
Time bar (total: 5.3s)
| 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 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 3 |
| 50% | 49.9% | 49.9% | 0.1% | 0% | 0% | 0% | 4 |
| 50% | 49.9% | 49.9% | 0.1% | 0% | 0% | 0% | 5 |
| 50% | 49.9% | 49.9% | 0.1% | 0% | 0% | 0% | 6 |
| 75% | 74.9% | 25% | 0.1% | 0% | 0% | 0% | 7 |
| 75% | 74.9% | 25% | 0.1% | 0% | 0% | 0% | 8 |
| 75% | 74.9% | 25% | 0.1% | 0% | 0% | 0% | 9 |
| 87.5% | 87.4% | 12.5% | 0.1% | 0% | 0% | 0% | 10 |
| 87.5% | 87.4% | 12.5% | 0.1% | 0% | 0% | 0% | 11 |
| 87.5% | 87.4% | 12.5% | 0.1% | 0% | 0% | 0% | 12 |
Compiled 9 to 8 computations (11.1% saved)
| 571.0ms | 8 256× | 0 | valid |
ival-sub: 211.0ms (60.9% of total)ival-div: 89.0ms (25.7% of total)ival-add: 36.0ms (10.4% of total)ival-true: 6.0ms (1.7% of total)ival-assert: 4.0ms (1.2% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 0 | 0 | - | 0 | - | (-.f64 y x) |
| 0 | 0 | - | 0 | - | (/.f64 (-.f64 y x) z) |
| 0 | 0 | - | 0 | - | y |
| 0 | 0 | - | 0 | - | (+.f64 x (/.f64 (-.f64 y x) z)) |
| 0 | 0 | - | 0 | - | z |
| 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 |
| 35.0ms | 512× | 0 | valid |
Compiled 47 to 22 computations (53.2% saved)
ival-div: 4.0ms (42.3% of total)ival-sub: 3.0ms (31.7% of total)ival-add: 2.0ms (21.1% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
| 624× | lower-fma.f64 |
| 624× | lower-fma.f32 |
| 480× | div-sub |
| 476× | times-frac |
| 430× | sub-neg |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 27 | 72 |
| 1 | 78 | 63 |
| 2 | 229 | 63 |
| 3 | 682 | 63 |
| 4 | 1689 | 63 |
| 5 | 3091 | 63 |
| 6 | 3495 | 63 |
| 7 | 3694 | 63 |
| 8 | 3817 | 63 |
| 9 | 3865 | 63 |
| 10 | 3865 | 63 |
| 0 | 6 | 7 |
| 0 | 9 | 7 |
| 1 | 15 | 7 |
| 2 | 26 | 7 |
| 3 | 45 | 7 |
| 4 | 88 | 7 |
| 5 | 158 | 7 |
| 6 | 350 | 7 |
| 7 | 636 | 7 |
| 8 | 905 | 7 |
| 9 | 986 | 7 |
| 10 | 1034 | 7 |
| 11 | 1073 | 7 |
| 0 | 1073 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(+.f64 x (/.f64 (-.f64 y x) z)) |
| Outputs |
|---|
(+.f64 x (/.f64 (-.f64 y x) z)) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
Compiled 7 to 6 computations (14.3% saved)
Compiled 0 to 3 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 100.0% | (+.f64 x (/.f64 (-.f64 y x) z)) |
Compiled 7 to 6 computations (14.3% saved)
| 1× | egg-herbie |
Found 3 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (-.f64 y x) | |
| cost-diff | 0 | (/.f64 (-.f64 y x) z) | |
| cost-diff | 0 | (+.f64 x (/.f64 (-.f64 y x) z)) |
| 624× | lower-fma.f64 |
| 624× | lower-fma.f32 |
| 256× | lower-*.f64 |
| 256× | lower-*.f32 |
| 160× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 0 | 9 | 18 |
| 1 | 15 | 18 |
| 2 | 26 | 18 |
| 3 | 45 | 18 |
| 4 | 88 | 18 |
| 5 | 158 | 18 |
| 6 | 350 | 18 |
| 7 | 636 | 18 |
| 8 | 905 | 18 |
| 9 | 986 | 18 |
| 10 | 1034 | 18 |
| 11 | 1073 | 18 |
| 0 | 1073 | 18 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(+.f64 x (/.f64 (-.f64 y x) z)) |
x |
(/.f64 (-.f64 y x) z) |
(-.f64 y x) |
y |
z |
| Outputs |
|---|
(+.f64 x (/.f64 (-.f64 y x) z)) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
x |
(/.f64 (-.f64 y x) z) |
(-.f64 y x) |
y |
z |
Found 3 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (-.f64 y x) | |
| accuracy | 0.0078125 | (+.f64 x (/.f64 (-.f64 y x) z)) | |
| accuracy | 0.0234375 | (/.f64 (-.f64 y x) z) |
| 11.0ms | 256× | 0 | valid |
Compiled 20 to 8 computations (60% saved)
ival-div: 2.0ms (44.5% of total)ival-sub: 1.0ms (22.2% of total)ival-add: 1.0ms (22.2% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ()) |
#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf z) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (/ y z)) (/ x z)) (taylor inf z) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (/ y z)) (/ x z)) (taylor inf z) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (/ y z)) (/ x z)) (taylor inf z) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor inf z) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor inf z) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor inf z) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor inf z) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf z) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (/ y z)) (/ x z)) (taylor -inf z) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (/ y z)) (/ x z)) (taylor -inf z) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (/ y z)) (/ x z)) (taylor -inf z) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor -inf z) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor -inf z) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor -inf z) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor -inf z) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (- x (/ x z)) (taylor 0 y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (/ y z)) (/ x z)) (taylor 0 y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (/ y z)) (/ x z)) (taylor 0 y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (/ y z)) (/ x z)) (taylor 0 y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ x z)) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (/ x z)) (/ y z)) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (/ x z)) (/ y z)) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (/ x z)) (/ y z)) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (/ y z) (taylor inf y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) (taylor inf y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) (taylor inf y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) (taylor inf y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ y z) (taylor inf y) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (* -1 (/ x (* y z))) (/ 1 z))) (taylor inf y) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (* -1 (/ x (* y z))) (/ 1 z))) (taylor inf y) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (* -1 (/ x (* y z))) (/ 1 z))) (taylor inf y) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt y (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (/ y z) (taylor -inf y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) (taylor -inf y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) (taylor -inf y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) (taylor -inf y) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ y z) (taylor -inf y) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (/ x (* y z)) (/ 1 z)))) (taylor -inf y) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (/ x (* y z)) (/ 1 z)))) (taylor -inf y) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (/ x (* y z)) (/ 1 z)))) (taylor -inf y) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt y (taylor -inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (/ x y) 1))) (taylor -inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (/ x y) 1))) (taylor -inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (/ x y) 1))) (taylor -inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (/ y z) (taylor 0 x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (- 1 (/ 1 z))) (/ y z)) (taylor 0 x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (- 1 (/ 1 z))) (/ y z)) (taylor 0 x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (- 1 (/ 1 z))) (/ y z)) (taylor 0 x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ y z) (taylor 0 x) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (/ x z)) (/ y z)) (taylor 0 x) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (/ x z)) (/ y z)) (taylor 0 x) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (/ x z)) (/ y z)) (taylor 0 x) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt y (taylor 0 x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (+ y (* -1 x)) (taylor 0 x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (+ y (* -1 x)) (taylor 0 x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (+ y (* -1 x)) (taylor 0 x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1 (/ 1 z))) (taylor inf x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (/ y (* x z))) (/ 1 z))) (taylor inf x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (/ y (* x z))) (/ 1 z))) (taylor inf x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (/ y (* x z))) (/ 1 z))) (taylor inf x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ x z)) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (/ y (* x z)) (/ 1 z))) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (/ y (* x z)) (/ 1 z))) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (/ y (* x z)) (/ 1 z))) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ 1 z) 1))) (taylor -inf x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt (+.f64 x (/.f64 (-.f64 y x) z)) (patch (+.f64 x (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ x z)) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ()) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 14.0ms | y | @ | 0 | ((+ x (/ (- y x) z)) (/ (- y x) z) (- y x)) |
