
Time bar (total: 5.7s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 0 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 1 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 2 |
| 25% | 25% | 74.9% | 0.1% | 0% | 0% | 0% | 3 |
| 37.5% | 37.5% | 62.4% | 0.1% | 0% | 0% | 0% | 4 |
| 56.3% | 56.2% | 43.7% | 0.1% | 0% | 0% | 0% | 5 |
| 65.6% | 65.6% | 34.3% | 0.1% | 0% | 0% | 0% | 6 |
| 76.6% | 76.5% | 23.4% | 0.1% | 0% | 0% | 0% | 7 |
| 82% | 82% | 18% | 0.1% | 0% | 0% | 0% | 8 |
| 87.9% | 87.8% | 12.1% | 0.1% | 0% | 0% | 0% | 9 |
| 90.8% | 90.7% | 9.2% | 0.1% | 0% | 0% | 0% | 10 |
| 93.8% | 93.8% | 6.1% | 0.1% | 0% | 0% | 0% | 11 |
| 95.4% | 95.3% | 4.6% | 0.1% | 0% | 0% | 0% | 12 |
Compiled 9 to 7 computations (22.2% saved)
| 1.5s | 8 256× | 0 | valid |
ival-div: 365.0ms (53% of total)ival-sub: 278.0ms (40.3% of total)ival-add: 38.0ms (5.5% of total)ival-true: 5.0ms (0.7% of total)ival-assert: 3.0ms (0.4% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 0 | 0 | - | 0 | - | (/.f64 (-.f64 x y) (+.f64 x y)) |
| 0 | 0 | - | 0 | - | y |
| 0 | 0 | - | 0 | - | (-.f64 x y) |
| 0 | 0 | - | 0 | - | (+.f64 x y) |
| 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 |
| 23.0ms | 512× | 0 | valid |
Compiled 43 to 19 computations (55.8% saved)
ival-sub: 3.0ms (32.2% of total)ival-div: 3.0ms (32.2% of total)ival-add: 3.0ms (32.2% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
| 410× | times-frac |
| 304× | lower-fma.f64 |
| 304× | lower-fma.f32 |
| 228× | associate-*l* |
| 182× | div-sub |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 15 | 41 |
| 1 | 50 | 37 |
| 2 | 122 | 35 |
| 3 | 313 | 35 |
| 4 | 821 | 35 |
| 5 | 1352 | 35 |
| 6 | 1401 | 35 |
| 7 | 1441 | 35 |
| 8 | 1484 | 35 |
| 9 | 1496 | 35 |
| 0 | 5 | 7 |
| 0 | 8 | 7 |
| 1 | 14 | 7 |
| 2 | 21 | 7 |
| 3 | 33 | 7 |
| 4 | 60 | 7 |
| 5 | 104 | 7 |
| 6 | 171 | 7 |
| 7 | 279 | 7 |
| 8 | 458 | 7 |
| 9 | 773 | 7 |
| 10 | 781 | 7 |
| 11 | 819 | 7 |
| 12 | 848 | 7 |
| 0 | 848 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(/.f64 (-.f64 x y) (+.f64 x y)) |
| Outputs |
|---|
(/.f64 (-.f64 x y) (+.f64 x y)) |
Compiled 9 to 5 computations (44.4% saved)
Compiled 2 to 2 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 100.0% | (/.f64 (-.f64 x y) (+.f64 x y)) |
Compiled 9 to 5 computations (44.4% saved)
| 1× | egg-herbie |
Found 3 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (+.f64 x y) | |
| cost-diff | 0 | (-.f64 x y) | |
| cost-diff | 0 | (/.f64 (-.f64 x y) (+.f64 x y)) |
| 304× | lower-fma.f64 |
| 304× | lower-fma.f32 |
| 176× | lower-*.f64 |
| 176× | lower-*.f32 |
| 142× | div-sub |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 5 | 15 |
| 0 | 8 | 15 |
| 1 | 14 | 15 |
| 2 | 21 | 15 |
| 3 | 33 | 15 |
| 4 | 60 | 15 |
| 5 | 104 | 15 |
| 6 | 171 | 15 |
| 7 | 279 | 15 |
| 8 | 458 | 15 |
| 9 | 773 | 15 |
| 10 | 781 | 15 |
| 11 | 819 | 15 |
| 12 | 848 | 15 |
| 0 | 848 | 15 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (-.f64 x y) (+.f64 x y)) |
(-.f64 x y) |
x |
y |
(+.f64 x y) |
| Outputs |
|---|
(/.f64 (-.f64 x y) (+.f64 x y)) |
(-.f64 x y) |
x |
y |
(+.f64 x y) |
Found 3 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (-.f64 x y) | |
| accuracy | 0 | (+.f64 x y) | |
| accuracy | 0.01953125 | (/.f64 (-.f64 x y) (+.f64 x y)) |
| 12.0ms | 256× | 0 | valid |
Compiled 17 to 7 computations (58.8% saved)
ival-sub: 2.0ms (43.7% of total)ival-div: 2.0ms (43.7% of total)ival-add: 1.0ms (21.8% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ()) |
#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ()) |
#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt -1 (taylor 0 x) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (* 2 (/ x y)) 1) (taylor 0 x) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1) (taylor 0 x) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (* x (+ (* x (- (* 2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 1) (taylor 0 x) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor inf x) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* -1 (/ y x))) (/ y x)) (taylor inf x) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (* -1 (/ (* y (- (* -1 y) y)) (pow x 2))))) (/ y x)) (taylor inf x) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3)))) (+ (/ y x) (/ (* y (- (* -1 y) y)) (pow x 2)))) (taylor inf x) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor -inf x) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* -1 (/ y x))) (/ y x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (/ (* y (- (* -1 y) y)) x)) x))) (taylor -inf x) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (* -1 (/ (+ (* -1 (* y (- (* -1 y) y))) (/ (* (pow y 2) (- (* -1 y) y)) x)) x))) x))) (taylor -inf x) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -2 (/ y x))) (taylor 0 y) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt -1 (taylor inf y) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ x y) (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (* -1 (/ (* x (- x (* -1 x))) (pow y 2))) (/ x y)) (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (/ x y) (/ (* (pow x 2) (- x (* -1 x))) (pow y 3))) (+ 1 (+ (* -1 (/ x y)) (/ (* x (- x (* -1 x))) (pow y 2))))) (taylor inf y) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt -1 (taylor -inf y) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1 (/ (- (* -1 x) x) y)) 1) (taylor -inf y) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (* x (- (* -1 x) x)) y))) x) y)) 1) (taylor -inf y) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (- (* -1 (/ (* (pow x 2) (- (* -1 x) x)) y)) (* -1 (* x (- (* -1 x) x)))) y))) x) y)) 1) (taylor -inf y) (#s(alt (/.f64 (-.f64 x y) (+.f64 x y)) (patch (/.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor 0 x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (- x y) (taylor 0 x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (- x y) (taylor 0 x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (- x y) (taylor 0 x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* y (- (/ x y) 1)) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* y (- (/ x y) 1)) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* y (- (/ x y) 1)) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (+ 1 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (+ 1 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (+ 1 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt y (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt y (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt y (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ()) |
18 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | inf | (/ (- x y) (+ x y)) |
| 0.0ms | y | @ | -inf | (/ (- x y) (+ x y)) |
| 0.0ms | x | @ | -inf | (/ (- x y) (+ x y)) |
| 0.0ms | y | @ | inf | (/ (- x y) (+ x y)) |
| 0.0ms | x | @ | 0 | (/ (- x y) (+ x y)) |
| 1× | egg-herbie |
| 11 876× | lower-fma.f64 |
| 11 876× | lower-fma.f32 |
| 3 410× | lower-*.f64 |
| 3 410× | lower-*.f32 |
| 2 360× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 142 | 462 |
| 1 | 439 | 432 |
| 2 | 1229 | 387 |
| 3 | 4744 | 375 |
| 0 | 8368 | 351 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
-1 |
(- (* 2 (/ x y)) 1) |
(- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1) |
(- (* x (+ (* x (- (* 2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 1) |
1 |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(- (+ 1 (+ (* -1 (/ y x)) (* -1 (/ (* y (- (* -1 y) y)) (pow x 2))))) (/ y x)) |
(- (+ 1 (+ (* -1 (/ y x)) (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3)))) (+ (/ y x) (/ (* y (- (* -1 y) y)) (pow x 2)))) |
1 |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (/ (* y (- (* -1 y) y)) x)) x))) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (* -1 (/ (+ (* -1 (* y (- (* -1 y) y))) (/ (* (pow y 2) (- (* -1 y) y)) x)) x))) x))) |
1 |
(+ 1 (* -2 (/ y x))) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) |
-1 |
(- (/ x y) (+ 1 (* -1 (/ x y)))) |
(- (+ (* -1 (/ (* x (- x (* -1 x))) (pow y 2))) (/ x y)) (+ 1 (* -1 (/ x y)))) |
(- (+ (/ x y) (/ (* (pow x 2) (- x (* -1 x))) (pow y 3))) (+ 1 (+ (* -1 (/ x y)) (/ (* x (- x (* -1 x))) (pow y 2))))) |
-1 |
(- (* -1 (/ (- (* -1 x) x) y)) 1) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (* x (- (* -1 x) x)) y))) x) y)) 1) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (- (* -1 (/ (* (pow x 2) (- (* -1 x) x)) y)) (* -1 (* x (- (* -1 x) x)))) y))) x) y)) 1) |
(* -1 y) |
(- x y) |
(- x y) |
(- x y) |
x |
(* x (+ 1 (* -1 (/ y x)))) |
(* x (+ 1 (* -1 (/ y x)))) |
(* x (+ 1 (* -1 (/ y x)))) |
x |
(* -1 (* x (- (/ y x) 1))) |
(* -1 (* x (- (/ y x) 1))) |
(* -1 (* x (- (/ y x) 1))) |
x |
(+ x (* -1 y)) |
(+ x (* -1 y)) |
(+ x (* -1 y)) |
(* -1 y) |
(* y (- (/ x y) 1)) |
(* y (- (/ x y) 1)) |
(* y (- (/ x y) 1)) |
(* -1 y) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
y |
(+ x y) |
(+ x y) |
(+ x y) |
x |
(* x (+ 1 (/ y x))) |
(* x (+ 1 (/ y x))) |
(* x (+ 1 (/ y x))) |
x |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
x |
(+ x y) |
(+ x y) |
(+ x y) |
y |
(* y (+ 1 (/ x y))) |
(* y (+ 1 (/ x y))) |
(* y (+ 1 (/ x y))) |
y |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
| Outputs |
|---|
-1 |
#s(literal -1 binary64) |
(- (* 2 (/ x y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1) |
(-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x (+.f64 (/.f64 (+.f64 x x) y) #s(literal -2 binary64))) y)) |
(- (* x (+ (* x (- (* 2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (-.f64 x (/.f64 (*.f64 x (fma.f64 x (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 x x) y)) x)) y))) y)) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -1 (/ y x)) (* -1 (/ (* y (- (* -1 y) y)) (pow x 2))))) (/ y x)) |
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 y (fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 2 binary64))) x)) |
(- (+ 1 (+ (* -1 (/ y x)) (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3)))) (+ (/ y x) (/ (* y (- (* -1 y) y)) (pow x 2)))) |
(+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (*.f64 y (*.f64 y (fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 2 binary64)))) x) (+.f64 y y)) x)) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (/ (* y (- (* -1 y) y)) x)) x))) |
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 y (fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 2 binary64))) x)) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (* -1 (/ (+ (* -1 (* y (- (* -1 y) y))) (/ (* (pow y 2) (- (* -1 y) y)) x)) x))) x))) |
(+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (*.f64 y (*.f64 y (fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 2 binary64)))) x) (+.f64 y y)) x)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -2 (/ y x))) |
(fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 y (fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 2 binary64))) x)) |
(+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) |
(+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (*.f64 y (*.f64 y (fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 2 binary64)))) x) (+.f64 y y)) x)) |
-1 |
#s(literal -1 binary64) |
(- (/ x y) (+ 1 (* -1 (/ x y)))) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(- (+ (* -1 (/ (* x (- x (* -1 x))) (pow y 2))) (/ x y)) (+ 1 (* -1 (/ x y)))) |
(-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x (+.f64 (/.f64 (+.f64 x x) y) #s(literal -2 binary64))) y)) |
(- (+ (/ x y) (/ (* (pow x 2) (- x (* -1 x))) (pow y 3))) (+ 1 (+ (* -1 (/ x y)) (/ (* x (- x (* -1 x))) (pow y 2))))) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (-.f64 x (/.f64 (*.f64 x (fma.f64 x (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 x x) y)) x)) y))) y)) |
-1 |
#s(literal -1 binary64) |
(- (* -1 (/ (- (* -1 x) x) y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (* x (- (* -1 x) x)) y))) x) y)) 1) |
(-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x (+.f64 (/.f64 (+.f64 x x) y) #s(literal -2 binary64))) y)) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (- (* -1 (/ (* (pow x 2) (- (* -1 x) x)) y)) (* -1 (* x (- (* -1 x) x)))) y))) x) y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (-.f64 x (/.f64 (*.f64 x (fma.f64 x (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 x x) y)) x)) y))) y)) |
(* -1 y) |
(neg.f64 y) |
(- x y) |
(-.f64 x y) |
(- x y) |
(-.f64 x y) |
(- x y) |
(-.f64 x y) |
x |
(* x (+ 1 (* -1 (/ y x)))) |
(-.f64 x y) |
(* x (+ 1 (* -1 (/ y x)))) |
(-.f64 x y) |
(* x (+ 1 (* -1 (/ y x)))) |
(-.f64 x y) |
x |
(* -1 (* x (- (/ y x) 1))) |
(-.f64 x y) |
(* -1 (* x (- (/ y x) 1))) |
(-.f64 x y) |
(* -1 (* x (- (/ y x) 1))) |
(-.f64 x y) |
x |
(+ x (* -1 y)) |
(-.f64 x y) |
(+ x (* -1 y)) |
(-.f64 x y) |
(+ x (* -1 y)) |
(-.f64 x y) |
(* -1 y) |
(neg.f64 y) |
(* y (- (/ x y) 1)) |
(-.f64 x y) |
(* y (- (/ x y) 1)) |
(-.f64 x y) |
(* y (- (/ x y) 1)) |
(-.f64 x y) |
(* -1 y) |
(neg.f64 y) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
(-.f64 x y) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
(-.f64 x y) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
(-.f64 x y) |
y |
(+ x y) |
(+.f64 x y) |
(+ x y) |
(+.f64 x y) |
(+ x y) |
(+.f64 x y) |
x |
(* x (+ 1 (/ y x))) |
(+.f64 x y) |
(* x (+ 1 (/ y x))) |
(+.f64 x y) |
(* x (+ 1 (/ y x))) |
(+.f64 x y) |
x |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(+.f64 x y) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(+.f64 x y) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(+.f64 x y) |
x |
(+ x y) |
(+.f64 x y) |
(+ x y) |
(+.f64 x y) |
(+ x y) |
(+.f64 x y) |
y |
(* y (+ 1 (/ x y))) |
(+.f64 x y) |
(* y (+ 1 (/ x y))) |
(+.f64 x y) |
(* y (+ 1 (/ x y))) |
(+.f64 x y) |
y |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(+.f64 x y) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(+.f64 x y) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(+.f64 x y) |
| 3 962× | lower-*.f64 |
| 3 962× | lower-*.f32 |
| 3 438× | lower-/.f32 |
| 3 436× | lower-/.f64 |
| 2 768× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 5 | 13 |
| 0 | 8 | 13 |
| 1 | 39 | 13 |
| 2 | 309 | 13 |
| 3 | 5153 | 13 |
| 0 | 8671 | 13 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (-.f64 x y) (+.f64 x y)) |
(-.f64 x y) |
(+.f64 x y) |
| Outputs |
|---|
(+.f64 (/.f64 x (+.f64 x y)) (/.f64 y (-.f64 (neg.f64 y) x))) |
(+.f64 (/.f64 x (+.f64 x y)) (*.f64 #s(literal 1 binary64) (/.f64 y (-.f64 (neg.f64 y) x)))) |
(+.f64 (/.f64 x (+.f64 x y)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (neg.f64 y))) |
(+.f64 (/.f64 (*.f64 x x) (*.f64 (+.f64 x y) (+.f64 x y))) (neg.f64 (/.f64 (*.f64 y y) (*.f64 (+.f64 x y) (+.f64 x y))))) |
(+.f64 (/.f64 (*.f64 x x) (*.f64 (+.f64 x y) (+.f64 x y))) (*.f64 (/.f64 y (-.f64 (neg.f64 y) x)) (/.f64 y (+.f64 x y)))) |
(+.f64 (/.f64 y (-.f64 (neg.f64 y) x)) (/.f64 x (+.f64 x y))) |
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (neg.f64 y)) (/.f64 x (+.f64 x y))) |
(+.f64 (*.f64 (/.f64 (-.f64 x y) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (*.f64 x x)) (*.f64 (/.f64 (-.f64 x y) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (*.f64 y (-.f64 y x)))) |
(+.f64 (*.f64 (/.f64 (-.f64 x y) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (*.f64 y (-.f64 y x))) (*.f64 (/.f64 (-.f64 x y) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (*.f64 x x))) |
(+.f64 (*.f64 (/.f64 x (+.f64 x y)) #s(literal 1 binary64)) (*.f64 (/.f64 y (-.f64 (neg.f64 y) x)) #s(literal 1 binary64))) |
(+.f64 (*.f64 (*.f64 x x) (/.f64 (-.f64 x y) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 y (-.f64 y x)) (/.f64 (-.f64 x y) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))))) |
(+.f64 (*.f64 (*.f64 y (-.f64 y x)) (/.f64 (-.f64 x y) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 x x) (/.f64 (-.f64 x y) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 x y) (-.f64 x y))) #s(literal -1 binary64))) |
(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y))) |
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 y x) (+.f64 x y))) |
(-.f64 (/.f64 (*.f64 x x) (*.f64 (+.f64 x y) (+.f64 x y))) (/.f64 (*.f64 y y) (*.f64 (+.f64 x y) (+.f64 x y)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 (neg.f64 y) x)) (/.f64 (-.f64 y x) (+.f64 x y))) |
(-.f64 (/.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 y (+.f64 x y) (*.f64 x x))) (+.f64 x y)) (/.f64 (/.f64 (*.f64 y (*.f64 y y)) (fma.f64 y (+.f64 x y) (*.f64 x x))) (+.f64 x y))) |
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x y) (fma.f64 y (+.f64 x y) (*.f64 x x)))) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 (+.f64 x y) (fma.f64 y (+.f64 x y) (*.f64 x x))))) |
(-.f64 (/.f64 (*.f64 x (+.f64 x y)) (*.f64 (+.f64 x y) (+.f64 x y))) (/.f64 (*.f64 y (+.f64 x y)) (*.f64 (+.f64 x y) (+.f64 x y)))) |
(-.f64 (/.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 x y))) (fma.f64 (/.f64 y (+.f64 x y)) #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 (+.f64 x y) (+.f64 x y))))) (/.f64 (/.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 x y))) (fma.f64 (/.f64 y (+.f64 x y)) #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 (+.f64 x y) (+.f64 x y)))))) |
