 |
| 1× | saturated |
| Inputs |
|---|
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
| Outputs |
|---|
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) |
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(+.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
| 18 662× | lower-fma.f64 |
| 18 662× | lower-fma.f32 |
| 10 958× | lower-fma.f64 |
| 10 958× | lower-fma.f32 |
| 4 426× | lower-fma.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 122 |
| 0 | 41 | 120 |
| 1 | 157 | 119 |
| 2 | 1045 | 119 |
| 0 | 8467 | 118 |
| 0 | 6 | 21 |
| 0 | 10 | 21 |
| 1 | 46 | 21 |
| 2 | 315 | 20 |
| 3 | 3400 | 20 |
| 0 | 8278 | 20 |
| 0 | 212 | 1825 |
| 1 | 647 | 1584 |
| 2 | 2218 | 1505 |
| 3 | 6411 | 1494 |
| 0 | 8111 | 1400 |
| 0 | 161 | 600 |
| 1 | 485 | 505 |
| 2 | 1633 | 483 |
| 3 | 5433 | 474 |
| 0 | 8374 | 430 |
| 1× | fuel |
| 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 |
| 1× | iter limit |
Compiled 411 to 175 computations (57.4% saved)
Compiled 366 to 84 computations (77% saved)
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