| 1.0ms | y | @ | -inf | ((+ x (/ (- y x) z)) (/ (- y x) z) (- y x)) |
| 1.0ms | y | @ | inf | ((+ x (/ (- y x) z)) (/ (- y x) z) (- y x)) |
| 1.0ms | z | @ | 0 | ((+ x (/ (- y x) z)) (/ (- y x) z) (- y x)) |
| 1.0ms | x | @ | inf | ((+ x (/ (- y x) z)) (/ (- y x) z) (- y x)) |
| 1× | egg-herbie |
| 6 368× | lower-fma.f64 |
| 6 368× | lower-fma.f32 |
| 2 116× | lower-*.f64 |
| 2 116× | lower-*.f32 |
| 1 680× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 71 | 460 |
| 1 | 198 | 460 |
| 2 | 553 | 460 |
| 3 | 1590 | 460 |
| 4 | 3540 | 460 |
| 5 | 5031 | 460 |
| 6 | 6478 | 460 |
| 7 | 6764 | 460 |
| 8 | 6864 | 460 |
| 9 | 6864 | 460 |
| 0 | 8148 | 457 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (- y x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(- x (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(* -1 (/ x z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(* -1 x) |
(- y x) |
(- y x) |
(- y x) |
(/ y z) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(/ y z) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
y |
(* y (+ 1 (* -1 (/ x y)))) |
(* y (+ 1 (* -1 (/ x y)))) |
(* y (+ 1 (* -1 (/ x y)))) |
(/ y z) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(/ y z) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
y |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (* y (- (/ x y) 1))) |
(/ y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(/ y z) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
y |
(+ y (* -1 x)) |
(+ y (* -1 x)) |
(+ y (* -1 x)) |
(* x (- 1 (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* -1 (/ x z)) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* -1 x) |
(* x (- (/ y x) 1)) |
(* x (- (/ y x) 1)) |
(* x (- (/ y x) 1)) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (/ x z)) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 x) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
| Outputs |
|---|
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- (+ y (* x z)) x) z) |
(/.f64 (fma.f64 z x (-.f64 y x)) z) |
(/ (- (+ y (* x z)) x) z) |
(/.f64 (fma.f64 z x (-.f64 y x)) z) |
(/ (- (+ y (* x z)) x) z) |
(/.f64 (fma.f64 z x (-.f64 y x)) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(- (+ x (/ y z)) (/ x z)) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(- (+ x (/ y z)) (/ x z)) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(- (+ x (/ y z)) (/ x z)) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(- (+ x (/ y z)) (/ x z)) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(- x (/ x z)) |
(-.f64 x (/.f64 x z)) |
(- (+ x (/ y z)) (/ x z)) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(- (+ x (/ y z)) (/ x z)) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(- (+ x (/ y z)) (/ x z)) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(* -1 (/ x z)) |
(/.f64 (neg.f64 x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(* -1 x) |
(neg.f64 x) |
(- y x) |
(-.f64 y x) |
(- y x) |
(-.f64 y x) |
(- y x) |
(-.f64 y x) |
(/ y z) |
(/.f64 y z) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(/ y z) |
(/.f64 y z) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(/.f64 (-.f64 y x) z) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(/.f64 (-.f64 y x) z) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(/.f64 (-.f64 y x) z) |
y |
(* y (+ 1 (* -1 (/ x y)))) |
(-.f64 y x) |
(* y (+ 1 (* -1 (/ x y)))) |
(-.f64 y x) |
(* y (+ 1 (* -1 (/ x y)))) |
(-.f64 y x) |
(/ y z) |
(/.f64 y z) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(/ y z) |
(/.f64 y z) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(/.f64 (-.f64 y x) z) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(/.f64 (-.f64 y x) z) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(/.f64 (-.f64 y x) z) |
y |
(* -1 (* y (- (/ x y) 1))) |
(-.f64 y x) |
(* -1 (* y (- (/ x y) 1))) |
(-.f64 y x) |
(* -1 (* y (- (/ x y) 1))) |
(-.f64 y x) |
(/ y z) |
(/.f64 y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(/ y z) |
(/.f64 y z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
y |
(+ y (* -1 x)) |
(-.f64 y x) |
(+ y (* -1 x)) |
(-.f64 y x) |
(+ y (* -1 x)) |
(-.f64 y x) |
(* x (- 1 (/ 1 z))) |
(-.f64 x (/.f64 x z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(* -1 (/ x z)) |
(/.f64 (neg.f64 x) z) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(/.f64 (-.f64 y x) z) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(/.f64 (-.f64 y x) z) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(/.f64 (-.f64 y x) z) |
(* -1 x) |
(neg.f64 x) |
(* x (- (/ y x) 1)) |
(-.f64 y x) |
(* x (- (/ y x) 1)) |
(-.f64 y x) |
(* x (- (/ y x) 1)) |
(-.f64 y x) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(* -1 (/ x z)) |
(/.f64 (neg.f64 x) z) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(/.f64 (-.f64 y x) z) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(/.f64 (-.f64 y x) z) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(/.f64 (-.f64 y x) z) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(-.f64 y x) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(-.f64 y x) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(-.f64 y x) |
| 3 808× | lower-*.f64 |
| 3 808× | lower-*.f32 |
| 3 560× | lower-fma.f64 |
| 3 560× | lower-fma.f32 |
| 2 654× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 15 |
| 0 | 9 | 15 |
| 1 | 46 | 15 |
| 2 | 408 | 15 |
| 3 | 5406 | 15 |
| 0 | 8250 | 15 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(+.f64 x (/.f64 (-.f64 y x) z)) |
(/.f64 (-.f64 y x) z) |
(-.f64 y x) |
| Outputs |
|---|
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Compiled 7 643 to 1 078 computations (85.9% saved)
9 alts after pruning (8 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 421 | 8 | 429 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 421 | 9 | 430 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.8% | (fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) |
| ▶ | 96.8% | (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) |
| ▶ | 99.9% | (+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) |
| ✓ | 100.0% | (+.f64 x (/.f64 (-.f64 y x) z)) |
| 99.8% | (+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z (-.f64 y x)))) | |
| 74.6% | (+.f64 x #s(approx (/ (- y x) z) (/.f64 y z))) | |
| ▶ | 71.4% | #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) |
| ▶ | 46.1% | #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
| 56.4% | #s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))) |
Compiled 125 to 116 computations (7.2% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (/.f64 x z) | |
| cost-diff | 0 | (-.f64 (/.f64 x z) x) | |
| cost-diff | 0 | (/.f64 y z) | |
| cost-diff | 704 | (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) | |
| cost-diff | 0 | (-.f64 x y) | |
| cost-diff | 0 | (/.f64 #s(literal -1 binary64) z) | |
| cost-diff | 192 | (fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) | |
| cost-diff | 0 | (-.f64 y x) | |
| cost-diff | 0 | (/.f64 (-.f64 y x) z) | |
| cost-diff | 0 | #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) | |
| cost-diff | 0 | (/.f64 y z) | |
| cost-diff | 0 | #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) | |
| cost-diff | 0 | (pow.f64 (-.f64 y x) #s(literal -1 binary64)) | |
| cost-diff | 0 | (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z) | |
| cost-diff | 0 | (+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) | |
| cost-diff | 7168 | (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) |
| 672× | lower-fma.f32 |
| 670× | lower-fma.f64 |