(-.f64 (/.f64 (/.f64 (*.f64 x x) (*.f64 (+.f64 x y) (+.f64 x y))) #s(literal 1 binary64)) (/.f64 (/.f64 (*.f64 y y) (*.f64 (+.f64 x y) (+.f64 x y))) #s(literal 1 binary64))) |
(fma.f64 x (/.f64 #s(literal 1 binary64) (+.f64 x y)) (/.f64 y (-.f64 (neg.f64 y) x))) |
(fma.f64 x (/.f64 #s(literal 1 binary64) (+.f64 x y)) (*.f64 #s(literal 1 binary64) (/.f64 y (-.f64 (neg.f64 y) x)))) |
(fma.f64 x (/.f64 #s(literal 1 binary64) (+.f64 x y)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (neg.f64 y))) |
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (/.f64 x (+.f64 x y))) (neg.f64 (/.f64 (*.f64 y y) (*.f64 (+.f64 x y) (+.f64 x y))))) |
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (/.f64 x (+.f64 x y))) (*.f64 (/.f64 y (-.f64 (neg.f64 y) x)) (/.f64 y (+.f64 x y)))) |
(fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 x y)) (/.f64 x (+.f64 x y))) |
(fma.f64 (-.f64 x y) (/.f64 x (*.f64 (-.f64 x y) (+.f64 x y))) (/.f64 y (-.f64 (neg.f64 y) x))) |
(fma.f64 (-.f64 x y) (/.f64 x (*.f64 (-.f64 x y) (+.f64 x y))) (*.f64 #s(literal 1 binary64) (/.f64 y (-.f64 (neg.f64 y) x)))) |
(fma.f64 (-.f64 x y) (/.f64 x (*.f64 (-.f64 x y) (+.f64 x y))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (neg.f64 y))) |
(fma.f64 (/.f64 x (+.f64 x y)) (/.f64 x (+.f64 x y)) (neg.f64 (/.f64 (*.f64 y y) (*.f64 (+.f64 x y) (+.f64 x y))))) |
(fma.f64 (/.f64 x (+.f64 x y)) (/.f64 x (+.f64 x y)) (*.f64 (/.f64 y (-.f64 (neg.f64 y) x)) (/.f64 y (+.f64 x y)))) |
(fma.f64 (/.f64 x (+.f64 x y)) #s(literal 1 binary64) (*.f64 (/.f64 y (-.f64 (neg.f64 y) x)) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x x) (/.f64 (-.f64 x y) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 y (-.f64 y x)) (/.f64 (-.f64 x y) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))))) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x y) (+.f64 x y))) (neg.f64 (/.f64 (*.f64 y y) (*.f64 (+.f64 x y) (+.f64 x y))))) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x y) (+.f64 x y))) (*.f64 (/.f64 y (-.f64 (neg.f64 y) x)) (/.f64 y (+.f64 x y)))) |
(fma.f64 (*.f64 y (-.f64 y x)) (/.f64 (-.f64 x y) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (/.f64 (-.f64 x y) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))))) |
(fma.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (/.f64 x (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (/.f64 y (-.f64 (neg.f64 y) x))) |
(fma.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (/.f64 x (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1 binary64) (/.f64 y (-.f64 (neg.f64 y) x)))) |
(fma.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (/.f64 x (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (neg.f64 y))) |
(fma.f64 #s(literal 1 binary64) (/.f64 x (+.f64 x y)) (/.f64 y (-.f64 (neg.f64 y) x))) |
(fma.f64 #s(literal 1 binary64) (/.f64 x (+.f64 x y)) (*.f64 #s(literal 1 binary64) (/.f64 y (-.f64 (neg.f64 y) x)))) |
(fma.f64 #s(literal 1 binary64) (/.f64 x (+.f64 x y)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (neg.f64 y))) |
(fma.f64 (neg.f64 y) (/.f64 #s(literal 1 binary64) (+.f64 x y)) (/.f64 x (+.f64 x y))) |
(fma.f64 #s(literal -1 binary64) (/.f64 y (+.f64 x y)) (/.f64 x (+.f64 x y))) |
(fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (+.f64 x y)) (/.f64 y (-.f64 (neg.f64 y) x))) |
(fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (+.f64 x y)) (*.f64 #s(literal 1 binary64) (/.f64 y (-.f64 (neg.f64 y) x)))) |
(fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (+.f64 x y)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (neg.f64 y))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) x (/.f64 y (-.f64 (neg.f64 y) x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) x (*.f64 #s(literal 1 binary64) (/.f64 y (-.f64 (neg.f64 y) x)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) x (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (neg.f64 y))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (neg.f64 y) (/.f64 x (+.f64 x y))) |
(fma.f64 (/.f64 y (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (neg.f64 (fma.f64 x (-.f64 x y) (*.f64 y y))) (/.f64 x (+.f64 x y))) |
(fma.f64 (/.f64 y (*.f64 (-.f64 x y) (+.f64 x y))) (-.f64 y x) (/.f64 x (+.f64 x y))) |
(fma.f64 (/.f64 (-.f64 x y) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (*.f64 x x) (*.f64 (/.f64 (-.f64 x y) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (*.f64 y (-.f64 y x)))) |
(fma.f64 (/.f64 (-.f64 x y) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (*.f64 y (-.f64 y x)) (*.f64 (/.f64 (-.f64 x y) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (*.f64 x x))) |
(fma.f64 (/.f64 x (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (fma.f64 x (-.f64 x y) (*.f64 y y)) (/.f64 y (-.f64 (neg.f64 y) x))) |
(fma.f64 (/.f64 x (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 #s(literal 1 binary64) (/.f64 y (-.f64 (neg.f64 y) x)))) |
(fma.f64 (/.f64 x (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (neg.f64 y))) |
(fma.f64 (/.f64 x (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (/.f64 x (+.f64 x y))) (neg.f64 (/.f64 (*.f64 y y) (*.f64 (+.f64 x y) (+.f64 x y))))) |
(fma.f64 (/.f64 x (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (/.f64 x (+.f64 x y))) (*.f64 (/.f64 y (-.f64 (neg.f64 y) x)) (/.f64 y (+.f64 x y)))) |
(fma.f64 (/.f64 x (*.f64 (-.f64 x y) (+.f64 x y))) (-.f64 x y) (/.f64 y (-.f64 (neg.f64 y) x))) |
(fma.f64 (/.f64 x (*.f64 (-.f64 x y) (+.f64 x y))) (-.f64 x y) (*.f64 #s(literal 1 binary64) (/.f64 y (-.f64 (neg.f64 y) x)))) |
(fma.f64 (/.f64 x (*.f64 (-.f64 x y) (+.f64 x y))) (-.f64 x y) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (neg.f64 y))) |
(fma.f64 (/.f64 x (*.f64 (-.f64 x y) (+.f64 x y))) (*.f64 (-.f64 x y) (/.f64 x (+.f64 x y))) (neg.f64 (/.f64 (*.f64 y y) (*.f64 (+.f64 x y) (+.f64 x y))))) |
(fma.f64 (/.f64 x (*.f64 (-.f64 x y) (+.f64 x y))) (*.f64 (-.f64 x y) (/.f64 x (+.f64 x y))) (*.f64 (/.f64 y (-.f64 (neg.f64 y) x)) (/.f64 y (+.f64 x y)))) |
(fma.f64 (*.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x y)) (/.f64 y (-.f64 (neg.f64 y) x))) |
(fma.f64 (*.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x y)) (*.f64 #s(literal 1 binary64) (/.f64 y (-.f64 (neg.f64 y) x)))) |
(fma.f64 (*.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x y)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (neg.f64 y))) |
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(/.f64 (neg.f64 (*.f64 (fma.f64 y (+.f64 x y) (*.f64 x x)) (-.f64 y x))) (neg.f64 (neg.f64 (fma.f64 x (-.f64 x y) (*.f64 y y))))) |
(/.f64 (/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (*.f64 (/.f64 (+.f64 x y) (fma.f64 y (+.f64 x y) (*.f64 x x))) #s(literal 1 binary64))) (fma.f64 x (-.f64 x y) (*.f64 y y))) |
(/.f64 (-.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (-.f64 x y) (-.f64 x y)) (-.f64 x y))) (/.f64 (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))) (*.f64 (*.f64 (-.f64 y x) (-.f64 y x)) (-.f64 y x)))) (fma.f64 (/.f64 (*.f64 x x) (-.f64 x y)) (/.f64 (*.f64 x x) (-.f64 x y)) (fma.f64 (/.f64 (*.f64 y y) (-.f64 x y)) (/.f64 (*.f64 y y) (-.f64 x y)) (*.f64 (/.f64 (*.f64 x x) (-.f64 x y)) (/.f64 (*.f64 y y) (-.f64 x y)))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x y)) (/.f64 (*.f64 x x) (-.f64 x y))) (*.f64 (/.f64 (*.f64 y y) (-.f64 x y)) (/.f64 (*.f64 y y) (-.f64 x y)))) (fma.f64 x (/.f64 x (-.f64 x y)) (/.f64 (*.f64 y y) (-.f64 x y)))) |
(/.f64 (*.f64 (*.f64 (/.f64 (+.f64 x y) (fma.f64 y (+.f64 x y) (*.f64 x x))) #s(literal 1 binary64)) (fma.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 x y)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (fma.f64 (*.f64 y (+.f64 x y)) (-.f64 (*.f64 y (+.f64 x y)) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x))))) |
(/.f64 (*.f64 (*.f64 (/.f64 (+.f64 x y) (fma.f64 y (+.f64 x y) (*.f64 x x))) #s(literal 1 binary64)) (*.f64 (fma.f64 y (+.f64 x y) (*.f64 x x)) (-.f64 (*.f64 x x) (*.f64 y (+.f64 x y))))) (-.f64 (*.f64 x x) (*.f64 y (+.f64 x y)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x y) (*.f64 y y)))) (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) (-.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x)))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x y) (*.f64 y y)))) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) |
(/.f64 (*.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 x y))) (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (*.f64 x (*.f64 x (*.f64 x x))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (-.f64 x y) (+.f64 x y))) (/.f64 #s(literal 1 binary64) (-.f64 x y))) (fma.f64 x x (*.f64 y y))) |
(/.f64 (/.f64 (*.f64 (+.f64 x y) (-.f64 y x)) #s(literal -1 binary64)) (-.f64 x y)) |
(pow.f64 (+.f64 x y) #s(literal 1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(*.f64 (+.f64 x y) #s(literal 1 binary64)) |
(*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (/.f64 (+.f64 x y) (fma.f64 x (-.f64 x y) (*.f64 y y)))) |
(*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 (+.f64 x y) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x y) (*.f64 y y))))) |
(*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x y) (*.f64 y y)))) |
(*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x y) (*.f64 y y))) #s(literal 1 binary64))) |
(*.f64 (fma.f64 y (+.f64 x y) (*.f64 x x)) (*.f64 (/.f64 (+.f64 x y) (fma.f64 y (+.f64 x y) (*.f64 x x))) #s(literal 1 binary64))) |
(*.f64 #s(literal 1 binary64) (+.f64 x y)) |
(*.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (/.f64 #s(literal 1 binary64) (-.f64 x y))) |
(*.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y)) #s(literal 1 binary64))) |
(*.f64 #s(literal -1 binary64) (-.f64 (neg.f64 y) x)) |
(*.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (-.f64 y x))) |
(*.f64 (*.f64 (fma.f64 y (+.f64 x y) (*.f64 x x)) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (-.f64 x y) (*.f64 y y))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y)) (*.f64 (-.f64 x y) (+.f64 x y))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x y) (*.f64 y y))) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) |
(*.f64 (/.f64 (+.f64 x y) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (/.f64 (-.f64 x y) (/.f64 #s(literal 1 binary64) (fma.f64 y (+.f64 x y) (*.f64 x x))))) |
(*.f64 (*.f64 (/.f64 (+.f64 x y) (fma.f64 y (+.f64 x y) (*.f64 x x))) #s(literal 1 binary64)) (fma.f64 y (+.f64 x y) (*.f64 x x))) |
(*.f64 (*.f64 (/.f64 (+.f64 x y) (fma.f64 y (+.f64 x y) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 (fma.f64 y (+.f64 x y) (*.f64 x x)) #s(literal 1 binary64))) |
(*.f64 (/.f64 (+.f64 x y) (*.f64 (/.f64 (+.f64 x y) (fma.f64 y (+.f64 x y) (*.f64 x x))) #s(literal 1 binary64))) (/.f64 (-.f64 x y) (fma.f64 x (-.f64 x y) (*.f64 y y)))) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 (/.f64 (+.f64 x y) (fma.f64 y (+.f64 x y) (*.f64 x x))) #s(literal 1 binary64))) (fma.f64 y (+.f64 x y) (*.f64 x x))) |
(*.f64 (/.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (*.f64 (-.f64 x y) (+.f64 x y))) (-.f64 (neg.f64 y) x)) |
(*.f64 (/.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (neg.f64 (fma.f64 y (+.f64 x y) (*.f64 x x)))) |
(*.f64 (/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (*.f64 (+.f64 x y) (-.f64 y x))) (-.f64 (neg.f64 y) x)) |
(*.f64 (/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (*.f64 (fma.f64 y (+.f64 x y) (*.f64 x x)) (-.f64 y x))) (neg.f64 (fma.f64 y (+.f64 x y) (*.f64 x x)))) |
(*.f64 (/.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 (-.f64 y x) (-.f64 y x)) (-.f64 y x))))) (fma.f64 (*.f64 y (-.f64 y x)) (-.f64 (*.f64 y (-.f64 y x)) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x))))) |
(*.f64 (/.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (-.f64 (*.f64 x x) (*.f64 y (-.f64 y x))))) (-.f64 (*.f64 x x) (*.f64 y (-.f64 y x)))) |
Compiled 14 469 to 1 238 computations (91.4% saved)
7 alts after pruning (6 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 554 | 6 | 560 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 554 | 7 | 561 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (/.f64 (-.f64 x y) (+.f64 x y)) |
| ▶ | 56.9% | (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) |
| ▶ | 99.8% | (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) |
| 43.8% | #s(approx (/ (- x y) (+ x y)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 y (fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 2 binary64))) x))) | |
| ▶ | 56.7% | #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) |
| ▶ | 43.7% | #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) |
| ▶ | 55.8% | #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) |
Compiled 115 to 73 computations (36.5% saved)
| 1× | egg-herbie |
Found 14 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (+.f64 x x) | |
| cost-diff | 0 | (/.f64 (+.f64 x x) y) | |
| cost-diff | 0 | (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) | |
| cost-diff | 0 | #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) | |
| cost-diff | 0 | (+.f64 x y) | |
| cost-diff | 0 | (neg.f64 y) | |
| cost-diff | 0 | #s(approx (- x y) (neg.f64 y)) | |
| cost-diff | 0 | (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) | |
| cost-diff | 0 | #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) | |
| cost-diff | 0 | (-.f64 x y) | |
| cost-diff | 0 | (+.f64 x y) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (+.f64 x y)) | |
| cost-diff | 320 | (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) |
| 768× | lower-fma.f64 |
| 768× | lower-fma.f32 |
| 432× | lower-*.f32 |
| 430× | lower-*.f64 |
| 256× | times-frac |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 20 | 99 |
| 0 | 29 | 99 |
| 1 | 44 | 97 |
| 2 | 69 | 97 |
| 3 | 143 | 97 |
| 4 | 235 | 97 |
| 5 | 337 | 97 |
| 6 | 483 | 97 |
| 7 | 685 | 97 |
| 8 | 1027 | 97 |
| 9 | 1255 | 97 |
| 10 | 1362 | 97 |
| 11 | 1417 | 97 |
| 12 | 1447 | 97 |
| 13 | 1459 | 97 |
| 14 | 1484 | 97 |
| 15 | 1492 | 97 |
| 0 | 1492 | 95 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) |
(/.f64 #s(literal 1 binary64) (+.f64 x y)) |
#s(literal 1 binary64) |
(+.f64 x y) |
x |
y |
(-.f64 x y) |
#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) |
#s(literal -1 binary64) |
#s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) |
#s(approx (- x y) (neg.f64 y)) |
(neg.f64 y) |
y |
(+.f64 x y) |
x |
#s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
#s(literal -1 binary64) |
(/.f64 (+.f64 x x) y) |
(+.f64 x x) |
x |
y |
| Outputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) |
(/.f64 (-.f64 x y) (+.f64 x y)) |
(/.f64 #s(literal 1 binary64) (+.f64 x y)) |
#s(literal 1 binary64) |
(+.f64 x y) |
x |
y |
(-.f64 x y) |
#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) |
#s(literal -1 binary64) |
#s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) |
#s(approx (- x y) (neg.f64 y)) |
(neg.f64 y) |
y |
(+.f64 x y) |
x |
#s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) |
#s(approx (/ (- x y) (+ x y)) (fma.f64 #s(literal 2 binary64) (/.f64 x y) #s(literal -1 binary64))) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(fma.f64 #s(literal 2 binary64) (/.f64 x y) #s(literal -1 binary64)) |
#s(literal -1 binary64) |
(/.f64 (+.f64 x x) y) |
(+.f64 x x) |
x |
y |
Found 14 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (/.f64 (+.f64 x x) y) | |
| accuracy | 0 | (+.f64 x x) | |
| accuracy | 0 | (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) | |
| accuracy | 27.686949538346948 | #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) | |
| accuracy | 0 | (+.f64 x y) | |
| accuracy | 0 | (neg.f64 y) | |
| accuracy | 0.01953125 | (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) | |
| accuracy | 27.750643003318256 | #s(approx (- x y) (neg.f64 y)) | |
| accuracy | 36.03116071657593 | #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) | |
| accuracy | 28.276924980265004 | #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) | |
| accuracy | 0 | (-.f64 x y) | |
| accuracy | 0 | (+.f64 x y) | |
| accuracy | 0.00390625 | (/.f64 #s(literal 1 binary64) (+.f64 x y)) | |
| accuracy | 0.135097509768442 | (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) |
| 30.0ms | 256× | 0 | valid |
Compiled 83 to 15 computations (81.9% saved)
ival-div: 8.0ms (44.6% of total)ival-add: 6.0ms (33.4% of total)ival-mult: 2.0ms (11.1% of total)ival-sub: 1.0ms (5.6% of total)ival-neg: 1.0ms (5.6% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) (patch (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (+.f64 x y)) (patch (/.f64 #s(literal 1 binary64) (+.f64 x y)) #<representation binary64>) () ()) |
#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ()) |
#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) (patch #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) (patch (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) #<representation binary64>) () ()) |