| 304× | lower-*.f64 |
| 304× | lower-*.f32 |
| 234× | times-frac |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 23 | 121 |
| 0 | 37 | 138 |
| 1 | 56 | 106 |
| 2 | 97 | 106 |
| 3 | 202 | 106 |
| 4 | 522 | 106 |
| 5 | 1016 | 106 |
| 6 | 1281 | 106 |
| 7 | 1384 | 106 |
| 8 | 1420 | 106 |
| 9 | 1426 | 106 |
| 0 | 1426 | 106 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) |
x |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z) |
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) |
#s(literal 1 binary64) |
(pow.f64 (-.f64 y x) #s(literal -1 binary64)) |
(-.f64 y x) |
y |
#s(literal -1 binary64) |
z |
#s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
(/.f64 y z) |
y |
z |
#s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) |
(/.f64 (-.f64 y x) z) |
(-.f64 y x) |
y |
x |
z |
(fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) |
(/.f64 #s(literal -1 binary64) z) |
#s(literal -1 binary64) |
z |
(-.f64 x y) |
x |
y |
(-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) |
(/.f64 y z) |
y |
z |
(-.f64 (/.f64 x z) x) |
(/.f64 x z) |
x |
| Outputs |
|---|
(+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
x |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z) |
(/.f64 (-.f64 y x) z) |
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) |
(-.f64 y x) |
#s(literal 1 binary64) |
(pow.f64 (-.f64 y x) #s(literal -1 binary64)) |
(-.f64 y x) |
y |
#s(literal -1 binary64) |
z |
#s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
(/.f64 y z) |
y |
z |
#s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) |
(/.f64 (-.f64 y x) z) |
(-.f64 y x) |
y |
x |
z |
(fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/.f64 #s(literal -1 binary64) z) |
#s(literal -1 binary64) |
z |
(-.f64 x y) |
x |
y |
(-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/.f64 y z) |
y |
z |
(-.f64 (/.f64 x z) x) |
(/.f64 x z) |
x |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (/.f64 y z) | |
| accuracy | 0 | (/.f64 x z) | |
| accuracy | 0.0078125 | (-.f64 (/.f64 x z) x) | |
| accuracy | 1.7695250574906176 | (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) | |
| accuracy | 0 | (/.f64 #s(literal -1 binary64) z) | |
| accuracy | 0 | (-.f64 x y) | |
| accuracy | 0.140625 | (fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) | |
| accuracy | 0 | (-.f64 y x) | |
| accuracy | 0.0234375 | (/.f64 (-.f64 y x) z) | |
| accuracy | 18.29859788591886 | #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) | |
| accuracy | 0 | (/.f64 y z) | |
| accuracy | 34.46789361848615 | #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) | |
| accuracy | 0.0078125 | (+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) | |
| accuracy | 0.015625 | (pow.f64 (-.f64 y x) #s(literal -1 binary64)) | |
| accuracy | 0.0234375 | (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z) | |
| accuracy | 0.16015625 | (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) |
| 72.0ms | 256× | 0 | valid |
Compiled 114 to 22 computations (80.7% saved)
ival-div: 10.0ms (39.5% of total)ival-pow: 6.0ms (23.7% of total)ival-sub: 5.0ms (19.8% of total)ival-add: 3.0ms (11.9% of total)ival-mult: 1.0ms (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 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) #<representation binary64>) () ()) |
#s(alt (+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) (patch (+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) #<representation binary64>) () ()) |
#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z) (patch (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z) #<representation binary64>) () ()) |
#s(alt (pow.f64 (-.f64 y x) #s(literal -1 binary64)) (patch (pow.f64 (-.f64 y x) #s(literal -1 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) #<representation binary64>) () ()) |
#s(alt (/.f64 y z) (patch (/.f64 y z) #<representation binary64>) () ()) |
#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ()) |
#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ()) |
#s(alt (fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) (patch (fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal -1 binary64) z) (patch (/.f64 #s(literal -1 binary64) z) #<representation binary64>) () ()) |
#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ()) |
#s(alt (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) (patch (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) #<representation binary64>) () ()) |
#s(alt (-.f64 (/.f64 x z) x) (patch (-.f64 (/.f64 x z) x) #<representation binary64>) () ()) |
#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) (patch (+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt (+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) (patch (+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt (+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) (patch (+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt (+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) (patch (+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z) (patch (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z) (patch (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z) (patch (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z) (patch (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) #<representation binary64>) () ())) ()) |
#s(alt (/ y z) (taylor 0 z) (#s(alt (/.f64 y z) (patch (/.f64 y z) #<representation binary64>) () ())) ()) |
#s(alt (/ y z) (taylor 0 z) (#s(alt (/.f64 y z) (patch (/.f64 y z) #<representation binary64>) () ())) ()) |
#s(alt (/ y z) (taylor 0 z) (#s(alt (/.f64 y z) (patch (/.f64 y z) #<representation binary64>) () ())) ()) |
#s(alt (/ y z) (taylor 0 z) (#s(alt (/.f64 y z) (patch (/.f64 y z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (/.f64 (-.f64 y x) z) (patch (/.f64 (-.f64 y x) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (- x y) z)) (taylor 0 z) (#s(alt (fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) (patch (fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1 (- x y)) (* x z)) z) (taylor 0 z) (#s(alt (fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) (patch (fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1 (- x y)) (* x z)) z) (taylor 0 z) (#s(alt (fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) (patch (fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1 (- x y)) (* x z)) z) (taylor 0 z) (#s(alt (fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) (patch (fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) #<representation binary64>) () ())) ()) |
#s(alt (/ -1 z) (taylor 0 z) (#s(alt (/.f64 #s(literal -1 binary64) z) (patch (/.f64 #s(literal -1 binary64) z) #<representation binary64>) () ())) ()) |
#s(alt (/ -1 z) (taylor 0 z) (#s(alt (/.f64 #s(literal -1 binary64) z) (patch (/.f64 #s(literal -1 binary64) z) #<representation binary64>) () ())) ()) |
#s(alt (/ -1 z) (taylor 0 z) (#s(alt (/.f64 #s(literal -1 binary64) z) (patch (/.f64 #s(literal -1 binary64) z) #<representation binary64>) () ())) ()) |
#s(alt (/ -1 z) (taylor 0 z) (#s(alt (/.f64 #s(literal -1 binary64) z) (patch (/.f64 #s(literal -1 binary64) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) (patch (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) (patch (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) (patch (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) (patch (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor 0 z) (#s(alt (-.f64 (/.f64 x z) x) (patch (-.f64 (/.f64 x z) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ x (* -1 (* x z))) z) (taylor 0 z) (#s(alt (-.f64 (/.f64 x z) x) (patch (-.f64 (/.f64 x z) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ x (* -1 (* x z))) z) (taylor 0 z) (#s(alt (-.f64 (/.f64 x z) x) (patch (-.f64 (/.f64 x z) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ x (* -1 (* x z))) z) (taylor 0 z) (#s(alt (-.f64 (/.f64 x z) x) (patch (-.f64 (/.f64 x z) x) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor 0 z) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor 0 z) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor 0 z) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor 0 z) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf z) (#s(alt (+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) (patch (+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) #<representation binary64>) () ())) ()) |
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#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 (* -1 (* x (- (/ 1 z) 1))) (taylor -inf x) (#s(alt (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) (patch (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) (patch (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) (patch (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) (patch (-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- 1 (/ 1 z)))) (taylor -inf x) (#s(alt (-.f64 (/.f64 x z) x) (patch (-.f64 (/.f64 x z) x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- 1 (/ 1 z)))) (taylor -inf x) (#s(alt (-.f64 (/.f64 x z) x) (patch (-.f64 (/.f64 x z) x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- 1 (/ 1 z)))) (taylor -inf x) (#s(alt (-.f64 (/.f64 x z) x) (patch (-.f64 (/.f64 x z) x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- 1 (/ 1 z)))) (taylor -inf x) (#s(alt (-.f64 (/.f64 x z) x) (patch (-.f64 (/.f64 x z) x) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor -inf x) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor -inf x) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor -inf x) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor -inf x) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | z | @ | -inf | ((/ 1 (pow (- y x) -1)) (+ x (/ (/ 1 (pow (- y x) -1)) z)) (/ (/ 1 (pow (- y x) -1)) z) (pow (- y x) -1) (+ x (/ (- y x) z)) (/ y z) (+ x (/ (- y x) z)) (/ (- y x) z) (- y x) (+ (* (/ -1 z) (- x y)) x) (/ -1 z) (- x y) (- (/ y z) (- (/ x z) x)) (- (/ x z) x) (/ x z)) |
| 1.0ms | x | @ | inf | ((/ 1 (pow (- y x) -1)) (+ x (/ (/ 1 (pow (- y x) -1)) z)) (/ (/ 1 (pow (- y x) -1)) z) (pow (- y x) -1) (+ x (/ (- y x) z)) (/ y z) (+ x (/ (- y x) z)) (/ (- y x) z) (- y x) (+ (* (/ -1 z) (- x y)) x) (/ -1 z) (- x y) (- (/ y z) (- (/ x z) x)) (- (/ x z) x) (/ x z)) |
| 1.0ms | z | @ | 0 | ((/ 1 (pow (- y x) -1)) (+ x (/ (/ 1 (pow (- y x) -1)) z)) (/ (/ 1 (pow (- y x) -1)) z) (pow (- y x) -1) (+ x (/ (- y x) z)) (/ y z) (+ x (/ (- y x) z)) (/ (- y x) z) (- y x) (+ (* (/ -1 z) (- x y)) x) (/ -1 z) (- x y) (- (/ y z) (- (/ x z) x)) (- (/ x z) x) (/ x z)) |
| 1.0ms | y | @ | inf | ((/ 1 (pow (- y x) -1)) (+ x (/ (/ 1 (pow (- y x) -1)) z)) (/ (/ 1 (pow (- y x) -1)) z) (pow (- y x) -1) (+ x (/ (- y x) z)) (/ y z) (+ x (/ (- y x) z)) (/ (- y x) z) (- y x) (+ (* (/ -1 z) (- x y)) x) (/ -1 z) (- x y) (- (/ y z) (- (/ x z) x)) (- (/ x z) x) (/ x z)) |
| 1.0ms | y | @ | -inf | ((/ 1 (pow (- y x) -1)) (+ x (/ (/ 1 (pow (- y x) -1)) z)) (/ (/ 1 (pow (- y x) -1)) z) (pow (- y x) -1) (+ x (/ (- y x) z)) (/ y z) (+ x (/ (- y x) z)) (/ (- y x) z) (- y x) (+ (* (/ -1 z) (- x y)) x) (/ -1 z) (- x y) (- (/ y z) (- (/ x z) x)) (- (/ x z) x) (/ x z)) |
| 1× | egg-herbie |
| 9 568× | lower-fma.f64 |
| 9 568× | lower-fma.f32 |
| 3 486× | lower-*.f64 |
| 3 486× | lower-*.f32 |
| 1 892× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 210 | 2282 |
| 1 | 601 | 2256 |
| 2 | 1611 | 2219 |
| 3 | 5866 | 2219 |
| 0 | 8380 | 2187 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (- y x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ (- y x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(* -1 (/ (- x y) z)) |
(/ (+ (* -1 (- x y)) (* x z)) z) |
(/ (+ (* -1 (- x y)) (* x z)) z) |
(/ (+ (* -1 (- x y)) (* x z)) z) |
(/ -1 z) |
(/ -1 z) |
(/ -1 z) |
(/ -1 z) |
(/ (- y x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ x z) |
(/ (+ x (* -1 (* x z))) z) |
(/ (+ x (* -1 (* x z))) z) |
(/ (+ x (* -1 (* x z))) z) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
x |
(+ x (* -1 (/ (- x y) z))) |
(+ x (* -1 (/ (- x y) z))) |
(+ x (* -1 (/ (- x y) z))) |
(/ -1 z) |
(/ -1 z) |
(/ -1 z) |
(/ -1 z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(* -1 x) |
(- (/ x z) x) |
(- (/ x z) x) |
(- (/ x z) x) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
x |
(+ x (* -1 (/ (- x y) z))) |
(+ x (* -1 (/ (- x y) z))) |
(+ x (* -1 (/ (- x y) z))) |
(/ -1 z) |
(/ -1 z) |
(/ -1 z) |
(/ -1 z) |
x |
(+ x (* -1 (/ (- (* -1 y) (* -1 x)) z))) |
(+ x (* -1 (/ (- (* -1 y) (* -1 x)) z))) |
(+ x (* -1 (/ (- (* -1 y) (* -1 x)) z))) |
(* -1 x) |
(- (/ x z) x) |
(- (/ x z) x) |
(- (/ x z) x) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
(* -1 x) |
(- y x) |
(- y x) |
(- y x) |
(- x (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(* -1 (/ x z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(/ -1 x) |
(- (* -1 (/ y (pow x 2))) (/ 1 x)) |
(- (* y (- (* -1 (/ 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)) |
(- x (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(- x (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(* -1 (/ x z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(* -1 x) |
(- y x) |
(- y x) |
(- y x) |
(+ x (* -1 (/ x z))) |
(+ x (+ (* -1 (/ x z)) (/ y z))) |
(+ x (+ (* -1 (/ x z)) (/ y z))) |
(+ x (+ (* -1 (/ x z)) (/ y z))) |
x |
(+ x (* -1 y)) |
(+ x (* -1 y)) |
(+ x (* -1 y)) |
(- x (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
y |
(* y (+ 1 (* -1 (/ x y)))) |
(* y (+ 1 (* -1 (/ x y)))) |
(* y (+ 1 (* -1 (/ x y)))) |
(/ y z) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(/ y z) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(/ 1 y) |
(/ (+ 1 (/ x y)) y) |
(/ (- (+ 1 (/ (pow x 2) (pow y 2))) (* -1 (/ x y))) y) |
(/ (- (+ 1 (/ (pow x 3) (pow y 3))) (+ (* -1 (/ x y)) (* -1 (/ (pow x 2) (pow y 2))))) y) |
(/ y z) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(/ y z) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
y |
(* y (+ 1 (* -1 (/ x y)))) |
(* y (+ 1 (* -1 (/ x y)))) |
(* y (+ 1 (* -1 (/ x y)))) |
(/ y z) |
(* y (+ (* -1 (/ x (* y z))) (+ (/ 1 z) (/ x y)))) |
(* y (+ (* -1 (/ x (* y z))) (+ (/ 1 z) (/ x y)))) |
(* y (+ (* -1 (/ x (* y z))) (+ (/ 1 z) (/ x y)))) |
(* -1 y) |
(* y (- (/ x y) 1)) |
(* y (- (/ x y) 1)) |
(* y (- (/ x y) 1)) |
(/ y z) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
y |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (* y (- (/ x y) 1))) |
(/ y z) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(/ y z) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(/ 1 y) |
(* -1 (/ (- (* -1 (/ x y)) 1) y)) |
(* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) (* -1 x)) y)) 1) y)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow x 3) y)) (pow x 2)) y)) (* -1 x)) y)) 1) y)) |
(/ y z) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(/ y z) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
y |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (* y (- (/ x y) 1))) |
(/ y z) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 y) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
(/ y z) |
(* -1 (* y (- (* -1 (/ (- x (/ x z)) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (- x (/ x z)) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (- x (/ x z)) y)) (/ 1 z)))) |
y |
(+ y (* -1 x)) |
(+ y (* -1 x)) |
(+ y (* -1 x)) |
(/ y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(/ y z) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(/ 1 y) |
(+ (/ 1 y) (/ x (pow y 2))) |
(+ (* x (+ (/ 1 (pow y 2)) (/ x (pow y 3)))) (/ 1 y)) |
(+ (* x (+ (* x (+ (/ 1 (pow y 3)) (/ x (pow y 4)))) (/ 1 (pow y 2)))) (/ 1 y)) |
(/ y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(/ y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(/ y z) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
y |
(+ y (* -1 x)) |
(+ y (* -1 x)) |
(+ y (* -1 x)) |
(/ y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(* -1 y) |
(- x y) |
(- x y) |
(- x y) |
(/ y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(* x (- (/ 1 z) 1)) |
(* x (- (/ 1 z) 1)) |
(* x (- (/ 1 z) 1)) |
(* x (- (/ 1 z) 1)) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
(* -1 x) |
(* x (- (/ y x) 1)) |
(* x (- (/ y x) 1)) |
(* x (- (/ y x) 1)) |
(* x (- 1 (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* -1 (/ x z)) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(/ -1 x) |
(/ (- (* -1 (/ y x)) 1) x) |
(/ (- (* -1 (/ (pow y 2) (pow x 2))) (+ 1 (/ y x))) x) |