#s(alt #s(approx (- x y) (neg.f64 y)) (patch #s(approx (- x y) (neg.f64 y)) #<representation binary64>) () ()) |
#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) (patch #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) #<representation binary64>) () ()) |
#s(alt (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) (patch (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) #<representation binary64>) () ()) |
#s(alt (/.f64 (+.f64 x x) y) (patch (/.f64 (+.f64 x x) y) #<representation binary64>) () ()) |
#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt -1 (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) (patch (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (* 2 (/ x y)) 1) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) (patch (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) (patch (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (* x (+ (* x (- (* 2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 1) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) (patch (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) (patch (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* -1 (/ y x))) (/ y x)) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) (patch (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (* -1 (/ (* y (- (* -1 y) y)) (pow x 2))))) (/ y x)) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) (patch (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3)))) (+ (/ y x) (/ (* y (- (* -1 y) y)) (pow x 2)))) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) (patch (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) (patch (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* -1 (/ y x))) (/ y x)) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) (patch (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (/ (* y (- (* -1 y) y)) x)) x))) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) (patch (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) #<representation binary64>) () ())) ()) |
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#s(alt (- (+ 1 (* -1 (/ y x))) (/ y x)) (taylor inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) (patch #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (* -1 (/ (* y (- (* -1 y) y)) (pow x 2))))) (/ y x)) (taylor inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) (patch #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3)))) (+ (/ y x) (/ (* y (- (* -1 y) y)) (pow x 2)))) (taylor inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) (patch #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor -inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) (patch #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* -1 (/ y x))) (/ y x)) (taylor -inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) (patch #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) #<representation binary64>) () ())) ()) |
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#s(alt (+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (* -1 (/ (+ (* -1 (* y (- (* -1 y) y))) (/ (* (pow y 2) (- (* -1 y) y)) x)) x))) x))) (taylor -inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) (patch #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) (patch #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -2 (/ y x))) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) (patch #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) #<representation binary64>) () ())) ()) |
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#s(alt (- (+ (* -1 (/ (* x (- x (* -1 x))) (pow y 2))) (/ x y)) (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) (patch #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) #<representation binary64>) () ())) ()) |
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#s(alt (- (* 2 (/ x y)) 1) (taylor 0 x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) (patch (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) #<representation binary64>) () ())) ()) |
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#s(alt (* -1 (* x (- (/ 1 x) (* 2 (/ 1 y))))) (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) (patch (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) #<representation binary64>) () ())) ()) |
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#s(alt (/ (+ (* -1 y) (* 2 x)) y) (taylor 0 y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) (patch (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1 y) (* 2 x)) y) (taylor 0 y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) (patch (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1 y) (* 2 x)) y) (taylor 0 y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) (patch (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) #<representation binary64>) () ())) ()) |
#s(alt -1 (taylor inf y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) (patch (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) #<representation binary64>) () ())) ()) |
#s(alt (- (* 2 (/ x y)) 1) (taylor inf y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) (patch (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) #<representation binary64>) () ())) ()) |
#s(alt (- (* 2 (/ x y)) 1) (taylor inf y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) (patch (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) #<representation binary64>) () ())) ()) |
#s(alt (- (* 2 (/ x y)) 1) (taylor inf y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) (patch (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) #<representation binary64>) () ())) ()) |
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#s(alt (* 2 (/ x y)) (taylor -inf y) (#s(alt (/.f64 (+.f64 x x) y) (patch (/.f64 (+.f64 x x) y) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ()) |
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#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ()) |
72 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | inf | (/ (+ x x) y) |
| 0.0ms | y | @ | inf | (neg y) |
| 0.0ms | x | @ | inf | (+ -1 (/ (+ x x) y)) |
| 0.0ms | x | @ | inf | (+ x x) |
| 0.0ms | y | @ | 0 | (+ -1 (/ (+ x x) y)) |
| 1× | egg-herbie |
| 17 652× | lower-fma.f64 |
| 17 652× | lower-fma.f32 |
| 4 986× | lower-*.f64 |
| 4 986× | lower-*.f32 |
| 2 602× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 241 | 2690 |
| 1 | 733 | 2460 |
| 2 | 1997 | 2092 |
| 3 | 7570 | 2092 |
| 0 | 8249 | 1944 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
-1 |
(- (* 2 (/ x y)) 1) |
(- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1) |
(- (* x (+ (* x (- (* 2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 1) |
1 |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(- (+ 1 (+ (* -1 (/ y x)) (* -1 (/ (* y (- (* -1 y) y)) (pow x 2))))) (/ y x)) |
(- (+ 1 (+ (* -1 (/ y x)) (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3)))) (+ (/ y x) (/ (* y (- (* -1 y) y)) (pow x 2)))) |
1 |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (/ (* y (- (* -1 y) y)) x)) x))) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (* -1 (/ (+ (* -1 (* y (- (* -1 y) y))) (/ (* (pow y 2) (- (* -1 y) y)) x)) x))) x))) |
1 |
(+ 1 (* -2 (/ y x))) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) |
-1 |
(- (/ x y) (+ 1 (* -1 (/ x y)))) |
(- (+ (* -1 (/ (* x (- x (* -1 x))) (pow y 2))) (/ x y)) (+ 1 (* -1 (/ x y)))) |
(- (+ (/ x y) (/ (* (pow x 2) (- x (* -1 x))) (pow y 3))) (+ 1 (+ (* -1 (/ x y)) (/ (* x (- x (* -1 x))) (pow y 2))))) |
-1 |
(- (* -1 (/ (- (* -1 x) x) y)) 1) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (* x (- (* -1 x) x)) y))) x) y)) 1) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (- (* -1 (/ (* (pow x 2) (- (* -1 x) x)) y)) (* -1 (* x (- (* -1 x) x)))) y))) x) y)) 1) |
(/ 1 y) |
(+ (* -1 (/ x (pow y 2))) (/ 1 y)) |
(+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y)) |
(+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y)) |
(/ 1 x) |
(/ (+ 1 (* -1 (/ y x))) x) |
(/ (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) x) |
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) x) |
(/ 1 x) |
(* -1 (/ (- (/ y x) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (/ (pow y 2) x) y) x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (pow y 2)) x)) y) x)) 1) x)) |
(/ 1 x) |
(+ (* -1 (/ y (pow x 2))) (/ 1 x)) |
(+ (* y (- (/ y (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x)) |
(+ (* y (- (* y (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x)) |
(/ 1 y) |
(/ (+ 1 (* -1 (/ x y))) y) |
(/ (- (+ 1 (/ (pow x 2) (pow y 2))) (/ x y)) y) |
(/ (- (+ 1 (* -1 (/ (pow x 3) (pow y 3)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))) y) |
(/ 1 y) |
(* -1 (/ (- (/ x y) 1) y)) |
(* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) x) y)) 1) y)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y)) x) y)) 1) y)) |
y |
(+ x y) |
(+ x y) |
(+ x y) |
x |
(* x (+ 1 (/ y x))) |
(* x (+ 1 (/ y x))) |
(* x (+ 1 (/ y x))) |
x |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
x |
(+ x y) |
(+ x y) |
(+ x y) |
y |
(* y (+ 1 (/ x y))) |
(* y (+ 1 (/ x y))) |
(* y (+ 1 (/ x y))) |
y |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(* -1 y) |
(- x y) |
(- x y) |
(- x y) |
x |
(* x (+ 1 (* -1 (/ y x)))) |
(* x (+ 1 (* -1 (/ y x)))) |
(* x (+ 1 (* -1 (/ y x)))) |
x |
(* -1 (* x (- (/ y x) 1))) |
(* -1 (* x (- (/ y x) 1))) |
(* -1 (* x (- (/ y x) 1))) |
x |
(+ x (* -1 y)) |
(+ x (* -1 y)) |
(+ x (* -1 y)) |
(* -1 y) |
(* y (- (/ x y) 1)) |
(* y (- (/ x y) 1)) |
(* y (- (/ x y) 1)) |
(* -1 y) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
-1 |
(- (* 2 (/ x y)) 1) |
(- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1) |
(- (* x (+ (* x (- (* 2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 1) |
1 |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(- (+ 1 (+ (* -1 (/ y x)) (* -1 (/ (* y (- (* -1 y) y)) (pow x 2))))) (/ y x)) |
(- (+ 1 (+ (* -1 (/ y x)) (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3)))) (+ (/ y x) (/ (* y (- (* -1 y) y)) (pow x 2)))) |
1 |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (/ (* y (- (* -1 y) y)) x)) x))) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (* -1 (/ (+ (* -1 (* y (- (* -1 y) y))) (/ (* (pow y 2) (- (* -1 y) y)) x)) x))) x))) |
1 |
(+ 1 (* -2 (/ y x))) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) |
-1 |
(- (/ x y) (+ 1 (* -1 (/ x y)))) |
(- (+ (* -1 (/ (* x (- x (* -1 x))) (pow y 2))) (/ x y)) (+ 1 (* -1 (/ x y)))) |
(- (+ (/ x y) (/ (* (pow x 2) (- x (* -1 x))) (pow y 3))) (+ 1 (+ (* -1 (/ x y)) (/ (* x (- x (* -1 x))) (pow y 2))))) |
-1 |
(- (* -1 (/ (- (* -1 x) x) y)) 1) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (* x (- (* -1 x) x)) y))) x) y)) 1) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (- (* -1 (/ (* (pow x 2) (- (* -1 x) x)) y)) (* -1 (* x (- (* -1 x) x)))) y))) x) y)) 1) |
-1 |
(- (* 2 (/ x y)) 1) |
(- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1) |
(- (* x (+ (* x (- (* 2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 1) |
1 |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(- (+ 1 (+ (* -1 (/ y x)) (* -1 (/ (* y (- (* -1 y) y)) (pow x 2))))) (/ y x)) |
(- (+ 1 (+ (* -1 (/ y x)) (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3)))) (+ (/ y x) (/ (* y (- (* -1 y) y)) (pow x 2)))) |
1 |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (/ (* y (- (* -1 y) y)) x)) x))) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (* -1 (/ (+ (* -1 (* y (- (* -1 y) y))) (/ (* (pow y 2) (- (* -1 y) y)) x)) x))) x))) |
1 |
(+ 1 (* -2 (/ y x))) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) |
-1 |
(- (/ x y) (+ 1 (* -1 (/ x y)))) |
(- (+ (* -1 (/ (* x (- x (* -1 x))) (pow y 2))) (/ x y)) (+ 1 (* -1 (/ x y)))) |
(- (+ (/ x y) (/ (* (pow x 2) (- x (* -1 x))) (pow y 3))) (+ 1 (+ (* -1 (/ x y)) (/ (* x (- x (* -1 x))) (pow y 2))))) |
-1 |
(- (* -1 (/ (- (* -1 x) x) y)) 1) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (* x (- (* -1 x) x)) y))) x) y)) 1) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (- (* -1 (/ (* (pow x 2) (- (* -1 x) x)) y)) (* -1 (* x (- (* -1 x) x)))) y))) x) y)) 1) |
-1 |
(- (* 2 (/ x y)) 1) |
(- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1) |
(- (* x (+ (* x (- (* 2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 1) |
1 |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(- (+ 1 (+ (* -1 (/ y x)) (* -1 (/ (* y (- (* -1 y) y)) (pow x 2))))) (/ y x)) |
(- (+ 1 (+ (* -1 (/ y x)) (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3)))) (+ (/ y x) (/ (* y (- (* -1 y) y)) (pow x 2)))) |
1 |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (/ (* y (- (* -1 y) y)) x)) x))) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (* -1 (/ (+ (* -1 (* y (- (* -1 y) y))) (/ (* (pow y 2) (- (* -1 y) y)) x)) x))) x))) |
1 |
(+ 1 (* -2 (/ y x))) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) |
-1 |
(- (/ x y) (+ 1 (* -1 (/ x y)))) |
(- (+ (* -1 (/ (* x (- x (* -1 x))) (pow y 2))) (/ x y)) (+ 1 (* -1 (/ x y)))) |
(- (+ (/ x y) (/ (* (pow x 2) (- x (* -1 x))) (pow y 3))) (+ 1 (+ (* -1 (/ x y)) (/ (* x (- x (* -1 x))) (pow y 2))))) |
-1 |
(- (* -1 (/ (- (* -1 x) x) y)) 1) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (* x (- (* -1 x) x)) y))) x) y)) 1) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (- (* -1 (/ (* (pow x 2) (- (* -1 x) x)) y)) (* -1 (* x (- (* -1 x) x)))) y))) x) y)) 1) |
(* -1 y) |
(- x y) |
(- x y) |
(- x y) |
x |
(* x (+ 1 (* -1 (/ y x)))) |
(* x (+ 1 (* -1 (/ y x)))) |
(* x (+ 1 (* -1 (/ y x)))) |
x |
(* -1 (* x (- (/ y x) 1))) |
(* -1 (* x (- (/ y x) 1))) |
(* -1 (* x (- (/ y x) 1))) |
x |
(+ x (* -1 y)) |
(+ x (* -1 y)) |
(+ x (* -1 y)) |
(* -1 y) |
(* y (- (/ x y) 1)) |
(* y (- (/ x y) 1)) |
(* y (- (/ x y) 1)) |
(* -1 y) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
-1 |
(- (* 2 (/ x y)) 1) |
(- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1) |
(- (* x (+ (* x (- (* 2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 1) |
1 |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(- (+ 1 (+ (* -1 (/ y x)) (* -1 (/ (* y (- (* -1 y) y)) (pow x 2))))) (/ y x)) |
(- (+ 1 (+ (* -1 (/ y x)) (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3)))) (+ (/ y x) (/ (* y (- (* -1 y) y)) (pow x 2)))) |
1 |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (/ (* y (- (* -1 y) y)) x)) x))) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (* -1 (/ (+ (* -1 (* y (- (* -1 y) y))) (/ (* (pow y 2) (- (* -1 y) y)) x)) x))) x))) |
1 |
(+ 1 (* -2 (/ y x))) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) |
-1 |
(- (/ x y) (+ 1 (* -1 (/ x y)))) |
(- (+ (* -1 (/ (* x (- x (* -1 x))) (pow y 2))) (/ x y)) (+ 1 (* -1 (/ x y)))) |
(- (+ (/ x y) (/ (* (pow x 2) (- x (* -1 x))) (pow y 3))) (+ 1 (+ (* -1 (/ x y)) (/ (* x (- x (* -1 x))) (pow y 2))))) |
-1 |
(- (* -1 (/ (- (* -1 x) x) y)) 1) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (* x (- (* -1 x) x)) y))) x) y)) 1) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (- (* -1 (/ (* (pow x 2) (- (* -1 x) x)) y)) (* -1 (* x (- (* -1 x) x)))) y))) x) y)) 1) |
-1 |
(- (* 2 (/ x y)) 1) |
(- (* 2 (/ x y)) 1) |
(- (* 2 (/ x y)) 1) |
(* 2 (/ x y)) |
(* x (- (* 2 (/ 1 y)) (/ 1 x))) |
(* x (- (* 2 (/ 1 y)) (/ 1 x))) |
(* x (- (* 2 (/ 1 y)) (/ 1 x))) |
(* 2 (/ x y)) |
(* -1 (* x (- (/ 1 x) (* 2 (/ 1 y))))) |
(* -1 (* x (- (/ 1 x) (* 2 (/ 1 y))))) |
(* -1 (* x (- (/ 1 x) (* 2 (/ 1 y))))) |
(* 2 (/ x y)) |
(/ (+ (* -1 y) (* 2 x)) y) |
(/ (+ (* -1 y) (* 2 x)) y) |
(/ (+ (* -1 y) (* 2 x)) y) |
-1 |
(- (* 2 (/ x y)) 1) |
(- (* 2 (/ x y)) 1) |
(- (* 2 (/ x y)) 1) |
-1 |
(- (* 2 (/ x y)) 1) |
(- (* 2 (/ x y)) 1) |
(- (* 2 (/ x y)) 1) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 (/ x y)) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
| Outputs |
|---|
-1 |
#s(literal -1 binary64) |
(- (* 2 (/ x y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1) |
(-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x (+.f64 (/.f64 (+.f64 x x) y) #s(literal -2 binary64))) y)) |
(- (* x (+ (* x (- (* 2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 1) |
(fma.f64 x (*.f64 #s(literal 2 binary64) (/.f64 (fma.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 x y)) y) #s(literal 1 binary64)) y)) #s(literal -1 binary64)) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -1 (/ y x)) (* -1 (/ (* y (- (* -1 y) y)) (pow x 2))))) (/ y x)) |
(fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -1 (/ y x)) (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3)))) (+ (/ y x) (/ (* y (- (* -1 y) y)) (pow x 2)))) |
(fma.f64 y (fma.f64 y (fma.f64 #s(literal -2 binary64) (/.f64 y (*.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) (*.f64 x x))) (/.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (/ (* y (- (* -1 y) y)) x)) x))) |
(fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64)) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (* -1 (/ (+ (* -1 (* y (- (* -1 y) y))) (/ (* (pow y 2) (- (* -1 y) y)) x)) x))) x))) |