(/ (- (* -1 (/ (pow y 3) (pow x 3))) (+ 1 (+ (/ y x) (/ (pow y 2) (pow x 2))))) x) |
(* x (- 1 (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- 1 (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* -1 (/ x z)) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* -1 x) |
(* x (- (/ y x) 1)) |
(* x (- (/ y x) 1)) |
(* x (- (/ y x) 1)) |
(* x (- 1 (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
x |
(* x (+ 1 (* -1 (/ y x)))) |
(* x (+ 1 (* -1 (/ y x)))) |
(* x (+ 1 (* -1 (/ y x)))) |
(* x (- 1 (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (/ 1 z) 1)) |
(* x (- (/ 1 z) 1)) |
(* x (- (/ 1 z) 1)) |
(* x (- (/ 1 z) 1)) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
(* -1 x) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (/ x z)) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(/ -1 x) |
(* -1 (/ (+ 1 (/ y x)) x)) |
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) y) x))) x)) |
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (* -1 (pow y 2))) x)) y) x))) x)) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (/ x z)) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 x) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
x |
(* -1 (* x (- (/ y x) 1))) |
(* -1 (* x (- (/ y x) 1))) |
(* -1 (* x (- (/ y x) 1))) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- 1 (/ 1 z)))) |
(* -1 (* x (- 1 (/ 1 z)))) |
(* -1 (* x (- 1 (/ 1 z)))) |
(* -1 (* x (- 1 (/ 1 z)))) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
| Outputs |
|---|
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- (+ y (* x z)) x) z) |
(/.f64 (fma.f64 z x (-.f64 y x)) z) |
(/ (- (+ y (* x z)) x) z) |
(/.f64 (fma.f64 z x (-.f64 y x)) z) |
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(/.f64 y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ y z) |
(/.f64 y z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(+ (/ 1 y) (/ x (pow y 2))) |
(/.f64 (-.f64 (/.f64 x y) #s(literal -1 binary64)) y) |
(+ (* x (+ (/ 1 (pow y 2)) (/ x (pow y 3)))) (/ 1 y)) |
(/.f64 (fma.f64 (-.f64 (/.f64 x y) #s(literal -1 binary64)) (/.f64 x y) #s(literal 1 binary64)) y) |
(+ (* x (+ (* x (+ (/ 1 (pow y 3)) (/ x (pow y 4)))) (/ 1 (pow y 2)))) (/ 1 y)) |
(fma.f64 (fma.f64 (/.f64 x (pow.f64 y #s(literal 4 binary64))) x (/.f64 x (pow.f64 y #s(literal 3 binary64)))) x (/.f64 (-.f64 (/.f64 x y) #s(literal -1 binary64)) y)) |
(/ y z) |
(/.f64 y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ y z) |
(/.f64 y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ y z) |
(/.f64 y z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
y |
(+ y (* -1 x)) |
(-.f64 y x) |
(+ y (* -1 x)) |
(-.f64 y x) |
(+ y (* -1 x)) |
(-.f64 y x) |
(/ y z) |
(/.f64 y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 y) |
(neg.f64 y) |
(- x y) |
(-.f64 x y) |
(- x y) |
(-.f64 x y) |
(- x y) |
(-.f64 x y) |
(/ y z) |
(/.f64 y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* x (- (/ 1 z) 1)) |
(-.f64 (/.f64 x z) x) |
(* x (- (/ 1 z) 1)) |
(-.f64 (/.f64 x z) x) |
(* x (- (/ 1 z) 1)) |
(-.f64 (/.f64 x z) x) |
(* x (- (/ 1 z) 1)) |
(-.f64 (/.f64 x z) x) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(* -1 x) |
(neg.f64 x) |
(* x (- (/ y x) 1)) |
(-.f64 y x) |
(* x (- (/ y x) 1)) |
(-.f64 y x) |
(* x (- (/ y x) 1)) |
(-.f64 y x) |
(* x (- 1 (/ 1 z))) |
(-.f64 x (/.f64 x z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (/ x z)) |
(/.f64 (neg.f64 x) z) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(/.f64 (-.f64 y x) z) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(/.f64 (-.f64 y x) z) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(/.f64 (-.f64 y x) z) |
(/ -1 x) |
(/.f64 #s(literal -1 binary64) x) |
(/ (- (* -1 (/ y x)) 1) x) |
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 y x)) x) |
(/ (- (* -1 (/ (pow y 2) (pow x 2))) (+ 1 (/ y x))) x) |
(/.f64 (fma.f64 (/.f64 y x) (-.f64 #s(literal -1 binary64) (/.f64 y x)) #s(literal -1 binary64)) x) |
(/ (- (* -1 (/ (pow y 3) (pow x 3))) (+ 1 (+ (/ y x) (/ (pow y 2) (pow x 2))))) x) |
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (/.f64 y x) (fma.f64 (/.f64 y x) y y) y) x)) x) |
(* x (- 1 (/ 1 z))) |
(-.f64 x (/.f64 x z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* x (- 1 (/ 1 z))) |
(-.f64 x (/.f64 x z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (/ x z)) |
(/.f64 (neg.f64 x) z) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(/.f64 (-.f64 y x) z) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(/.f64 (-.f64 y x) z) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(/.f64 (-.f64 y x) z) |
(* -1 x) |
(neg.f64 x) |
(* x (- (/ y x) 1)) |
(-.f64 y x) |
(* x (- (/ y x) 1)) |
(-.f64 y x) |
(* x (- (/ y x) 1)) |
(-.f64 y x) |
(* x (- 1 (/ 1 z))) |
(-.f64 x (/.f64 x z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
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 (/ 1 z))) |
(-.f64 x (/.f64 x z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* x (- (/ 1 z) 1)) |
(-.f64 (/.f64 x z) x) |
(* x (- (/ 1 z) 1)) |
(-.f64 (/.f64 x z) x) |
(* x (- (/ 1 z) 1)) |
(-.f64 (/.f64 x z) x) |
(* x (- (/ 1 z) 1)) |
(-.f64 (/.f64 x z) x) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(-.f64 y x) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(-.f64 y x) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(-.f64 y x) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (/ x z)) |
(/.f64 (neg.f64 x) z) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(/.f64 (-.f64 y x) z) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(/.f64 (-.f64 y x) z) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(/.f64 (-.f64 y x) z) |
(/ -1 x) |
(/.f64 #s(literal -1 binary64) x) |
(* -1 (/ (+ 1 (/ y x)) x)) |
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 y x)) x) |
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) y) x))) x)) |
(/.f64 (fma.f64 (/.f64 y x) (-.f64 #s(literal -1 binary64) (/.f64 y x)) #s(literal -1 binary64)) x) |
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (* -1 (pow y 2))) x)) y) x))) x)) |
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (/.f64 y x) (fma.f64 (/.f64 y x) y y) y) x)) x) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (/ x z)) |
(/.f64 (neg.f64 x) z) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(/.f64 (-.f64 y x) z) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(/.f64 (-.f64 y x) z) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(/.f64 (-.f64 y x) z) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(-.f64 y x) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(-.f64 y x) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(-.f64 y x) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
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) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (* x (- 1 (/ 1 z)))) |
(-.f64 (/.f64 x z) x) |
(* -1 (* x (- 1 (/ 1 z)))) |
(-.f64 (/.f64 x z) x) |
(* -1 (* x (- 1 (/ 1 z)))) |
(-.f64 (/.f64 x z) x) |
(* -1 (* x (- 1 (/ 1 z)))) |
(-.f64 (/.f64 x z) x) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
| 5 040× | lower-*.f64 |
| 5 040× | lower-*.f32 |
| 4 582× | lower-/.f32 |
| 4 572× | lower-/.f64 |
| 2 412× | lower-fma.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 23 | 98 |
| 0 | 37 | 96 |
| 1 | 170 | 84 |
| 2 | 1604 | 84 |
| 0 | 8664 | 84 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) |
(+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z) |
(pow.f64 (-.f64 y x) #s(literal -1 binary64)) |
#s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
(/.f64 y z) |
#s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) |
(/.f64 (-.f64 y x) z) |
(-.f64 y x) |
(fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) |
(/.f64 #s(literal -1 binary64) z) |
(-.f64 x y) |
(-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) |
(-.f64 (/.f64 x z) x) |
(/.f64 x z) |
| Outputs |
|---|
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Compiled 26 778 to 2 359 computations (91.2% saved)
11 alts after pruning (7 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 413 | 6 | 1 419 |
| Fresh | 2 | 1 | 3 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 417 | 11 | 1 428 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.8% | (fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) |
| ▶ | 74.5% | (fma.f64 (/.f64 #s(literal -1 binary64) z) #s(approx (- x y) (neg.f64 y)) x) |
| 68.3% | (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) | |
| ✓ | 100.0% | (+.f64 x (/.f64 (-.f64 y x) z)) |
| ▶ | 99.8% | (+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z (-.f64 y x)))) |
| ▶ | 74.6% | (+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) |
| ▶ | 56.4% | #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) |
| ✓ | 71.4% | #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) |
| ▶ | 28.6% | #s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) |
| ✓ | 46.1% | #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
| 71.1% | #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) |
Compiled 131 to 126 computations (3.8% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (neg.f64 y) | |
| cost-diff | 0 | #s(approx (- x y) (neg.f64 y)) | |
| cost-diff | 0 | (/.f64 #s(literal -1 binary64) z) | |
| cost-diff | 192 | (fma.f64 (/.f64 #s(literal -1 binary64) z) #s(approx (- x y) (neg.f64 y)) x) | |
| cost-diff | 0 | (/.f64 y z) | |
| cost-diff | 0 | #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z)) | |
| cost-diff | 0 | (+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) | |
| cost-diff | 0 | (/.f64 x z) | |
| cost-diff | 0 | (-.f64 x (/.f64 x z)) | |
| cost-diff | 0 | #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) | |
| cost-diff | 0 | (neg.f64 x) | |
| cost-diff | 0 | #s(approx (- y x) (neg.f64 x)) | |
| cost-diff | 0 | (/.f64 #s(approx (- y x) (neg.f64 x)) z) | |
| cost-diff | 0 | #s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) | |
| cost-diff | 0 | (-.f64 y x) | |
| cost-diff | 0 | (/.f64 z (-.f64 y x)) | |
| cost-diff | 0 | (+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z (-.f64 y x)))) | |
| cost-diff | 704 | (/.f64 #s(literal 1 binary64) (/.f64 z (-.f64 y x))) |
| 896× | lower-fma.f32 |
| 894× | lower-fma.f64 |
| 448× | lower-*.f64 |
| 448× | lower-*.f32 |
| 248× | lower-+.f32 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 34 | 147 |
| 0 | 48 | 145 |
| 1 | 75 | 133 |
| 2 | 124 | 133 |
| 3 | 244 | 132 |
| 4 | 552 | 132 |
| 5 | 979 | 132 |
| 6 | 1303 | 132 |
| 7 | 1478 | 132 |
| 8 | 1639 | 132 |
| 9 | 1728 | 132 |
| 10 | 1738 | 132 |
| 11 | 1740 | 132 |
| 12 | 1743 | 132 |
| 13 | 1744 | 132 |
| 0 | 1744 | 132 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z (-.f64 y x)))) |
x |
(/.f64 #s(literal 1 binary64) (/.f64 z (-.f64 y x))) |
#s(literal 1 binary64) |
(/.f64 z (-.f64 y x)) |
z |
(-.f64 y x) |
y |
#s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) |
(/.f64 #s(approx (- y x) (neg.f64 x)) z) |
#s(approx (- y x) (neg.f64 x)) |
(neg.f64 x) |
x |
z |
#s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) |
(-.f64 x (/.f64 x z)) |
x |
(/.f64 x z) |
z |
(+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) |
x |
#s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z)) |
(/.f64 y z) |
y |
z |
(fma.f64 (/.f64 #s(literal -1 binary64) z) #s(approx (- x y) (neg.f64 y)) x) |
(/.f64 #s(literal -1 binary64) z) |
#s(literal -1 binary64) |
z |
#s(approx (- x y) (neg.f64 y)) |
(neg.f64 y) |
y |
x |
| Outputs |
|---|
(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z (-.f64 y x)))) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
x |
(/.f64 #s(literal 1 binary64) (/.f64 z (-.f64 y x))) |
(/.f64 (-.f64 y x) z) |
#s(literal 1 binary64) |
(/.f64 z (-.f64 y x)) |
z |
(-.f64 y x) |
y |
#s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) |
(/.f64 #s(approx (- y x) (neg.f64 x)) z) |
#s(approx (- y x) (neg.f64 x)) |
(neg.f64 x) |
x |
z |
#s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) |
#s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))) |
(-.f64 x (/.f64 x z)) |
x |
(/.f64 x z) |
z |
(+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) |
(+.f64 #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z)) x) |
x |
#s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z)) |
(/.f64 y z) |
y |
z |
(fma.f64 (/.f64 #s(literal -1 binary64) z) #s(approx (- x y) (neg.f64 y)) x) |
(-.f64 x (/.f64 #s(approx (- x y) (neg.f64 y)) z)) |
(/.f64 #s(literal -1 binary64) z) |
#s(literal -1 binary64) |
z |
#s(approx (- x y) (neg.f64 y)) |
(neg.f64 y) |
y |
x |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (/.f64 #s(literal -1 binary64) z) | |
| accuracy | 0 | (neg.f64 y) | |
| accuracy | 0.140625 | (fma.f64 (/.f64 #s(literal -1 binary64) z) #s(approx (- x y) (neg.f64 y)) x) | |
| accuracy | 30.187121826136348 | #s(approx (- x y) (neg.f64 y)) | |
| accuracy | 0 | (/.f64 y z) | |
| accuracy | 0.0078125 | (+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) | |
| accuracy | 29.117897998409568 | #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z)) | |
| accuracy | 0 | (/.f64 x z) | |
| accuracy | 0.0078125 | (-.f64 x (/.f64 x z)) | |
| accuracy | 27.884221081691866 | #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) | |
| accuracy | 0 | (neg.f64 x) | |
| accuracy | 0.0234375 | (/.f64 #s(approx (- y x) (neg.f64 x)) z) | |
| accuracy | 18.29859788591886 | #s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) | |
| accuracy | 33.42899144467678 | #s(approx (- y x) (neg.f64 x)) | |
| accuracy | 0 | (-.f64 y x) | |
| accuracy | 0.0078125 | (+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z (-.f64 y x)))) | |
| accuracy | 0.01171875 | (/.f64 z (-.f64 y x)) | |
| accuracy | 0.2265625 | (/.f64 #s(literal 1 binary64) (/.f64 z (-.f64 y x))) |
| 68.0ms | 256× | 0 | valid |
Compiled 115 to 28 computations (75.7% saved)
ival-div: 16.0ms (33.2% of total)ival-sub: 15.0ms (31.1% of total)ival-pow: 6.0ms (12.4% of total)ival-add: 5.0ms (10.4% of total)ival-neg: 4.0ms (8.3% of total)ival-mult: 2.0ms (4.1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 z (-.f64 y x))) (patch (/.f64 #s(literal 1 binary64) (/.f64 z (-.f64 y x))) #<representation binary64>) () ()) |
#s(alt (+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z (-.f64 y x)))) (patch (+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z (-.f64 y x)))) #<representation binary64>) () ()) |
#s(alt (/.f64 z (-.f64 y x)) (patch (/.f64 z (-.f64 y x)) #<representation binary64>) () ()) |
#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ()) |
#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(approx (- y x) (neg.f64 x)) z) (patch (/.f64 #s(approx (- y x) (neg.f64 x)) z) #<representation binary64>) () ()) |
#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ()) |
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ()) |
#s(alt #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) (patch #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) #<representation binary64>) () ()) |
#s(alt (-.f64 x (/.f64 x z)) (patch (-.f64 x (/.f64 x z)) #<representation binary64>) () ()) |
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#s(alt #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z)) (patch #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z)) #<representation binary64>) () ()) |
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#s(alt (/.f64 #s(literal -1 binary64) z) (patch (/.f64 #s(literal -1 binary64) z) #<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>) () ()) |
| Outputs |
|---|