(+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (*.f64 y (*.f64 y (fma.f64 #s(literal -2 binary64) (/.f64 y x) #s(literal 2 binary64)))) x) (+.f64 y y)) x)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -2 (/ y x))) |
(fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64)) |
(+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) |
(fma.f64 y (fma.f64 y (fma.f64 #s(literal -2 binary64) (/.f64 y (*.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) (*.f64 x x))) (/.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) |
-1 |
#s(literal -1 binary64) |
(- (/ x y) (+ 1 (* -1 (/ x y)))) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(- (+ (* -1 (/ (* x (- x (* -1 x))) (pow y 2))) (/ x y)) (+ 1 (* -1 (/ x y)))) |
(-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x (+.f64 (/.f64 (+.f64 x x) y) #s(literal -2 binary64))) y)) |
(- (+ (/ x y) (/ (* (pow x 2) (- x (* -1 x))) (pow y 3))) (+ 1 (+ (* -1 (/ x y)) (/ (* x (- x (* -1 x))) (pow y 2))))) |
(-.f64 (fma.f64 x (*.f64 x (/.f64 (+.f64 x x) (*.f64 y (*.f64 y y)))) #s(literal -1 binary64)) (/.f64 (*.f64 x (+.f64 (/.f64 (+.f64 x x) y) #s(literal -2 binary64))) y)) |
-1 |
#s(literal -1 binary64) |
(- (* -1 (/ (- (* -1 x) x) y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (* x (- (* -1 x) x)) y))) x) y)) 1) |
(-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x (+.f64 (/.f64 (+.f64 x x) y) #s(literal -2 binary64))) y)) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (- (* -1 (/ (* (pow x 2) (- (* -1 x) x)) y)) (* -1 (* x (- (* -1 x) x)))) y))) x) y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (-.f64 x (/.f64 (*.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal -2 binary64) y) #s(literal 1 binary64)) x)) y))) y)) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(+ (* -1 (/ x (pow y 2))) (/ 1 y)) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y) |
(+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y)) |
(/.f64 (fma.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 x y)) y) #s(literal 1 binary64)) y) |
(+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y)) |
(fma.f64 x (-.f64 (/.f64 x (*.f64 y (*.f64 y y))) (*.f64 x (/.f64 x (pow.f64 y #s(literal 4 binary64))))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ (+ 1 (* -1 (/ y x))) x) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x) |
(/ (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) x) |
(/.f64 (fma.f64 y (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64)) x) |
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) x) |
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 y (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y y) x) y)) x)) x)) (neg.f64 x)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(* -1 (/ (- (/ y x) 1) x)) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x) |
(* -1 (/ (- (* -1 (/ (- (/ (pow y 2) x) y) x)) 1) x)) |
(/.f64 (fma.f64 y (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64)) x) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (pow y 2)) x)) y) x)) 1) x)) |
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 y (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y y) x) y)) x)) x)) (neg.f64 x)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(+ (* -1 (/ y (pow x 2))) (/ 1 x)) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x) |
(+ (* y (- (/ y (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x)) |
(/.f64 (fma.f64 y (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64)) x) |
(+ (* y (- (* y (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x)) |
(fma.f64 y (-.f64 (/.f64 y (*.f64 x (*.f64 x x))) (/.f64 (*.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ (+ 1 (* -1 (/ x y))) y) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y) |
(/ (- (+ 1 (/ (pow x 2) (pow y 2))) (/ x y)) y) |
(/.f64 (fma.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 x y)) y) #s(literal 1 binary64)) y) |
(/ (- (+ 1 (* -1 (/ (pow x 3) (pow y 3)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))) y) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (neg.f64 x) (/.f64 (*.f64 x (-.f64 (/.f64 (*.f64 x x) y) x)) y)) y)) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(* -1 (/ (- (/ x y) 1) y)) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y) |
(* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) x) y)) 1) y)) |
(/.f64 (fma.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 x y)) y) #s(literal 1 binary64)) y) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y)) x) y)) 1) y)) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (neg.f64 x) (/.f64 (*.f64 x (-.f64 (/.f64 (*.f64 x x) y) x)) y)) y)) y) |
y |
(+ x y) |
(+.f64 x y) |
(+ x y) |
(+.f64 x y) |
(+ x y) |
(+.f64 x y) |
x |
(* x (+ 1 (/ y x))) |
(+.f64 x y) |
(* x (+ 1 (/ y x))) |
(+.f64 x y) |
(* x (+ 1 (/ y x))) |
(+.f64 x y) |
x |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(+.f64 x y) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(+.f64 x y) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(+.f64 x y) |
x |
(+ x y) |
(+.f64 x y) |
(+ x y) |
(+.f64 x y) |
(+ x y) |
(+.f64 x y) |
y |
(* y (+ 1 (/ x y))) |
(fma.f64 x (/.f64 y y) y) |
(* y (+ 1 (/ x y))) |
(fma.f64 x (/.f64 y y) y) |
(* y (+ 1 (/ x y))) |
(fma.f64 x (/.f64 y y) y) |
y |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(fma.f64 x (/.f64 y y) y) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(fma.f64 x (/.f64 y y) y) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(fma.f64 x (/.f64 y y) y) |
(* -1 y) |
(neg.f64 y) |
(- x y) |
(-.f64 x y) |
(- x y) |
(-.f64 x y) |
(- x y) |
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(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(- (* 2 (/ x y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* x (- (* 2 (/ 1 y)) (/ 1 x))) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(* x (- (* 2 (/ 1 y)) (/ 1 x))) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(* x (- (* 2 (/ 1 y)) (/ 1 x))) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* -1 (* x (- (/ 1 x) (* 2 (/ 1 y))))) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(* -1 (* x (- (/ 1 x) (* 2 (/ 1 y))))) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(* -1 (* x (- (/ 1 x) (* 2 (/ 1 y))))) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(/ (+ (* -1 y) (* 2 x)) y) |
(/.f64 (+.f64 x (-.f64 x y)) y) |
(/ (+ (* -1 y) (* 2 x)) y) |
(/.f64 (+.f64 x (-.f64 x y)) y) |
(/ (+ (* -1 y) (* 2 x)) y) |
(/.f64 (+.f64 x (-.f64 x y)) y) |
-1 |
#s(literal -1 binary64) |
(- (* 2 (/ x y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(- (* 2 (/ x y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(- (* 2 (/ x y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
-1 |
#s(literal -1 binary64) |
(- (* 2 (/ x y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(- (* 2 (/ x y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(- (* 2 (/ x y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 (/ x y)) |
(/.f64 (+.f64 x x) y) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
| 436× | lower-/.f32 |
| 430× | lower-/.f64 |
| 360× | lower-*.f32 |
| 358× | lower-*.f64 |
| 184× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 20 | 86 |
| 0 | 29 | 84 |
| 1 | 101 | 84 |
| 0 | 772 | 82 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) |
(/.f64 #s(literal 1 binary64) (+.f64 x y)) |
(+.f64 x y) |
(-.f64 x y) |
#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) |
#s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) |
(/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) |
#s(approx (- x y) (neg.f64 y)) |
(neg.f64 y) |
#s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(/.f64 (+.f64 x x) y) |
(+.f64 x x) |
| Outputs |
|---|
(+.f64 (/.f64 x (+.f64 x y)) (neg.f64 (/.f64 y (+.f64 x y)))) |
(+.f64 (/.f64 x (+.f64 x y)) (*.f64 (neg.f64 y) (/.f64 #s(literal 1 binary64) (+.f64 x y)))) |
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) x) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (neg.f64 y))) |
(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y))) |
(fma.f64 x (/.f64 #s(literal 1 binary64) (+.f64 x y)) (neg.f64 (/.f64 y (+.f64 x y)))) |
(fma.f64 x (/.f64 #s(literal 1 binary64) (+.f64 x y)) (*.f64 (neg.f64 y) (/.f64 #s(literal 1 binary64) (+.f64 x y)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) x (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (neg.f64 y))) |
(fma.f64 (/.f64 x (fma.f64 x (*.f64 x x) (*.f64 y (*.f64 y y)))) (fma.f64 y (-.f64 y x) (*.f64 x x)) (neg.f64 (/.f64 y (+.f64 x y)))) |
(fma.f64 (/.f64 x (fma.f64 x (*.f64 x x) (*.f64 y (*.f64 y y)))) (fma.f64 y (-.f64 y x) (*.f64 x x)) (*.f64 (neg.f64 y) (/.f64 #s(literal 1 binary64) (+.f64 x y)))) |
(fma.f64 (/.f64 x (*.f64 (+.f64 x y) (-.f64 x y))) (-.f64 x y) (neg.f64 (/.f64 y (+.f64 x y)))) |
(fma.f64 (/.f64 x (*.f64 (+.f64 x y) (-.f64 x y))) (-.f64 x y) (*.f64 (neg.f64 y) (/.f64 #s(literal 1 binary64) (+.f64 x y)))) |
(neg.f64 (/.f64 (-.f64 x y) (neg.f64 (+.f64 x y)))) |
(neg.f64 (/.f64 (neg.f64 (-.f64 x y)) (+.f64 x y))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x y) (-.f64 x y))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 x y) (-.f64 x y)) #s(literal 1 binary64))) |
(/.f64 (-.f64 x y) (+.f64 x y)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x y) (-.f64 x y)))) |
(/.f64 (neg.f64 (-.f64 x y)) (neg.f64 (+.f64 x y))) |
(/.f64 (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)) (*.f64 (+.f64 x y) (fma.f64 x x (*.f64 y (+.f64 x y))))) |
(/.f64 (*.f64 (+.f64 x y) (-.f64 x y)) (*.f64 (+.f64 x y) (+.f64 x y))) |
(/.f64 (-.f64 (*.f64 x (+.f64 x y)) (*.f64 (+.f64 x y) y)) (*.f64 (+.f64 x y) (+.f64 x y))) |
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))) (*.f64 (+.f64 x y) (fma.f64 x x (*.f64 y (+.f64 x y))))) |
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (+.f64 x y) (-.f64 x y))) (*.f64 (+.f64 x y) (+.f64 x y))) |
(/.f64 (*.f64 #s(literal -1 binary64) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))) (*.f64 (neg.f64 (+.f64 x y)) (fma.f64 x x (*.f64 y (+.f64 x y))))) |
(/.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 x y) (-.f64 x y))) (*.f64 (neg.f64 (+.f64 x y)) (+.f64 x y))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)) #s(literal 1 binary64)) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (+.f64 x y))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)) #s(literal -1 binary64)) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (neg.f64 (+.f64 x y)))) |
(/.f64 (*.f64 (*.f64 (+.f64 x y) (-.f64 x y)) #s(literal 1 binary64)) (*.f64 (+.f64 x y) (+.f64 x y))) |
(/.f64 (*.f64 (*.f64 (+.f64 x y) (-.f64 x y)) #s(literal -1 binary64)) (*.f64 (+.f64 x y) (neg.f64 (+.f64 x y)))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 x y))) (neg.f64 (neg.f64 (+.f64 x y)))) |
(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x y)) #s(literal 3 binary64)) (pow.f64 (/.f64 y (+.f64 x y)) #s(literal 3 binary64))) (fma.f64 (/.f64 x (+.f64 x y)) (/.f64 x (+.f64 x y)) (fma.f64 (/.f64 y (+.f64 x y)) (/.f64 y (+.f64 x y)) (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))))) |
(/.f64 (-.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 x (+.f64 x y))) (*.f64 (/.f64 y (+.f64 x y)) (/.f64 y (+.f64 x y)))) (+.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))) |
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))) (fma.f64 x x (*.f64 y (+.f64 x y)))) |
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (*.f64 (+.f64 x y) (-.f64 x y))) (+.f64 x y)) |
(/.f64 (*.f64 (-.f64 x y) #s(literal -1 binary64)) (neg.f64 (+.f64 x y))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (+.f64 x y))) (fma.f64 x x (*.f64 y (+.f64 x y)))) |
(pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (+.f64 x y))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) |
(*.f64 (-.f64 x y) (/.f64 #s(literal 1 binary64) (+.f64 x y))) |
(*.f64 (neg.f64 (-.f64 x y)) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 x y)))) |
(*.f64 (/.f64 (-.f64 x y) (*.f64 (+.f64 x y) (-.f64 x y))) (-.f64 x y)) |
(*.f64 (/.f64 (-.f64 x y) (fma.f64 x (*.f64 x x) (*.f64 y (*.f64 y y)))) (fma.f64 y (-.f64 y x) (*.f64 x x))) |
(exp.f64 (*.f64 (log.f64 (+.f64 x y)) #s(literal -1 binary64))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 x y))) |
(/.f64 #s(literal 1 binary64) (+.f64 x y)) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (+.f64 x y)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (+.f64 x y))) |
(pow.f64 (+.f64 x y) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x y))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 x y)))) |
(*.f64 (pow.f64 (+.f64 x y) #s(literal -1/2 binary64)) (pow.f64 (+.f64 x y) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) (*.f64 y (*.f64 y y)))) (fma.f64 y (-.f64 y x) (*.f64 x x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x y) (-.f64 x y))) (-.f64 x y)) |
(+.f64 x y) |
(+.f64 y x) |
(-.f64 (/.f64 (*.f64 x x) (-.f64 x y)) (/.f64 (*.f64 y y) (-.f64 x y))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x y))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y (-.f64 y x) (*.f64 x x)) (fma.f64 x (*.f64 x x) (*.f64 y (*.f64 y y))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (*.f64 (+.f64 x y) (-.f64 x y)))) |
(/.f64 (+.f64 x y) #s(literal 1 binary64)) |
(/.f64 (neg.f64 (+.f64 x y)) #s(literal -1 binary64)) |
(/.f64 (fma.f64 x (*.f64 x x) (*.f64 y (*.f64 y y))) (fma.f64 y (-.f64 y x) (*.f64 x x))) |
(/.f64 (fma.f64 x (*.f64 x x) (*.f64 y (*.f64 y y))) (fma.f64 y y (-.f64 (*.f64 x x) (*.f64 x y)))) |
(/.f64 (fma.f64 x (*.f64 x x) (*.f64 y (*.f64 y y))) (*.f64 #s(literal 1 binary64) (fma.f64 y (-.f64 y x) (*.f64 x x)))) |
(/.f64 (*.f64 (+.f64 x y) (-.f64 x y)) (-.f64 x y)) |
(/.f64 (neg.f64 (*.f64 (+.f64 x y) (-.f64 x y))) (neg.f64 (-.f64 x y))) |
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 y (*.f64 y y)))) (neg.f64 (fma.f64 y (-.f64 y x) (*.f64 x x)))) |
(/.f64 (-.f64 (*.f64 y y) (*.f64 x x)) (-.f64 y x)) |
(*.f64 (+.f64 x y) #s(literal 1 binary64)) |
(*.f64 (fma.f64 x (*.f64 x x) (*.f64 y (*.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y (-.f64 y x) (*.f64 x x)))) |
(*.f64 (*.f64 (+.f64 x y) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (-.f64 x y))) |
(*.f64 (/.f64 (*.f64 (+.f64 x y) (-.f64 x y)) (*.f64 (+.f64 x y) (-.f64 x y))) (+.f64 x y)) |
(*.f64 (/.f64 (*.f64 (+.f64 x y) (-.f64 x y)) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))) (fma.f64 x x (*.f64 y (+.f64 x y)))) |
(+.f64 x (neg.f64 y)) |
(+.f64 (neg.f64 y) x) |
(+.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 1 binary64) (neg.f64 y))) |
(+.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 (neg.f64 y) #s(literal 1 binary64))) |
(-.f64 x y) |
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x x (*.f64 y (+.f64 x y)))) (/.f64 (*.f64 y (*.f64 y y)) (fma.f64 x x (*.f64 y (+.f64 x y))))) |
(-.f64 (/.f64 (*.f64 x x) (+.f64 x y)) (/.f64 (*.f64 y y) (+.f64 x y))) |
(-.f64 (+.f64 x #s(literal 0 binary64)) y) |
(fma.f64 #s(literal 1 binary64) x (*.f64 #s(literal 1 binary64) (neg.f64 y))) |
(fma.f64 x #s(literal 1 binary64) (*.f64 (neg.f64 y) #s(literal 1 binary64))) |
(fma.f64 y #s(literal -1 binary64) x) |
(fma.f64 #s(literal -1 binary64) y x) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x y) (*.f64 (+.f64 x y) (-.f64 x y)))) |
(/.f64 (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)) (fma.f64 x x (*.f64 y (+.f64 x y)))) |
(/.f64 (*.f64 (+.f64 x y) (-.f64 x y)) (+.f64 x y)) |
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))) (fma.f64 x x (*.f64 y (+.f64 x y)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (+.f64 x y) (-.f64 x y))) (+.f64 x y)) |
(/.f64 (neg.f64 (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))) (neg.f64 (fma.f64 x x (*.f64 y (+.f64 x y))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 x y) (-.f64 x y))) (neg.f64 (+.f64 x y))) |
(/.f64 (fma.f64 x (*.f64 x x) (pow.f64 (neg.f64 y) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (*.f64 (neg.f64 y) (neg.f64 y)) (*.f64 x (neg.f64 y))))) |
(/.f64 (-.f64 (*.f64 x x) (*.f64 (neg.f64 y) (neg.f64 y))) (-.f64 x (neg.f64 y))) |
(*.f64 #s(literal 1 binary64) (-.f64 x y)) |
(*.f64 (-.f64 x y) #s(literal 1 binary64)) |
(*.f64 (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 y (+.f64 x y))))) |
(*.f64 (*.f64 (+.f64 x y) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (+.f64 x y))) |
(*.f64 (/.f64 (*.f64 (+.f64 x y) (-.f64 x y)) (fma.f64 x (*.f64 x x) (*.f64 y (*.f64 y y)))) (fma.f64 y (-.f64 y x) (*.f64 x x))) |
(*.f64 (/.f64 (*.f64 (+.f64 x y) (-.f64 x y)) (*.f64 (+.f64 x y) (-.f64 x y))) (-.f64 x y)) |
#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) |
#s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) |
(neg.f64 (/.f64 #s(approx (- x y) (neg.f64 y)) (neg.f64 (+.f64 x y)))) |