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#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) (patch #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) (patch #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ 1 z) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 x z)) (patch (-.f64 x (/.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ 1 z) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 x z)) (patch (-.f64 x (/.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ 1 z) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 x z)) (patch (-.f64 x (/.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ 1 z) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 x z)) (patch (-.f64 x (/.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor -inf x) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor -inf x) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor -inf x) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor -inf x) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ 1 z) 1))) (taylor -inf x) (#s(alt (+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) (patch (+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt (+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) (patch (+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt (+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) (patch (+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt (+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) (patch (+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ x z)) (taylor -inf x) (#s(alt #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z)) (patch #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) (taylor -inf x) (#s(alt #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z)) (patch #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) (taylor -inf x) (#s(alt #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z)) (patch #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) (taylor -inf x) (#s(alt #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z)) (patch #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ 1 z) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal -1 binary64) z) #s(approx (- x y) (neg.f64 y)) x) (patch (fma.f64 (/.f64 #s(literal -1 binary64) z) #s(approx (- x y) (neg.f64 y)) x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal -1 binary64) z) #s(approx (- x y) (neg.f64 y)) x) (patch (fma.f64 (/.f64 #s(literal -1 binary64) z) #s(approx (- x y) (neg.f64 y)) x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal -1 binary64) z) #s(approx (- x y) (neg.f64 y)) x) (patch (fma.f64 (/.f64 #s(literal -1 binary64) z) #s(approx (- x y) (neg.f64 y)) x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal -1 binary64) z) #s(approx (- x y) (neg.f64 y)) x) (patch (fma.f64 (/.f64 #s(literal -1 binary64) z) #s(approx (- x y) (neg.f64 y)) x) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt #s(approx (- x y) (neg.f64 y)) (patch #s(approx (- x y) (neg.f64 y)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt #s(approx (- x y) (neg.f64 y)) (patch #s(approx (- x y) (neg.f64 y)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt #s(approx (- x y) (neg.f64 y)) (patch #s(approx (- x y) (neg.f64 y)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt #s(approx (- x y) (neg.f64 y)) (patch #s(approx (- x y) (neg.f64 y)) #<representation binary64>) () ())) ()) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | y | @ | inf | ((/ 1 (/ z (- y x))) (+ x (/ 1 (/ z (- y x)))) (/ z (- y x)) (- y x) (+ x (/ (- y x) z)) (/ (- y x) z) (- y x) (neg x) (- (/ y z) (- (/ x z) x)) (- x (/ x z)) (/ x z) (+ x (/ (/ 1 (pow (- y x) -1)) z)) (/ (/ 1 (pow (- y x) -1)) z) (/ y z) (+ (* (/ -1 z) (- x y)) x) (/ -1 z) (- x y) (neg y)) |
| 1.0ms | z | @ | -inf | ((/ 1 (/ z (- y x))) (+ x (/ 1 (/ z (- y x)))) (/ z (- y x)) (- y x) (+ x (/ (- y x) z)) (/ (- y x) z) (- y x) (neg x) (- (/ y z) (- (/ x z) x)) (- x (/ x z)) (/ x z) (+ x (/ (/ 1 (pow (- y x) -1)) z)) (/ (/ 1 (pow (- y x) -1)) z) (/ y z) (+ (* (/ -1 z) (- x y)) x) (/ -1 z) (- x y) (neg y)) |
| 1.0ms | z | @ | 0 | ((/ 1 (/ z (- y x))) (+ x (/ 1 (/ z (- y x)))) (/ z (- y x)) (- y x) (+ x (/ (- y x) z)) (/ (- y x) z) (- y x) (neg x) (- (/ y z) (- (/ x z) x)) (- x (/ x z)) (/ x z) (+ x (/ (/ 1 (pow (- y x) -1)) z)) (/ (/ 1 (pow (- y x) -1)) z) (/ y z) (+ (* (/ -1 z) (- x y)) x) (/ -1 z) (- x y) (neg y)) |
| 1.0ms | x | @ | inf | ((/ 1 (/ z (- y x))) (+ x (/ 1 (/ z (- y x)))) (/ z (- y x)) (- y x) (+ x (/ (- y x) z)) (/ (- y x) z) (- y x) (neg x) (- (/ y z) (- (/ x z) x)) (- x (/ x z)) (/ x z) (+ x (/ (/ 1 (pow (- y x) -1)) z)) (/ (/ 1 (pow (- y x) -1)) z) (/ y z) (+ (* (/ -1 z) (- x y)) x) (/ -1 z) (- x y) (neg y)) |
| 1.0ms | y | @ | -inf | ((/ 1 (/ z (- y x))) (+ x (/ 1 (/ z (- y x)))) (/ z (- y x)) (- y x) (+ x (/ (- y x) z)) (/ (- y x) z) (- y x) (neg x) (- (/ y z) (- (/ x z) x)) (- x (/ x z)) (/ x z) (+ x (/ (/ 1 (pow (- y x) -1)) z)) (/ (/ 1 (pow (- y x) -1)) z) (/ y z) (+ (* (/ -1 z) (- x y)) x) (/ -1 z) (- x y) (neg y)) |
| 1× | egg-herbie |
| 9 848× | lower-fma.f64 |
| 9 848× | lower-fma.f32 |
| 3 650× | lower-*.f64 |
| 3 650× | lower-*.f32 |
| 2 248× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 221 | 2935 |
| 1 | 639 | 2915 |
| 2 | 1771 | 2530 |
| 3 | 6049 | 2522 |
| 0 | 8277 | 2495 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ z (- y x)) |
(/ z (- y x)) |
(/ z (- y x)) |
(/ z (- y x)) |
(/ (- y x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(* -1 (/ x z)) |
(/ (- (* x z) x) z) |
(/ (- (* x z) x) z) |
(/ (- (* x z) x) z) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ (- y x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(* -1 (/ (- x y) z)) |
(/ (+ (* -1 (- x y)) (* x z)) z) |
(/ (+ (* -1 (- x y)) (* x z)) z) |
(/ (+ (* -1 (- x y)) (* x z)) z) |
(/ -1 z) |
(/ -1 z) |
(/ -1 z) |
(/ -1 z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ z (- y x)) |
(/ z (- y x)) |
(/ z (- y x)) |
(/ z (- y x)) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
x |
(+ x (* -1 (/ x z))) |
(+ x (* -1 (/ x z))) |
(+ x (* -1 (/ x z))) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
x |
(+ x (* -1 (/ (- x y) z))) |
(+ x (* -1 (/ (- x y) z))) |
(+ x (* -1 (/ (- x y) z))) |
(/ -1 z) |
(/ -1 z) |
(/ -1 z) |
(/ -1 z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ z (- y x)) |
(/ z (- y x)) |
(/ z (- y x)) |
(/ z (- y x)) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
x |
(+ x (* -1 (/ (- (* -1 y) (* -1 x)) z))) |
(+ x (* -1 (/ (- (* -1 y) (* -1 x)) z))) |
(+ x (* -1 (/ (- (* -1 y) (* -1 x)) z))) |
x |
(+ x (* -1 (/ x z))) |
(+ x (* -1 (/ x z))) |
(+ x (* -1 (/ x z))) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
x |
(+ x (* -1 (/ (- x y) z))) |
(+ x (* -1 (/ (- x y) z))) |
(+ x (* -1 (/ (- x y) z))) |
(/ -1 z) |
(/ -1 z) |
(/ -1 z) |
(/ -1 z) |
(* -1 (/ x z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(- x (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(* -1 (/ z x)) |
(+ (* -1 (/ z x)) (* -1 (/ (* y z) (pow x 2)))) |
(+ (* -1 (/ z x)) (* y (- (* -1 (/ (* y z) (pow x 3))) (/ z (pow x 2))))) |
(+ (* -1 (/ z x)) (* y (- (* y (- (* -1 (/ (* y z) (pow x 4))) (/ z (pow x 3)))) (/ z (pow x 2))))) |
(* -1 x) |
(- y x) |
(- y x) |
(- y x) |
(- x (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(* -1 (/ x z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(* -1 x) |
(- y x) |
(- y x) |
(- y x) |
(- x (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- x (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(* -1 (/ x z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(+ x (* -1 (/ x z))) |
(+ x (+ (* -1 (/ x z)) (/ y z))) |
(+ x (+ (* -1 (/ x z)) (/ y z))) |
(+ x (+ (* -1 (/ x z)) (/ y z))) |
x |
(+ x (* -1 y)) |
(+ x (* -1 y)) |
(+ x (* -1 y)) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(/ y z) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(/ y z) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(/ z y) |
(/ (+ z (/ (* x z) y)) y) |
(/ (- (+ z (/ (* (pow x 2) z) (pow y 2))) (* -1 (/ (* x z) y))) y) |
(/ (- (+ z (/ (* (pow x 3) z) (pow y 3))) (+ (* -1 (/ (* x z) y)) (* -1 (/ (* (pow x 2) z) (pow y 2))))) y) |
y |
(* y (+ 1 (* -1 (/ x y)))) |
(* y (+ 1 (* -1 (/ x y)))) |
(* y (+ 1 (* -1 (/ x y)))) |
(/ y z) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(/ y z) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
y |
(* y (+ 1 (* -1 (/ x y)))) |
(* y (+ 1 (* -1 (/ x y)))) |
(* y (+ 1 (* -1 (/ x y)))) |
(/ y z) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(/ y z) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(/ y z) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(* y (+ (* -1 (/ x (* y z))) (+ (/ 1 z) (/ x y)))) |
(* y (+ (* -1 (/ x (* y z))) (+ (/ 1 z) (/ x y)))) |
(* y (+ (* -1 (/ x (* y z))) (+ (/ 1 z) (/ x y)))) |
(* -1 y) |
(* y (- (/ x y) 1)) |
(* y (- (/ x y) 1)) |
(* y (- (/ x y) 1)) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(/ y z) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(/ y z) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(/ z y) |
(* -1 (/ (+ (* -1 z) (* -1 (/ (* x z) y))) y)) |
(* -1 (/ (+ (* -1 z) (* -1 (/ (+ (* x z) (/ (* (pow x 2) z) y)) y))) y)) |