(neg.f64 (/.f64 (neg.f64 #s(approx (- x y) (neg.f64 y))) (+.f64 x y))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x y) #s(approx (- x y) (neg.f64 y)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 x y) #s(approx (- x y) (neg.f64 y))) #s(literal 1 binary64))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x y) #s(approx (- x y) (neg.f64 y))))) |
(/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) |
(/.f64 (neg.f64 #s(approx (- x y) (neg.f64 y))) (neg.f64 (+.f64 x y))) |
(/.f64 (neg.f64 (neg.f64 #s(approx (- x y) (neg.f64 y)))) (neg.f64 (neg.f64 (+.f64 x y)))) |
(/.f64 (*.f64 #s(approx (- x y) (neg.f64 y)) #s(literal 1 binary64)) (+.f64 x y)) |
(/.f64 (*.f64 #s(approx (- x y) (neg.f64 y)) #s(literal -1 binary64)) (neg.f64 (+.f64 x y))) |
(pow.f64 (/.f64 (+.f64 x y) #s(approx (- x y) (neg.f64 y))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) #s(approx (- x y) (neg.f64 y))) |
(*.f64 #s(approx (- x y) (neg.f64 y)) (/.f64 #s(literal 1 binary64) (+.f64 x y))) |
(*.f64 (neg.f64 #s(approx (- x y) (neg.f64 y))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 x y)))) |
(*.f64 (*.f64 #s(approx (- x y) (neg.f64 y)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x y))) |
(*.f64 (/.f64 #s(approx (- x y) (neg.f64 y)) (fma.f64 x (*.f64 x x) (*.f64 y (*.f64 y y)))) (fma.f64 y (-.f64 y x) (*.f64 x x))) |
(*.f64 (/.f64 #s(approx (- x y) (neg.f64 y)) (*.f64 (+.f64 x y) (-.f64 x y))) (-.f64 x y)) |
#s(approx (- x y) (neg.f64 y)) |
(+.f64 #s(literal 0 binary64) (neg.f64 y)) |
(-.f64 #s(literal 0 binary64) y) |
(neg.f64 y) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 y (*.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 #s(literal 0 binary64) y)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 y y)) (+.f64 #s(literal 0 binary64) y)) |
(*.f64 y #s(literal -1 binary64)) |
(*.f64 #s(literal -1 binary64) y) |
#s(approx (/ (- x y) (+ x y)) (fma.f64 #s(literal 2 binary64) (/.f64 x y) #s(literal -1 binary64))) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(+.f64 (/.f64 (+.f64 x x) y) #s(literal -1 binary64)) |
(-.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 x y) #s(literal -1 binary64))) (/.f64 (/.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 y y)) (fma.f64 #s(literal 2 binary64) (/.f64 x y) #s(literal -1 binary64)))) |
(fma.f64 #s(literal 1 binary64) (/.f64 (+.f64 x x) y) #s(literal -1 binary64)) |
(fma.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y) #s(literal -1 binary64)) |
(fma.f64 (+.f64 x x) (/.f64 #s(literal 1 binary64) y) #s(literal -1 binary64)) |
(fma.f64 (+.f64 x x) (/.f64 #s(literal 1 binary64) (neg.f64 y)) #s(literal -1 binary64)) |
(fma.f64 (/.f64 (+.f64 x x) y) #s(literal -1 binary64) #s(literal -1 binary64)) |
(fma.f64 (/.f64 #s(literal 1 binary64) y) (+.f64 x x) #s(literal -1 binary64)) |
(fma.f64 #s(literal 2 binary64) (*.f64 x (/.f64 #s(literal 1 binary64) y)) #s(literal -1 binary64)) |
(fma.f64 #s(literal 2 binary64) (/.f64 x y) #s(literal -1 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (+.f64 x x) y) (-.f64 (/.f64 (+.f64 x x) y) #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (/.f64 (+.f64 x x) y) (/.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 y y)) #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) (/.f64 x y) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 y y))))) |
(/.f64 (fma.f64 (/.f64 (+.f64 x x) y) (/.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 y y)) #s(literal -1 binary64)) (fma.f64 (/.f64 (+.f64 x x) y) (-.f64 (/.f64 (+.f64 x x) y) #s(literal -1 binary64)) #s(literal 1 binary64))) |
(/.f64 (fma.f64 (/.f64 (+.f64 x x) y) (/.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 y y)) #s(literal -1 binary64)) (+.f64 (/.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 y y)) (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 x x) y)))) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 y y))) (fma.f64 #s(literal 2 binary64) (/.f64 x y) #s(literal -1 binary64))) |
(/.f64 (neg.f64 (fma.f64 (/.f64 (+.f64 x x) y) (/.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 y y)) #s(literal -1 binary64))) (neg.f64 (fma.f64 (/.f64 (+.f64 x x) y) (-.f64 (/.f64 (+.f64 x x) y) #s(literal -1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 y y)))) (neg.f64 (fma.f64 #s(literal 2 binary64) (/.f64 x y) #s(literal -1 binary64)))) |
(/.f64 (-.f64 #s(literal -1 binary64) (*.f64 (/.f64 (+.f64 x x) y) (/.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 y y)))) (fma.f64 (/.f64 (+.f64 x x) y) (-.f64 (/.f64 (+.f64 x x) y) #s(literal -1 binary64)) #s(literal 1 binary64))) |
(/.f64 (-.f64 (/.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 y y)) #s(literal 1 binary64)) (-.f64 (/.f64 (+.f64 x x) y) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (/.f64 (+.f64 x x) y) (/.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 y y)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (+.f64 x x) y) (-.f64 (/.f64 (+.f64 x x) y) #s(literal -1 binary64)) #s(literal 1 binary64)))) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 x y) #s(literal -1 binary64)))) |
(neg.f64 (/.f64 (+.f64 x x) y)) |
(/.f64 #s(literal 1 binary64) (*.f64 y (+.f64 x x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 y (+.f64 x x)) #s(literal 1 binary64))) |
(/.f64 #s(literal -1 binary64) (*.f64 y (+.f64 x x))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 y (+.f64 x x)))) |
(/.f64 (+.f64 x x) y) |
(/.f64 (+.f64 x x) (neg.f64 y)) |
(/.f64 (+.f64 x x) (neg.f64 (neg.f64 y))) |
(/.f64 #s(literal 0 binary64) (*.f64 #s(literal 0 binary64) y)) |
(/.f64 #s(literal 0 binary64) (*.f64 y #s(literal 0 binary64))) |
(/.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (*.f64 y (fma.f64 x x #s(literal 0 binary64)))) |
(/.f64 (*.f64 (+.f64 x x) #s(literal 1 binary64)) y) |
(/.f64 (*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) #s(literal 1 binary64)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) y)) |
(/.f64 (*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (/.f64 #s(literal 1 binary64) y)) (fma.f64 x x #s(literal 0 binary64))) |
(/.f64 (*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) y)) #s(literal 0 binary64)) |
(/.f64 (/.f64 (+.f64 x x) #s(literal -1 binary64)) y) |
(pow.f64 (*.f64 y (+.f64 x x)) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 (+.f64 x x) y)) |
(*.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(*.f64 (+.f64 x x) (/.f64 #s(literal 1 binary64) y)) |
(*.f64 (+.f64 x x) (/.f64 #s(literal 1 binary64) (neg.f64 y))) |
(*.f64 (/.f64 (+.f64 x x) y) #s(literal -1 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) y) (+.f64 x x)) |
(*.f64 #s(literal 2 binary64) (*.f64 x (/.f64 #s(literal 1 binary64) y))) |
(*.f64 #s(literal 2 binary64) (/.f64 x y)) |
(+.f64 x x) |
(+.f64 (neg.f64 x) (neg.f64 x)) |
(-.f64 #s(literal 0 binary64) (+.f64 x x)) |
(-.f64 (/.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 (*.f64 x x) #s(literal 0 binary64))) |
(neg.f64 (+.f64 x x)) |
(/.f64 #s(literal 1 binary64) (+.f64 x x)) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)))) |
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) |
(/.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (fma.f64 x x #s(literal 0 binary64))) |
(/.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (neg.f64 (fma.f64 x x #s(literal 0 binary64)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (fma.f64 x x #s(literal 0 binary64))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (neg.f64 (fma.f64 x x #s(literal 0 binary64)))) |
(*.f64 x #s(literal 2 binary64)) |
(*.f64 #s(literal -1 binary64) (+.f64 x x)) |
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64))) |
(*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))) |
(*.f64 #s(literal 2 binary64) x) |
(*.f64 #s(literal 2 binary64) (neg.f64 x)) |
(*.f64 #s(literal -2 binary64) x) |
Compiled 6 576 to 626 computations (90.5% saved)
7 alts after pruning (1 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 512 | 1 | 513 |
| Fresh | 1 | 0 | 1 |
| Picked | 0 | 5 | 5 |
| Done | 0 | 1 | 1 |
| Total | 513 | 7 | 520 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (/.f64 (-.f64 x y) (+.f64 x y)) |
| ✓ | 56.9% | (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) |
| ✓ | 99.8% | (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) |
| ▶ | 43.8% | #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) |
| ✓ | 56.7% | #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) |
| ✓ | 43.7% | #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) |
| ✓ | 55.8% | #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) |
Compiled 62 to 38 computations (38.7% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) | |
| cost-diff | 0 | (+.f64 y y) | |
| cost-diff | 0 | (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) |
| 7 144× | lower-fma.f32 |
| 7 142× | lower-fma.f64 |
| 1 848× | lower-*.f64 |
| 1 848× | lower-*.f32 |
| 1 218× | div-sub |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 54 |
| 0 | 19 | 54 |
| 1 | 34 | 54 |
| 2 | 59 | 54 |
| 3 | 133 | 54 |
| 4 | 246 | 54 |
| 5 | 427 | 54 |
| 6 | 904 | 54 |
| 7 | 2221 | 54 |
| 8 | 4867 | 54 |
| 9 | 5772 | 54 |
| 10 | 6094 | 54 |
| 11 | 6206 | 54 |
| 12 | 6268 | 54 |
| 13 | 6299 | 54 |
| 14 | 6385 | 54 |
| 15 | 6385 | 54 |
| 16 | 6397 | 54 |
| 17 | 6399 | 54 |
| 18 | 6399 | 54 |
| 19 | 6399 | 54 |
| 20 | 7032 | 54 |
| 21 | 7224 | 54 |
| 22 | 7272 | 54 |
| 23 | 7272 | 54 |
| 24 | 7272 | 54 |
| 0 | 7272 | 52 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) |
(fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64)) |
(+.f64 y y) |
y |
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
#s(literal -1 binary64) |
(/.f64 y x) |
x |
#s(literal 1 binary64) |
| Outputs |
|---|
#s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) |
(fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64)) |
(+.f64 y y) |
y |
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
#s(literal -1 binary64) |
(/.f64 y x) |
x |
#s(literal 1 binary64) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.00390625 | (+.f64 #s(literal -1 binary64) (/.f64 y x)) | |
| accuracy | 0.07421875 | (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) | |
| accuracy | 2.5765096842248116 | (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64)) | |
| accuracy | 35.93956588396426 | #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) |
| 21.0ms | 256× | 0 | valid |
Compiled 44 to 15 computations (65.9% saved)
ival-div: 5.0ms (38% of total)ival-add: 4.0ms (30.4% of total)ival-sub: 2.0ms (15.2% of total)ival-mult: 2.0ms (15.2% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ()) |
#s(alt (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) (patch (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #<representation binary64>) () ()) |
#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt -1 (taylor 0 x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (* 2 (/ x y)) 1) (taylor 0 x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1) (taylor 0 x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (* x (+ (* x (- (* 2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 1) (taylor 0 x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* -1 (/ y x))) (/ y x)) (taylor inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (* -1 (/ (* y (- (* -1 y) y)) (pow x 2))))) (/ y x)) (taylor inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3)))) (+ (/ y x) (/ (* y (- (* -1 y) y)) (pow x 2)))) (taylor inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor -inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* -1 (/ y x))) (/ y x)) (taylor -inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (/ (* y (- (* -1 y) y)) x)) x))) (taylor -inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (* -1 (/ (+ (* -1 (* y (- (* -1 y) y))) (/ (* (pow y 2) (- (* -1 y) y)) x)) x))) x))) (taylor -inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
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#s(alt (* -1 (/ (+ 1 (* -1 (/ y x))) x)) (taylor -inf x) (#s(alt (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) (patch (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (+ 1 (* -1 (/ y x))) x)) (taylor -inf x) (#s(alt (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) (patch (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #<representation binary64>) () ())) ()) |
#s(alt -1 (taylor 0 y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ y x) 1) (taylor 0 y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ y x) 1) (taylor 0 y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ y x) 1) (taylor 0 y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (/ y x) (taylor inf y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* y (- (/ 1 x) (/ 1 y))) (taylor inf y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* y (- (/ 1 x) (/ 1 y))) (taylor inf y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* y (- (/ 1 x) (/ 1 y))) (taylor inf y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (/ y x) (taylor -inf y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (/ 1 y) (/ 1 x)))) (taylor -inf y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (/ 1 y) (/ 1 x)))) (taylor -inf y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (/ 1 y) (/ 1 x)))) (taylor -inf y) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (/ y x) (taylor 0 x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ y (* -1 x)) x) (taylor 0 x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ y (* -1 x)) x) (taylor 0 x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ y (* -1 x)) x) (taylor 0 x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt -1 (taylor inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ y x) 1) (taylor inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ y x) 1) (taylor inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ y x) 1) (taylor inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt -1 (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ y x) 1) (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ y x) 1) (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ y x) 1) (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 y x)) (patch (+.f64 #s(literal -1 binary64) (/.f64 y x)) #<representation binary64>) () ())) ()) |
27 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | y | @ | 0 | (+ (* (+ y y) (/ (+ -1 (/ y x)) x)) 1) |
| 1.0ms | y | @ | inf | (+ (* (+ y y) (/ (+ -1 (/ y x)) x)) 1) |
| 0.0ms | x | @ | 0 | (+ (* (+ y y) (/ (+ -1 (/ y x)) x)) 1) |
| 0.0ms | x | @ | -inf | (/ (+ -1 (/ y x)) x) |
| 0.0ms | x | @ | -inf | (+ (* (+ y y) (/ (+ -1 (/ y x)) x)) 1) |
| 1× | egg-herbie |
| 14 780× | lower-fma.f64 |
| 14 780× | lower-fma.f32 |
| 4 150× | lower-*.f64 |
| 4 150× | lower-*.f32 |
| 2 264× | lower--.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 174 | 1022 |
| 1 | 509 | 907 |
| 2 | 1433 | 802 |
| 3 | 5137 | 790 |
| 0 | 8955 | 748 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
-1 |
(- (* 2 (/ x y)) 1) |
(- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1) |
(- (* x (+ (* x (- (* 2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 1) |
1 |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(- (+ 1 (+ (* -1 (/ y x)) (* -1 (/ (* y (- (* -1 y) y)) (pow x 2))))) (/ y x)) |
(- (+ 1 (+ (* -1 (/ y x)) (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3)))) (+ (/ y x) (/ (* y (- (* -1 y) y)) (pow x 2)))) |
1 |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (/ (* y (- (* -1 y) y)) x)) x))) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (* -1 (/ (+ (* -1 (* y (- (* -1 y) y))) (/ (* (pow y 2) (- (* -1 y) y)) x)) x))) x))) |
1 |
(+ 1 (* -2 (/ y x))) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) |
-1 |
(- (/ x y) (+ 1 (* -1 (/ x y)))) |
(- (+ (* -1 (/ (* x (- x (* -1 x))) (pow y 2))) (/ x y)) (+ 1 (* -1 (/ x y)))) |
(- (+ (/ x y) (/ (* (pow x 2) (- x (* -1 x))) (pow y 3))) (+ 1 (+ (* -1 (/ x y)) (/ (* x (- x (* -1 x))) (pow y 2))))) |
-1 |
(- (* -1 (/ (- (* -1 x) x) y)) 1) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (* x (- (* -1 x) x)) y))) x) y)) 1) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (- (* -1 (/ (* (pow x 2) (- (* -1 x) x)) y)) (* -1 (* x (- (* -1 x) x)))) y))) x) y)) 1) |
1 |
(+ 1 (* -2 (/ y x))) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(* 2 (/ (pow y 2) (pow x 2))) |
(* (pow y 2) (- (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 (* x y))))) |
(* (pow y 2) (- (+ (* 2 (/ 1 (pow x 2))) (/ 1 (pow y 2))) (/ 2 (* x y)))) |
(* (pow y 2) (- (+ (* 2 (/ 1 (pow x 2))) (/ 1 (pow y 2))) (/ 2 (* x y)))) |
(* 2 (/ (pow y 2) (pow x 2))) |
(* (pow y 2) (- (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 (* x y))))) |
(* (pow y 2) (+ (* -1 (/ (- (* 2 (/ 1 x)) (/ 1 y)) y)) (* 2 (/ 1 (pow x 2))))) |
(* (pow y 2) (+ (* -1 (/ (- (* 2 (/ 1 x)) (/ 1 y)) y)) (* 2 (/ 1 (pow x 2))))) |
(* 2 (/ (pow y 2) (pow x 2))) |
(/ (+ (* -2 (* x y)) (* 2 (pow y 2))) (pow x 2)) |
(/ (+ (* 2 (pow y 2)) (* x (+ x (* -2 y)))) (pow x 2)) |
(/ (+ (* 2 (pow y 2)) (* x (+ x (* -2 y)))) (pow x 2)) |
1 |
(+ 1 (* -2 (/ y x))) |
(+ 1 (+ (* -2 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))) |
(+ 1 (+ (* -2 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))) |
1 |
(+ 1 (* -2 (/ y x))) |
(+ 1 (* -1 (/ (+ (* -2 (/ (pow y 2) x)) (* 2 y)) x))) |
(+ 1 (* -1 (/ (+ (* -2 (/ (pow y 2) x)) (* 2 y)) x))) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(/ -1 x) |
(- (/ y (pow x 2)) (/ 1 x)) |
(- (/ y (pow x 2)) (/ 1 x)) |
(- (/ y (pow x 2)) (/ 1 x)) |
(/ y (pow x 2)) |
(* y (- (/ 1 (pow x 2)) (/ 1 (* x y)))) |
(* y (- (/ 1 (pow x 2)) (/ 1 (* x y)))) |
(* y (- (/ 1 (pow x 2)) (/ 1 (* x y)))) |
(/ y (pow x 2)) |
(* -1 (* y (- (/ 1 (* x y)) (/ 1 (pow x 2))))) |
(* -1 (* y (- (/ 1 (* x y)) (/ 1 (pow x 2))))) |
(* -1 (* y (- (/ 1 (* x y)) (/ 1 (pow x 2))))) |
(/ y (pow x 2)) |
(/ (+ y (* -1 x)) (pow x 2)) |
(/ (+ y (* -1 x)) (pow x 2)) |
(/ (+ y (* -1 x)) (pow x 2)) |
(/ -1 x) |
(/ (- (/ y x) 1) x) |
(/ (- (/ y x) 1) x) |
(/ (- (/ y x) 1) x) |
(/ -1 x) |
(* -1 (/ (+ 1 (* -1 (/ y x))) x)) |
(* -1 (/ (+ 1 (* -1 (/ y x))) x)) |
(* -1 (/ (+ 1 (* -1 (/ y x))) x)) |
-1 |
(- (/ y x) 1) |
(- (/ y x) 1) |
(- (/ y x) 1) |
(/ y x) |
(* y (- (/ 1 x) (/ 1 y))) |
(* y (- (/ 1 x) (/ 1 y))) |
(* y (- (/ 1 x) (/ 1 y))) |
(/ y x) |
(* -1 (* y (- (/ 1 y) (/ 1 x)))) |
(* -1 (* y (- (/ 1 y) (/ 1 x)))) |
(* -1 (* y (- (/ 1 y) (/ 1 x)))) |
(/ y x) |
(/ (+ y (* -1 x)) x) |
(/ (+ y (* -1 x)) x) |
(/ (+ y (* -1 x)) x) |
-1 |
(- (/ y x) 1) |
(- (/ y x) 1) |
(- (/ y x) 1) |
-1 |
(- (/ y x) 1) |
(- (/ y x) 1) |
(- (/ y x) 1) |
| Outputs |
|---|
-1 |
#s(literal -1 binary64) |
(- (* 2 (/ x y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1) |
(fma.f64 (/.f64 (+.f64 x x) y) (-.f64 #s(literal 1 binary64) (/.f64 x y)) #s(literal -1 binary64)) |
(- (* x (+ (* x (- (* 2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (/.f64 x y) (*.f64 x (-.f64 (/.f64 (+.f64 x x) y) #s(literal 2 binary64))) (+.f64 x x)) y)) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -1 (/ y x)) (* -1 (/ (* y (- (* -1 y) y)) (pow x 2))))) (/ y x)) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -1 (/ y x)) (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3)))) (+ (/ y x) (/ (* y (- (* -1 y) y)) (pow x 2)))) |
(+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 y (*.f64 (*.f64 y #s(literal -2 binary64)) (/.f64 (-.f64 y x) (*.f64 x x)))) (+.f64 y y)) x)) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (/ (* y (- (* -1 y) y)) x)) x))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (* -1 (/ (+ (* -1 (* y (- (* -1 y) y))) (/ (* (pow y 2) (- (* -1 y) y)) x)) x))) x))) |
(+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 y (*.f64 (*.f64 y #s(literal -2 binary64)) (/.f64 (-.f64 y x) (*.f64 x x)))) (+.f64 y y)) x)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -2 (/ y x))) |
(fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) |
(+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 y (*.f64 (*.f64 y #s(literal -2 binary64)) (/.f64 (-.f64 y x) (*.f64 x x)))) (+.f64 y y)) x)) |
-1 |
#s(literal -1 binary64) |
(- (/ x y) (+ 1 (* -1 (/ x y)))) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(- (+ (* -1 (/ (* x (- x (* -1 x))) (pow y 2))) (/ x y)) (+ 1 (* -1 (/ x y)))) |
(fma.f64 (/.f64 (+.f64 x x) y) (-.f64 #s(literal 1 binary64) (/.f64 x y)) #s(literal -1 binary64)) |
(- (+ (/ x y) (/ (* (pow x 2) (- x (* -1 x))) (pow y 3))) (+ 1 (+ (* -1 (/ x y)) (/ (* x (- x (* -1 x))) (pow y 2))))) |
(+.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (/.f64 x y) (*.f64 x (-.f64 (/.f64 (+.f64 x x) y) #s(literal 2 binary64))) (+.f64 x x)) y)) |
-1 |
#s(literal -1 binary64) |
(- (* -1 (/ (- (* -1 x) x) y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (* x (- (* -1 x) x)) y))) x) y)) 1) |
(fma.f64 (/.f64 (+.f64 x x) y) (-.f64 #s(literal 1 binary64) (/.f64 x y)) #s(literal -1 binary64)) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (- (* -1 (/ (* (pow x 2) (- (* -1 x) x)) y)) (* -1 (* x (- (* -1 x) x)))) y))) x) y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (/.f64 x y) (*.f64 x (-.f64 (/.f64 (+.f64 x x) y) #s(literal 2 binary64))) (+.f64 x x)) y)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -2 (/ y x))) |
(fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(* 2 (/ (pow y 2) (pow x 2))) |
(/.f64 (*.f64 y (+.f64 y y)) (*.f64 x x)) |
(* (pow y 2) (- (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 (* x y))))) |
(*.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x))) |
(* (pow y 2) (- (+ (* 2 (/ 1 (pow x 2))) (/ 1 (pow y 2))) (/ 2 (* x y)))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(* (pow y 2) (- (+ (* 2 (/ 1 (pow x 2))) (/ 1 (pow y 2))) (/ 2 (* x y)))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(* 2 (/ (pow y 2) (pow x 2))) |
(/.f64 (*.f64 y (+.f64 y y)) (*.f64 x x)) |
(* (pow y 2) (- (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 (* x y))))) |
(*.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x))) |
(* (pow y 2) (+ (* -1 (/ (- (* 2 (/ 1 x)) (/ 1 y)) y)) (* 2 (/ 1 (pow x 2))))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(* (pow y 2) (+ (* -1 (/ (- (* 2 (/ 1 x)) (/ 1 y)) y)) (* 2 (/ 1 (pow x 2))))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(* 2 (/ (pow y 2) (pow x 2))) |
(/.f64 (*.f64 y (+.f64 y y)) (*.f64 x x)) |
(/ (+ (* -2 (* x y)) (* 2 (pow y 2))) (pow x 2)) |
(/.f64 (*.f64 y (fma.f64 x #s(literal -2 binary64) (+.f64 y y))) (*.f64 x x)) |
(/ (+ (* 2 (pow y 2)) (* x (+ x (* -2 y)))) (pow x 2)) |
(/.f64 (fma.f64 x (-.f64 x (+.f64 y y)) (*.f64 y (+.f64 y y))) (*.f64 x x)) |
(/ (+ (* 2 (pow y 2)) (* x (+ x (* -2 y)))) (pow x 2)) |
(/.f64 (fma.f64 x (-.f64 x (+.f64 y y)) (*.f64 y (+.f64 y y))) (*.f64 x x)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -2 (/ y x))) |
(fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) |
(+ 1 (+ (* -2 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(+ 1 (+ (* -2 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -2 (/ y x))) |
(fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) |
(+ 1 (* -1 (/ (+ (* -2 (/ (pow y 2) x)) (* 2 y)) x))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(+ 1 (* -1 (/ (+ (* -2 (/ (pow y 2) x)) (* 2 y)) x))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(/ -1 x) |
(/.f64 #s(literal -1 binary64) x) |
(- (/ y (pow x 2)) (/ 1 x)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(- (/ y (pow x 2)) (/ 1 x)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(- (/ y (pow x 2)) (/ 1 x)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(* y (- (/ 1 (pow x 2)) (/ 1 (* x y)))) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(* y (- (/ 1 (pow x 2)) (/ 1 (* x y)))) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(* y (- (/ 1 (pow x 2)) (/ 1 (* x y)))) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(* -1 (* y (- (/ 1 (* x y)) (/ 1 (pow x 2))))) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(* -1 (* y (- (/ 1 (* x y)) (/ 1 (pow x 2))))) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(* -1 (* y (- (/ 1 (* x y)) (/ 1 (pow x 2))))) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ (+ y (* -1 x)) (pow x 2)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ (+ y (* -1 x)) (pow x 2)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ (+ y (* -1 x)) (pow x 2)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ -1 x) |
(/.f64 #s(literal -1 binary64) x) |
(/ (- (/ y x) 1) x) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ (- (/ y x) 1) x) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ (- (/ y x) 1) x) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ -1 x) |
(/.f64 #s(literal -1 binary64) x) |
(* -1 (/ (+ 1 (* -1 (/ y x))) x)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(* -1 (/ (+ 1 (* -1 (/ y x))) x)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(* -1 (/ (+ 1 (* -1 (/ y x))) x)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
-1 |
#s(literal -1 binary64) |
(- (/ y x) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
(- (/ y x) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
(- (/ y x) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
(/ y x) |
(/.f64 y x) |
(* y (- (/ 1 x) (/ 1 y))) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
(* y (- (/ 1 x) (/ 1 y))) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
(* y (- (/ 1 x) (/ 1 y))) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
(/ y x) |
(/.f64 y x) |
(* -1 (* y (- (/ 1 y) (/ 1 x)))) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
(* -1 (* y (- (/ 1 y) (/ 1 x)))) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
(* -1 (* y (- (/ 1 y) (/ 1 x)))) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
(/ y x) |
(/.f64 y x) |
(/ (+ y (* -1 x)) x) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
(/ (+ y (* -1 x)) x) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
(/ (+ y (* -1 x)) x) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
-1 |
#s(literal -1 binary64) |
(- (/ y x) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
(- (/ y x) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
(- (/ y x) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
-1 |
#s(literal -1 binary64) |
(- (/ y x) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
(- (/ y x) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
(- (/ y x) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
| 520× | lower-/.f32 |
| 516× | lower-/.f64 |
| 496× | lower-*.f64 |
| 496× | lower-*.f32 |
| 308× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 47 |
| 0 | 19 | 47 |
| 1 | 99 | 47 |
| 0 | 874 | 47 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) |
(fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64)) |
(+.f64 y y) |
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
| Outputs |
|---|
#s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) |
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) x)) |
(+.f64 (/.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) x) #s(literal 1 binary64)) |
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x)))) (*.f64 x x)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal -1 binary64)))) |
(fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64)) |
(fma.f64 (+.f64 y y) (*.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(fma.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 y y)) #s(literal 1 binary64)) |
(fma.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) (+.f64 y y) #s(literal 1 binary64)) |
(fma.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) (*.f64 (+.f64 y y) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) x) #s(literal 1 binary64)) |
(fma.f64 (/.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) x) #s(literal 1 binary64) #s(literal 1 binary64)) |
(fma.f64 #s(literal 2 binary64) (*.f64 y (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x)) #s(literal 1 binary64)) |
(fma.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) |
(fma.f64 (*.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 2 binary64)) y #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x)))) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) x))) (fma.f64 (/.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) x) (/.f64 (*.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x)))) (*.f64 x x)) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal -1 binary64)) (+.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x)))) (*.f64 x x)) #s(literal -1 binary64)))) |
(/.f64 (fma.f64 (/.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) x) (/.f64 (*.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x)))) (*.f64 x x)) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x)))) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) x)))) |
(/.f64 (fma.f64 (/.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) x) (/.f64 (*.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x)))) (*.f64 x x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x)))) (*.f64 x x)) (/.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) x)))) |
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x)))) (*.f64 x x)) #s(literal -1 binary64)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal -1 binary64))) |
(/.f64 (neg.f64 (fma.f64 (/.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) x) (/.f64 (*.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x)))) (*.f64 x x)) #s(literal 1 binary64))) (neg.f64 (+.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x)))) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) x))))) |
(/.f64 (neg.f64 (+.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x)))) (*.f64 x x)) #s(literal -1 binary64))) (neg.f64 (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal -1 binary64)))) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x)))) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) x))) |
(*.f64 (fma.f64 (/.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) x) (/.f64 (*.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x)))) (*.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x)))) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) x))))) |
(*.f64 (+.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (*.f64 (+.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x)))) (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal -1 binary64)))) |
(+.f64 y y) |
(-.f64 (/.f64 (*.f64 y y) #s(literal 0 binary64)) (/.f64 (*.f64 y y) #s(literal 0 binary64))) |
(/.f64 #s(literal 1 binary64) (+.f64 y y)) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)))) |
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (fma.f64 y y #s(literal 0 binary64))) |
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) |
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (neg.f64 (fma.f64 y y #s(literal 0 binary64)))) |
(*.f64 y #s(literal 2 binary64)) |
(*.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64)))) |
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64))) |
(*.f64 #s(literal 2 binary64) y) |
(neg.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) (neg.f64 x))) |
(neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 y x))) x)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (/.f64 y x))))) |
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) |
(/.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal -1 binary64) (/.f64 y x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (/.f64 y x))) #s(literal 1 binary64))) |
(/.f64 (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 y x))) (neg.f64 x)) |
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x)))) (*.f64 x (fma.f64 (/.f64 y x) (-.f64 (/.f64 y x) #s(literal -1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 y y) (*.f64 x x))) (*.f64 x (-.f64 #s(literal -1 binary64) (/.f64 y x)))) |
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (*.f64 (fma.f64 (/.f64 y x) (-.f64 (/.f64 y x) #s(literal -1 binary64)) #s(literal 1 binary64)) x)) |
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 y y) (*.f64 x x))) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal -1 binary64) (/.f64 y x)) x)) |
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 y x)))) (neg.f64 (neg.f64 x))) |
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) #s(literal 1 binary64)) x) |
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x)) (fma.f64 (/.f64 y x) (-.f64 (/.f64 y x) #s(literal -1 binary64)) #s(literal 1 binary64))) |
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 y y) (*.f64 x x))) (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (/.f64 y x))) |
(pow.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (/.f64 y x))) #s(literal -1 binary64)) |
(*.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x)) |
(*.f64 (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 y x))) (/.f64 #s(literal 1 binary64) (neg.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal -1 binary64) (/.f64 y x))) |
(+.f64 #s(literal -1 binary64) (/.f64 y x)) |
(+.f64 (/.f64 y x) #s(literal -1 binary64)) |
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 y x))) (/.f64 (/.f64 (*.f64 y y) (*.f64 x x)) (-.f64 #s(literal -1 binary64) (/.f64 y x)))) |
(fma.f64 y (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) |
(fma.f64 #s(literal 1 binary64) (/.f64 y x) #s(literal -1 binary64)) |
(fma.f64 (neg.f64 y) (/.f64 #s(literal 1 binary64) (neg.f64 x)) #s(literal -1 binary64)) |
(fma.f64 (/.f64 #s(literal 1 binary64) x) y #s(literal -1 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 y x) (-.f64 (/.f64 y x) #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 y x)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 y y) (*.f64 x x))))) |
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x)))) (fma.f64 (/.f64 y x) (-.f64 (/.f64 y x) #s(literal -1 binary64)) #s(literal 1 binary64))) |
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x)))) (+.f64 (/.f64 (*.f64 y y) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 y x))))) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 y y) (*.f64 x x))) (-.f64 #s(literal -1 binary64) (/.f64 y x))) |
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x))))) (neg.f64 (fma.f64 (/.f64 y x) (-.f64 (/.f64 y x) #s(literal -1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 y y) (*.f64 x x)))) (neg.f64 (-.f64 #s(literal -1 binary64) (/.f64 y x)))) |
(/.f64 (-.f64 (/.f64 (*.f64 y y) (*.f64 x x)) #s(literal 1 binary64)) (-.f64 (/.f64 y x) #s(literal -1 binary64))) |
(*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 y x) (-.f64 (/.f64 y x) #s(literal -1 binary64)) #s(literal 1 binary64)))) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 y y) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 y x)))) |
Compiled 3 163 to 256 computations (91.9% saved)
7 alts after pruning (1 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 179 | 1 | 180 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 6 | 6 |
| Total | 180 | 7 | 187 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (/.f64 (-.f64 x y) (+.f64 x y)) |
| ✓ | 56.9% | (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) |
| ✓ | 99.8% | (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) |
| ▶ | 42.7% | #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) |
| ✓ | 56.7% | #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) |
| ✓ | 43.7% | #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) |
| ✓ | 55.8% | #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) |
Compiled 62 to 37 computations (40.3% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (/.f64 (-.f64 y x) (*.f64 x x)) | |
| cost-diff | 0 | (+.f64 y y) | |
| cost-diff | 0 | (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) |
| 13 528× | lower-fma.f32 |
| 13 526× | lower-fma.f64 |
| 2 814× | lower-*.f32 |
| 2 812× | lower-*.f64 |
| 1 412× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 12 | 51 |
| 0 | 18 | 51 |
| 1 | 39 | 51 |
| 2 | 81 | 51 |
| 3 | 208 | 51 |
| 4 | 565 | 51 |
| 5 | 1558 | 51 |
| 6 | 4450 | 51 |
| 7 | 7931 | 51 |
| 0 | 8135 | 49 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(+.f64 y y) |
y |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(-.f64 y x) |
x |
(*.f64 x x) |
#s(literal 1 binary64) |
| Outputs |
|---|
#s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(+.f64 y y) |
y |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(-.f64 y x) |
x |
(*.f64 x x) |
#s(literal 1 binary64) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (*.f64 x x) | |
| accuracy | 2.5765096842248116 | (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) | |
| accuracy | 18.14880442099138 | (/.f64 (-.f64 y x) (*.f64 x x)) | |
| accuracy | 35.93956588396426 | #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) |
| 44.0ms | 256× | 0 | valid |
Compiled 41 to 14 computations (65.9% saved)
ival-sub: 3.0ms (23.4% of total)ival-div: 3.0ms (23.4% of total)ival-add: 3.0ms (23.4% of total)ival-mult: 3.0ms (23.4% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt -1 (taylor 0 x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (* 2 (/ x y)) 1) (taylor 0 x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1) (taylor 0 x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (* x (+ (* x (- (* 2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 1) (taylor 0 x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* -1 (/ y x))) (/ y x)) (taylor inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (* -1 (/ (* y (- (* -1 y) y)) (pow x 2))))) (/ y x)) (taylor inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3)))) (+ (/ y x) (/ (* y (- (* -1 y) y)) (pow x 2)))) (taylor inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor -inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* -1 (/ y x))) (/ y x)) (taylor -inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (/ (* y (- (* -1 y) y)) x)) x))) (taylor -inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (* -1 (/ (+ (* -1 (* y (- (* -1 y) y))) (/ (* (pow y 2) (- (* -1 y) y)) x)) x))) x))) (taylor -inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -2 (/ y x))) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt -1 (taylor inf y) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (/ x y) (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (* -1 (/ (* x (- x (* -1 x))) (pow y 2))) (/ x y)) (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (/ x y) (/ (* (pow x 2) (- x (* -1 x))) (pow y 3))) (+ 1 (+ (* -1 (/ x y)) (/ (* x (- x (* -1 x))) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt -1 (taylor -inf y) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1 (/ (- (* -1 x) x) y)) 1) (taylor -inf y) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (* x (- (* -1 x) x)) y))) x) y)) 1) (taylor -inf y) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (- (* -1 (/ (* (pow x 2) (- (* -1 x) x)) y)) (* -1 (* x (- (* -1 x) x)))) y))) x) y)) 1) (taylor -inf y) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 y) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -2 (/ y x))) (taylor 0 y) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 (/ (pow y 2) (pow x 2))) (taylor inf y) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (- (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 (* x y))))) (taylor inf y) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (- (+ (* 2 (/ 1 (pow x 2))) (/ 1 (pow y 2))) (/ 2 (* x y)))) (taylor inf y) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (- (+ (* 2 (/ 1 (pow x 2))) (/ 1 (pow y 2))) (/ 2 (* x y)))) (taylor inf y) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 (/ (pow y 2) (pow x 2))) (taylor -inf y) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (- (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 (* x y))))) (taylor -inf y) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (+ (* -1 (/ (- (* 2 (/ 1 x)) (/ 1 y)) y)) (* 2 (/ 1 (pow x 2))))) (taylor -inf y) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (+ (* -1 (/ (- (* 2 (/ 1 x)) (/ 1 y)) y)) (* 2 (/ 1 (pow x 2))))) (taylor -inf y) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 (/ (pow y 2) (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -2 (* x y)) (* 2 (pow y 2))) (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 2 (pow y 2)) (* x (+ x (* -2 y)))) (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 2 (pow y 2)) (* x (+ x (* -2 y)))) (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor inf x) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -2 (/ y x))) (taylor inf x) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (+ (* -2 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (+ (* -2 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor -inf x) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -2 (/ y x))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1 (/ (+ (* -2 (/ (pow y 2) x)) (* 2 y)) x))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1 (/ (+ (* -2 (/ (pow y 2) x)) (* 2 y)) x))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 y) (taylor 0 y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (* 2 y) (taylor 0 y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (* 2 y) (taylor 0 y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (* 2 y) (taylor 0 y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (* 2 y) (taylor inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (* 2 y) (taylor inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (* 2 y) (taylor inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (* 2 y) (taylor inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (* 2 y) (taylor -inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (* 2 y) (taylor -inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (* 2 y) (taylor -inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (* 2 y) (taylor -inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ()) |
#s(alt (/ -1 x) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ y (pow x 2)) (/ 1 x)) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ y (pow x 2)) (/ 1 x)) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ y (pow x 2)) (/ 1 x)) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (/ y (pow x 2)) (taylor inf y) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* y (- (/ 1 (pow x 2)) (/ 1 (* x y)))) (taylor inf y) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* y (- (/ 1 (pow x 2)) (/ 1 (* x y)))) (taylor inf y) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* y (- (/ 1 (pow x 2)) (/ 1 (* x y)))) (taylor inf y) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (/ y (pow x 2)) (taylor -inf y) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (/ 1 (* x y)) (/ 1 (pow x 2))))) (taylor -inf y) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (/ 1 (* x y)) (/ 1 (pow x 2))))) (taylor -inf y) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (/ 1 (* x y)) (/ 1 (pow x 2))))) (taylor -inf y) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (/ y (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ y (* -1 x)) (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ y (* -1 x)) (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ y (* -1 x)) (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (/ -1 x) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (/ y x) 1) x) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (/ y x) 1) x) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (/ y x) 1) x) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (/ -1 x) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (+ 1 (* -1 (/ y x))) x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (+ 1 (* -1 (/ y x))) x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (+ 1 (* -1 (/ y x))) x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) (*.f64 x x)) (patch (/.f64 (-.f64 y x) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
24 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | y | @ | 0 | (+ (* (+ y y) (/ (- y x) (* x x))) 1) |
| 0.0ms | y | @ | inf | (+ (* (+ y y) (/ (- y x) (* x x))) 1) |
| 0.0ms | y | @ | -inf | (/ (- y x) (* x x)) |
| 0.0ms | y | @ | 0 | (/ (- y x) (* x x)) |
| 0.0ms | y | @ | -inf | (+ (* (+ y y) (/ (- y x) (* x x))) 1) |
| 1× | egg-herbie |
| 14 262× | lower-fma.f64 |
| 14 262× | lower-fma.f32 |
| 4 046× | lower-*.f64 |
| 4 046× | lower-*.f32 |
| 2 182× | lower--.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 168 | 956 |
| 1 | 496 | 841 |
| 2 | 1384 | 744 |
| 3 | 5048 | 724 |
| 0 | 8788 | 682 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
-1 |
(- (* 2 (/ x y)) 1) |
(- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1) |
(- (* x (+ (* x (- (* 2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 1) |
1 |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(- (+ 1 (+ (* -1 (/ y x)) (* -1 (/ (* y (- (* -1 y) y)) (pow x 2))))) (/ y x)) |
(- (+ 1 (+ (* -1 (/ y x)) (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3)))) (+ (/ y x) (/ (* y (- (* -1 y) y)) (pow x 2)))) |
1 |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (/ (* y (- (* -1 y) y)) x)) x))) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (* -1 (/ (+ (* -1 (* y (- (* -1 y) y))) (/ (* (pow y 2) (- (* -1 y) y)) x)) x))) x))) |
1 |
(+ 1 (* -2 (/ y x))) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) |
-1 |
(- (/ x y) (+ 1 (* -1 (/ x y)))) |
(- (+ (* -1 (/ (* x (- x (* -1 x))) (pow y 2))) (/ x y)) (+ 1 (* -1 (/ x y)))) |
(- (+ (/ x y) (/ (* (pow x 2) (- x (* -1 x))) (pow y 3))) (+ 1 (+ (* -1 (/ x y)) (/ (* x (- x (* -1 x))) (pow y 2))))) |
-1 |
(- (* -1 (/ (- (* -1 x) x) y)) 1) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (* x (- (* -1 x) x)) y))) x) y)) 1) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (- (* -1 (/ (* (pow x 2) (- (* -1 x) x)) y)) (* -1 (* x (- (* -1 x) x)))) y))) x) y)) 1) |
1 |
(+ 1 (* -2 (/ y x))) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(* 2 (/ (pow y 2) (pow x 2))) |
(* (pow y 2) (- (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 (* x y))))) |
(* (pow y 2) (- (+ (* 2 (/ 1 (pow x 2))) (/ 1 (pow y 2))) (/ 2 (* x y)))) |
(* (pow y 2) (- (+ (* 2 (/ 1 (pow x 2))) (/ 1 (pow y 2))) (/ 2 (* x y)))) |
(* 2 (/ (pow y 2) (pow x 2))) |
(* (pow y 2) (- (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 (* x y))))) |
(* (pow y 2) (+ (* -1 (/ (- (* 2 (/ 1 x)) (/ 1 y)) y)) (* 2 (/ 1 (pow x 2))))) |
(* (pow y 2) (+ (* -1 (/ (- (* 2 (/ 1 x)) (/ 1 y)) y)) (* 2 (/ 1 (pow x 2))))) |
(* 2 (/ (pow y 2) (pow x 2))) |
(/ (+ (* -2 (* x y)) (* 2 (pow y 2))) (pow x 2)) |
(/ (+ (* 2 (pow y 2)) (* x (+ x (* -2 y)))) (pow x 2)) |
(/ (+ (* 2 (pow y 2)) (* x (+ x (* -2 y)))) (pow x 2)) |
1 |
(+ 1 (* -2 (/ y x))) |
(+ 1 (+ (* -2 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))) |
(+ 1 (+ (* -2 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))) |
1 |
(+ 1 (* -2 (/ y x))) |
(+ 1 (* -1 (/ (+ (* -2 (/ (pow y 2) x)) (* 2 y)) x))) |
(+ 1 (* -1 (/ (+ (* -2 (/ (pow y 2) x)) (* 2 y)) x))) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(* 2 y) |
(/ -1 x) |
(- (/ y (pow x 2)) (/ 1 x)) |
(- (/ y (pow x 2)) (/ 1 x)) |
(- (/ y (pow x 2)) (/ 1 x)) |
(/ y (pow x 2)) |
(* y (- (/ 1 (pow x 2)) (/ 1 (* x y)))) |
(* y (- (/ 1 (pow x 2)) (/ 1 (* x y)))) |
(* y (- (/ 1 (pow x 2)) (/ 1 (* x y)))) |
(/ y (pow x 2)) |
(* -1 (* y (- (/ 1 (* x y)) (/ 1 (pow x 2))))) |
(* -1 (* y (- (/ 1 (* x y)) (/ 1 (pow x 2))))) |
(* -1 (* y (- (/ 1 (* x y)) (/ 1 (pow x 2))))) |
(/ y (pow x 2)) |
(/ (+ y (* -1 x)) (pow x 2)) |
(/ (+ y (* -1 x)) (pow x 2)) |
(/ (+ y (* -1 x)) (pow x 2)) |
(/ -1 x) |
(/ (- (/ y x) 1) x) |
(/ (- (/ y x) 1) x) |
(/ (- (/ y x) 1) x) |
(/ -1 x) |
(* -1 (/ (+ 1 (* -1 (/ y x))) x)) |
(* -1 (/ (+ 1 (* -1 (/ y x))) x)) |
(* -1 (/ (+ 1 (* -1 (/ y 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) |
| Outputs |
|---|
-1 |
#s(literal -1 binary64) |
(- (* 2 (/ x y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1) |
(fma.f64 (/.f64 x y) (-.f64 #s(literal 2 binary64) (/.f64 (+.f64 x x) y)) #s(literal -1 binary64)) |
(- (* x (+ (* x (- (* 2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (*.f64 x (/.f64 (+.f64 x x) y)) (+.f64 #s(literal -1 binary64) (/.f64 x y)) (+.f64 x x)) y)) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) x)) |
(- (+ 1 (+ (* -1 (/ y x)) (* -1 (/ (* y (- (* -1 y) y)) (pow x 2))))) (/ y x)) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -1 (/ y x)) (/ (* (pow y 2) (- (* -1 y) y)) (pow x 3)))) (+ (/ y x) (/ (* y (- (* -1 y) y)) (pow x 2)))) |
(+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 y (neg.f64 (*.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x))))) (+.f64 y y)) x)) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -1 (/ y x))) (/ y x)) |
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) x)) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (/ (* y (- (* -1 y) y)) x)) x))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (* -1 (/ (+ (* -1 (* y (- (* -1 y) y))) (/ (* (pow y 2) (- (* -1 y) y)) x)) x))) x))) |
(+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 y (neg.f64 (*.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x))))) (+.f64 y y)) x)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -2 (/ y x))) |
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) x)) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) |
(+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 y (neg.f64 (*.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x))))) (+.f64 y y)) x)) |
-1 |
#s(literal -1 binary64) |
(- (/ x y) (+ 1 (* -1 (/ x y)))) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(- (+ (* -1 (/ (* x (- x (* -1 x))) (pow y 2))) (/ x y)) (+ 1 (* -1 (/ x y)))) |
(fma.f64 (/.f64 x y) (-.f64 #s(literal 2 binary64) (/.f64 (+.f64 x x) y)) #s(literal -1 binary64)) |
(- (+ (/ x y) (/ (* (pow x 2) (- x (* -1 x))) (pow y 3))) (+ 1 (+ (* -1 (/ x y)) (/ (* x (- x (* -1 x))) (pow y 2))))) |
(+.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (*.f64 x (/.f64 (+.f64 x x) y)) (+.f64 #s(literal -1 binary64) (/.f64 x y)) (+.f64 x x)) y)) |
-1 |
#s(literal -1 binary64) |
(- (* -1 (/ (- (* -1 x) x) y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y)) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (* x (- (* -1 x) x)) y))) x) y)) 1) |
(fma.f64 (/.f64 x y) (-.f64 #s(literal 2 binary64) (/.f64 (+.f64 x x) y)) #s(literal -1 binary64)) |
(- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (- (* -1 (/ (* (pow x 2) (- (* -1 x) x)) y)) (* -1 (* x (- (* -1 x) x)))) y))) x) y)) 1) |
(+.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (*.f64 x (/.f64 (+.f64 x x) y)) (+.f64 #s(literal -1 binary64) (/.f64 x y)) (+.f64 x x)) y)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -2 (/ y x))) |
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) x)) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(* 2 (/ (pow y 2) (pow x 2))) |
(/.f64 (*.f64 y (+.f64 y y)) (*.f64 x x)) |
(* (pow y 2) (- (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 (* x y))))) |
(*.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x))) |
(* (pow y 2) (- (+ (* 2 (/ 1 (pow x 2))) (/ 1 (pow y 2))) (/ 2 (* x y)))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(* (pow y 2) (- (+ (* 2 (/ 1 (pow x 2))) (/ 1 (pow y 2))) (/ 2 (* x y)))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(* 2 (/ (pow y 2) (pow x 2))) |
(/.f64 (*.f64 y (+.f64 y y)) (*.f64 x x)) |
(* (pow y 2) (- (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 (* x y))))) |
(*.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x))) |
(* (pow y 2) (+ (* -1 (/ (- (* 2 (/ 1 x)) (/ 1 y)) y)) (* 2 (/ 1 (pow x 2))))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(* (pow y 2) (+ (* -1 (/ (- (* 2 (/ 1 x)) (/ 1 y)) y)) (* 2 (/ 1 (pow x 2))))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(* 2 (/ (pow y 2) (pow x 2))) |
(/.f64 (*.f64 y (+.f64 y y)) (*.f64 x x)) |
(/ (+ (* -2 (* x y)) (* 2 (pow y 2))) (pow x 2)) |
(/.f64 (*.f64 y (fma.f64 x #s(literal -2 binary64) (+.f64 y y))) (*.f64 x x)) |
(/ (+ (* 2 (pow y 2)) (* x (+ x (* -2 y)))) (pow x 2)) |
(/.f64 (fma.f64 x (-.f64 x (+.f64 y y)) (*.f64 y (+.f64 y y))) (*.f64 x x)) |
(/ (+ (* 2 (pow y 2)) (* x (+ x (* -2 y)))) (pow x 2)) |
(/.f64 (fma.f64 x (-.f64 x (+.f64 y y)) (*.f64 y (+.f64 y y))) (*.f64 x x)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -2 (/ y x))) |
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) x)) |
(+ 1 (+ (* -2 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(+ 1 (+ (* -2 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -2 (/ y x))) |
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) x)) |
(+ 1 (* -1 (/ (+ (* -2 (/ (pow y 2) x)) (* 2 y)) x))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(+ 1 (* -1 (/ (+ (* -2 (/ (pow y 2) x)) (* 2 y)) x))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(* 2 y) |
(+.f64 y y) |
(/ -1 x) |
(/.f64 #s(literal -1 binary64) x) |
(- (/ y (pow x 2)) (/ 1 x)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(- (/ y (pow x 2)) (/ 1 x)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(- (/ y (pow x 2)) (/ 1 x)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(* y (- (/ 1 (pow x 2)) (/ 1 (* x y)))) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(* y (- (/ 1 (pow x 2)) (/ 1 (* x y)))) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(* y (- (/ 1 (pow x 2)) (/ 1 (* x y)))) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(* -1 (* y (- (/ 1 (* x y)) (/ 1 (pow x 2))))) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(* -1 (* y (- (/ 1 (* x y)) (/ 1 (pow x 2))))) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(* -1 (* y (- (/ 1 (* x y)) (/ 1 (pow x 2))))) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ (+ y (* -1 x)) (pow x 2)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ (+ y (* -1 x)) (pow x 2)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ (+ y (* -1 x)) (pow x 2)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ -1 x) |
(/.f64 #s(literal -1 binary64) x) |
(/ (- (/ y x) 1) x) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ (- (/ y x) 1) x) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ (- (/ y x) 1) x) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/ -1 x) |
(/.f64 #s(literal -1 binary64) x) |
(* -1 (/ (+ 1 (* -1 (/ y x))) x)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(* -1 (/ (+ 1 (* -1 (/ y x))) x)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(* -1 (/ (+ 1 (* -1 (/ y x))) x)) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
| 524× | lower-/.f32 |
| 522× | lower-/.f64 |
| 472× | lower-*.f32 |
| 470× | lower-*.f64 |
| 320× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 12 | 45 |
| 0 | 18 | 45 |
| 1 | 96 | 45 |
| 0 | 868 | 45 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(+.f64 y y) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(*.f64 x x) |
| Outputs |
|---|
#s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) |
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 x x))) |
(+.f64 (/.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 x x)) #s(literal 1 binary64)) |
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 (+.f64 y y) (-.f64 y x))) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal -1 binary64)))) |
(fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) |
(fma.f64 (+.f64 y y) (*.f64 (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(fma.f64 (-.f64 y x) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 y y)) #s(literal 1 binary64)) |
(fma.f64 (/.f64 (-.f64 y x) (*.f64 x x)) (+.f64 y y) #s(literal 1 binary64)) |
(fma.f64 (/.f64 (-.f64 y x) (*.f64 x x)) (*.f64 (+.f64 y y) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 x x)) #s(literal 1 binary64)) |
(fma.f64 (/.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 x x)) #s(literal 1 binary64) #s(literal 1 binary64)) |
(fma.f64 #s(literal 2 binary64) (*.f64 y (/.f64 (-.f64 y x) (*.f64 x x))) #s(literal 1 binary64)) |
(fma.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) |
(fma.f64 (/.f64 (+.f64 y y) x) (/.f64 (-.f64 y x) x) #s(literal 1 binary64)) |
(fma.f64 (*.f64 (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 2 binary64)) y #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 (+.f64 y y) (-.f64 y x))) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 x x)))) (fma.f64 (/.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 (+.f64 y y) (-.f64 y x))) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal -1 binary64)) (+.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 (+.f64 y y) (-.f64 y x))) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1 binary64)))) |
(/.f64 (fma.f64 (/.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 (+.f64 y y) (-.f64 y x))) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 (+.f64 y y) (-.f64 y x))) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 x x))))) |
(/.f64 (fma.f64 (/.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 (+.f64 y y) (-.f64 y x))) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 (+.f64 y y) (-.f64 y x))) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 x x))))) |
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 (+.f64 y y) (-.f64 y x))) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1 binary64)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal -1 binary64))) |
(/.f64 (neg.f64 (fma.f64 (/.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 (+.f64 y y) (-.f64 y x))) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1 binary64))) (neg.f64 (+.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 (+.f64 y y) (-.f64 y x))) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 x x)))))) |
(/.f64 (neg.f64 (+.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 (+.f64 y y) (-.f64 y x))) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1 binary64))) (neg.f64 (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal -1 binary64)))) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 (+.f64 y y) (-.f64 y x))) (*.f64 (*.f64 x x) (*.f64 x x)))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 x x)))) |
(*.f64 (fma.f64 (/.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 (+.f64 y y) (-.f64 y x))) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 (+.f64 y y) (-.f64 y x))) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 x x)))))) |
(*.f64 (+.f64 (/.f64 (*.f64 (*.f64 (+.f64 y y) (-.f64 y x)) (*.f64 (+.f64 y y) (-.f64 y x))) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal -1 binary64)))) |
(+.f64 y y) |
(-.f64 (/.f64 (*.f64 y y) #s(literal 0 binary64)) (/.f64 (*.f64 y y) #s(literal 0 binary64))) |
(/.f64 #s(literal 1 binary64) (+.f64 y y)) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)))) |
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (fma.f64 y y #s(literal 0 binary64))) |
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) |
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (neg.f64 (fma.f64 y y #s(literal 0 binary64)))) |
(*.f64 y #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) y) |
(*.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64)))) |
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64))) |
(+.f64 (/.f64 y (*.f64 x x)) (neg.f64 (/.f64 x (*.f64 x x)))) |
(-.f64 (/.f64 y (*.f64 x x)) (/.f64 x (*.f64 x x))) |
(fma.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x x)) (neg.f64 (/.f64 x (*.f64 x x)))) |
(neg.f64 (/.f64 (-.f64 y x) (neg.f64 (*.f64 x x)))) |
(neg.f64 (/.f64 (neg.f64 (-.f64 y x)) (*.f64 x x))) |
(/.f64 (-.f64 y x) (*.f64 x x)) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (-.f64 y x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) (-.f64 y x)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (-.f64 y x) x))) |
(/.f64 (neg.f64 (-.f64 y x)) (neg.f64 (*.f64 x x))) |
(/.f64 (*.f64 (fma.f64 x (+.f64 x y) (*.f64 y y)) (-.f64 y x)) (*.f64 (*.f64 x x) (fma.f64 x (+.f64 x y) (*.f64 y y)))) |
(/.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (*.f64 (*.f64 x x) (+.f64 x y))) |
(/.f64 (/.f64 (-.f64 y x) x) x) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) (-.f64 y x)))) |
(/.f64 (-.f64 (*.f64 y (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (+.f64 x y) (*.f64 y y)) (-.f64 y x)) #s(literal 1 binary64)) (*.f64 (fma.f64 x (+.f64 x y) (*.f64 y y)) (*.f64 x x))) |
(/.f64 (*.f64 (*.f64 (+.f64 x y) (-.f64 y x)) #s(literal 1 binary64)) (*.f64 (+.f64 x y) (*.f64 x x))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 y x))) (neg.f64 (neg.f64 (*.f64 x x)))) |
(/.f64 (neg.f64 (/.f64 (-.f64 y x) x)) (neg.f64 x)) |
(/.f64 (-.f64 (pow.f64 (/.f64 y (*.f64 x x)) #s(literal 3 binary64)) (pow.f64 (/.f64 x (*.f64 x x)) #s(literal 3 binary64))) (fma.f64 (/.f64 y (*.f64 x x)) (/.f64 y (*.f64 x x)) (fma.f64 (/.f64 x (*.f64 x x)) (/.f64 x (*.f64 x x)) (*.f64 (/.f64 y (*.f64 x x)) (/.f64 x (*.f64 x x)))))) |
(/.f64 (-.f64 (*.f64 (/.f64 y (*.f64 x x)) (/.f64 y (*.f64 x x))) (*.f64 (/.f64 x (*.f64 x x)) (/.f64 x (*.f64 x x)))) (+.f64 (/.f64 y (*.f64 x x)) (/.f64 x (*.f64 x x)))) |
(/.f64 (*.f64 (-.f64 y x) #s(literal 1 binary64)) (*.f64 x x)) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (+.f64 x y) (*.f64 y y)) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (fma.f64 x (+.f64 x y) (*.f64 y y))) |
(/.f64 (*.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x y)) |
(pow.f64 (/.f64 (*.f64 x x) (-.f64 y x)) #s(literal -1 binary64)) |
(*.f64 (-.f64 y x) (/.f64 #s(literal 1 binary64) (*.f64 x x))) |
(*.f64 #s(literal 1 binary64) (/.f64 (-.f64 y x) (*.f64 x x))) |
(*.f64 (neg.f64 (-.f64 y x)) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 y x)) |
(*.f64 (/.f64 (-.f64 y x) x) (/.f64 #s(literal 1 binary64) x)) |
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) |
(pow.f64 x #s(literal 2 binary64)) |
(*.f64 x x) |
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64))) |
Compiled 2 913 to 237 computations (91.9% saved)
7 alts after pruning (0 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 166 | 0 | 166 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 6 | 6 |
| Total | 166 | 7 | 173 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (/.f64 (-.f64 x y) (+.f64 x y)) |
| ✓ | 56.9% | (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) |
| ✓ | 99.8% | (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) |
| ✓ | 42.7% | #s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) |
| ✓ | 56.7% | #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) |
| ✓ | 43.7% | #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) |
| ✓ | 55.8% | #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) |
Compiled 138 to 67 computations (51.4% saved)
| Inputs |
|---|
#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) |
#s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) |
(/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) |
#s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) |
(/.f64 (-.f64 x y) (+.f64 x y)) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)) |
#s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (-.f64 y x) (*.f64 x x)) #s(literal 1 binary64))) |
#s(approx (/ (- x y) (+ x y)) (fma.f64 (+.f64 y y) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x) #s(literal 1 binary64))) |
#s(approx (/ (- x y) (+ x y)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 y (fma.f64 y (/.f64 #s(literal -2 binary64) x) #s(literal 2 binary64))) x))) |
| Outputs |
|---|
(/.f64 (-.f64 x y) (+.f64 x y)) |
3 calls:
| 4.0ms | (/.f64 (-.f64 x y) (+.f64 x y)) |
| 3.0ms | y |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | y |
| 100.0% | 1 | (/.f64 (-.f64 x y) (+.f64 x y)) |
Compiled 15 to 9 computations (40% saved)
| Inputs |
|---|
#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) |
#s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) |
(/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) |
#s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) |
| Outputs |
|---|
#s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) |
#s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) |
3 calls:
| 2.0ms | x |
| 2.0ms | y |
| 2.0ms | (/.f64 (-.f64 x y) (+.f64 x y)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 77.8% | 3 | x |
| 75.9% | 3 | y |
| 98.4% | 2 | (/.f64 (-.f64 x y) (+.f64 x y)) |
Compiled 15 to 9 computations (40% saved)
| Inputs |
|---|
#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) |
#s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) |
(/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) |
| Outputs |
|---|
(/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) |
#s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) |
1 calls:
| 1.0ms | (/.f64 (-.f64 x y) (+.f64 x y)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.0% | 2 | (/.f64 (-.f64 x y) (+.f64 x y)) |
Compiled 9 to 5 computations (44.4% saved)
| Inputs |
|---|
#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) |
#s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) |
| Outputs |
|---|
#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) |
#s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)) |
1 calls:
| 1.0ms | (/.f64 (-.f64 x y) (+.f64 x y)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.0% | 2 | (/.f64 (-.f64 x y) (+.f64 x y)) |
Compiled 9 to 5 computations (44.4% saved)
Total -0.0b remaining (-0%)
Threshold costs -0b (-0%)
| Inputs |
|---|
#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) |
| Outputs |
|---|
#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) |
3 calls:
| 45.0ms | y |
| 1.0ms | x |
| 1.0ms | (/.f64 (-.f64 x y) (+.f64 x y)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 55.8% | 1 | y |
| 55.8% | 1 | x |
| 55.8% | 1 | (/.f64 (-.f64 x y) (+.f64 x y)) |
Compiled 15 to 9 computations (40% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -0.07048979427363986 | 1.0 |
Compiled 12 to 10 computations (16.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -0.07048979427363986 | 1.0 |
Compiled 12 to 10 computations (16.7% saved)
| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 12.0ms | -0.07048979427363986 | 1.0 |
| 4.0ms | 240× | 0 | valid |
Compiled 162 to 130 computations (19.8% saved)
ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
| 8× | +-commutative_binary64 |
| 4× | sub-neg_binary64 |
| 2× | *-commutative_binary64 |
| 2× | 1-exp_binary64 |
| 2× | neg-sub0_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 26 | 107 |
| 1 | 34 | 107 |
| 2 | 37 | 107 |
| 3 | 38 | 107 |
| 1× | saturated |
| Inputs |
|---|
(/.f64 (-.f64 x y) (+.f64 x y)) |
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 x y)) #s(literal -3602879701896397/72057594037927936 binary64)) #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64))) |
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 x y)) #s(literal -3602879701896397/72057594037927936 binary64)) (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64))) |
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 x y)) #s(literal -202402253307311/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64))) |
#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) |
| Outputs |
|---|
(/.f64 (-.f64 x y) (+.f64 x y)) |
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 x y)) #s(literal -3602879701896397/72057594037927936 binary64)) #s(approx (/ (- x y) (+ x y)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x x) y))) #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64))) |
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 x y)) #s(literal -3602879701896397/72057594037927936 binary64)) (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64))) |
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 x y)) #s(literal -202402253307311/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64))) |
#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) |
| 11 876× | lower-fma.f64 |
| 11 876× | lower-fma.f32 |
| 3 410× | lower-*.f64 |
| 3 410× | lower-*.f32 |
| 2 360× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 142 | 462 |
| 1 | 439 | 432 |
| 2 | 1229 | 387 |
| 3 | 4744 | 375 |
| 0 | 8368 | 351 |
| 1× | done |
| 1× | iter limit |
| 1× | node limit |
Compiled 96 to 45 computations (53.1% saved)
Compiled 172 to 60 computations (65.1% saved)
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