(* -1 (/ (+ (* -1 z) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow x 2) z)) (* -1 (/ (* (pow x 3) z) y))) y)) (* x z)) y))) y)) |
y |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (* y (- (/ x y) 1))) |
(/ y z) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(/ y z) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
y |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (* y (- (/ x y) 1))) |
(/ y z) |
(* -1 (* y (- (* -1 (/ (- x (/ x z)) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (- x (/ x z)) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (- x (/ x z)) y)) (/ 1 z)))) |
(/ y z) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(/ y z) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -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) |
(/ y z) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(/ y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(/ z y) |
(+ (/ z y) (/ (* x z) (pow y 2))) |
(+ (* x (- (/ (* x z) (pow y 3)) (* -1 (/ z (pow y 2))))) (/ z y)) |
(+ (* x (- (* x (- (/ (* x z) (pow y 4)) (* -1 (/ z (pow y 3))))) (* -1 (/ z (pow y 2))))) (/ z y)) |
y |
(+ y (* -1 x)) |
(+ y (* -1 x)) |
(+ y (* -1 x)) |
(/ y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(/ y z) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
y |
(+ y (* -1 x)) |
(+ y (* -1 x)) |
(+ y (* -1 x)) |
(* -1 x) |
(* -1 x) |
(* -1 x) |
(* -1 x) |
(/ y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(* x (- 1 (/ 1 z))) |
(* x (- 1 (/ 1 z))) |
(* x (- 1 (/ 1 z))) |
(* x (- 1 (/ 1 z))) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(/ y z) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(/ y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(* -1 y) |
(- x y) |
(- x y) |
(- x y) |
(* -1 (/ x z)) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* x (- 1 (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* -1 (/ z x)) |
(/ (+ (* -1 z) (* -1 (/ (* y z) x))) x) |
(/ (- (+ (* -1 z) (* -1 (/ (* (pow y 2) z) (pow x 2)))) (/ (* y z) x)) x) |
(/ (- (+ (* -1 z) (* -1 (/ (* (pow y 3) z) (pow x 3)))) (+ (/ (* y z) x) (/ (* (pow y 2) z) (pow x 2)))) x) |
(* -1 x) |
(* x (- (/ y x) 1)) |
(* x (- (/ y x) 1)) |
(* x (- (/ y x) 1)) |
(* x (- 1 (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* -1 (/ x z)) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* -1 x) |
(* x (- (/ y x) 1)) |
(* x (- (/ y x) 1)) |
(* x (- (/ y x) 1)) |
(* -1 x) |
(* -1 x) |
(* -1 x) |
(* -1 x) |
(* x (- 1 (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- 1 (/ 1 z))) |
(* x (- 1 (/ 1 z))) |
(* x (- 1 (/ 1 z))) |
(* x (- 1 (/ 1 z))) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
(* x (- 1 (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* -1 (/ x z)) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* x (- 1 (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
x |
(* x (+ 1 (* -1 (/ y x)))) |
(* x (+ 1 (* -1 (/ y x)))) |
(* x (+ 1 (* -1 (/ y x)))) |
(* -1 (/ x z)) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (/ z x)) |
(* -1 (/ (+ z (/ (* y z) x)) x)) |
(* -1 (/ (+ z (* -1 (/ (- (* -1 (/ (* (pow y 2) z) x)) (* y z)) x))) x)) |
(* -1 (/ (+ z (* -1 (/ (- (* -1 (/ (- (/ (* (pow y 3) z) x) (* -1 (* (pow y 2) z))) x)) (* y z)) x))) x)) |
(* -1 x) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (/ x z)) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 x) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 x) |
(* -1 x) |
(* -1 x) |
(* -1 x) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (/ 1 z) 1))) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (/ x z)) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
x |
(* -1 (* x (- (/ y x) 1))) |
(* -1 (* x (- (/ y x) 1))) |
(* -1 (* x (- (/ y x) 1))) |
| Outputs |
|---|
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- (+ y (* x z)) x) z) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ (- (+ y (* x z)) x) z) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ (- (+ y (* x z)) x) z) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ z (- y x)) |
(/.f64 z (-.f64 y x)) |
(/ z (- y x)) |
(/.f64 z (-.f64 y x)) |
(/ z (- y x)) |
(/.f64 z (-.f64 y x)) |
(/ z (- y x)) |
(/.f64 z (-.f64 y x)) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- (+ y (* x z)) x) z) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ (- (+ y (* x z)) x) z) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ (- (+ y (* x z)) x) z) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- (+ y (* x z)) x) z) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ (- (+ y (* x z)) x) z) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ (- (+ y (* x z)) x) z) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (/ x z)) |
(/.f64 (neg.f64 x) z) |
(/ (- (* x z) x) z) |
(-.f64 x (/.f64 x z)) |
(/ (- (* x z) x) z) |
(-.f64 x (/.f64 x z)) |
(/ (- (* x z) x) z) |
(-.f64 x (/.f64 x z)) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- (+ y (* x z)) x) z) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ (- (+ y (* x z)) x) z) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ (- (+ y (* x z)) x) z) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ y z) |
(/.f64 y z) |
(/ y z) |
(/.f64 y z) |
(/ y z) |
(/.f64 y z) |
(/ y z) |
(/.f64 y z) |
(* -1 (/ (- x y) z)) |
(/.f64 (-.f64 y x) z) |
(/ (+ (* -1 (- x y)) (* x z)) z) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ (+ (* -1 (- x y)) (* x z)) z) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ (+ (* -1 (- x y)) (* x z)) z) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ -1 z) |
(/.f64 #s(literal -1 binary64) z) |
(/ -1 z) |
(/.f64 #s(literal -1 binary64) z) |
(/ -1 z) |
(/.f64 #s(literal -1 binary64) z) |
(/ -1 z) |
(/.f64 #s(literal -1 binary64) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ z (- y x)) |
(/.f64 z (-.f64 y x)) |
(/ z (- y x)) |
(/.f64 z (-.f64 y x)) |
(/ z (- y x)) |
(/.f64 z (-.f64 y x)) |
(/ z (- y x)) |
(/.f64 z (-.f64 y x)) |
x |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
x |
(+ x (* -1 (/ x z))) |
(-.f64 x (/.f64 x z)) |
(+ x (* -1 (/ x z))) |
(-.f64 x (/.f64 x z)) |
(+ x (* -1 (/ x z))) |
(-.f64 x (/.f64 x z)) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ y z) |
(/.f64 y z) |
(/ y z) |
(/.f64 y z) |
(/ y z) |
(/.f64 y z) |
(/ y z) |
(/.f64 y z) |
x |
(+ x (* -1 (/ (- x y) z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ x (* -1 (/ (- x y) z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ x (* -1 (/ (- x y) z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ -1 z) |
(/.f64 #s(literal -1 binary64) z) |
(/ -1 z) |
(/.f64 #s(literal -1 binary64) z) |
(/ -1 z) |
(/.f64 #s(literal -1 binary64) z) |
(/ -1 z) |
(/.f64 #s(literal -1 binary64) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ z (- y x)) |
(/.f64 z (-.f64 y x)) |
(/ z (- y x)) |
(/.f64 z (-.f64 y x)) |
(/ z (- y x)) |
(/.f64 z (-.f64 y x)) |
(/ z (- y x)) |
(/.f64 z (-.f64 y x)) |
x |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
x |
(+ x (* -1 (/ (- (* -1 y) (* -1 x)) z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ x (* -1 (/ (- (* -1 y) (* -1 x)) z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ x (* -1 (/ (- (* -1 y) (* -1 x)) z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
x |
(+ x (* -1 (/ x z))) |
(-.f64 x (/.f64 x z)) |
(+ x (* -1 (/ x z))) |
(-.f64 x (/.f64 x z)) |
(+ x (* -1 (/ x z))) |
(-.f64 x (/.f64 x z)) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ y z) |
(/.f64 y z) |
(/ y z) |
(/.f64 y z) |
(/ y z) |
(/.f64 y z) |
(/ y z) |
(/.f64 y z) |
x |
(+ x (* -1 (/ (- x y) z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ x (* -1 (/ (- x y) z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ x (* -1 (/ (- x y) z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ -1 z) |
(/.f64 #s(literal -1 binary64) z) |
(/ -1 z) |
(/.f64 #s(literal -1 binary64) z) |
(/ -1 z) |
(/.f64 #s(literal -1 binary64) z) |
(/ -1 z) |
(/.f64 #s(literal -1 binary64) z) |
(* -1 (/ x z)) |
(/.f64 (neg.f64 x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(- x (/ x z)) |
(-.f64 x (/.f64 x z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (/ z x)) |
(/.f64 z (neg.f64 x)) |
(+ (* -1 (/ z x)) (* -1 (/ (* y z) (pow x 2)))) |
(*.f64 (/.f64 z x) (-.f64 #s(literal -1 binary64) (/.f64 y x))) |
(+ (* -1 (/ z x)) (* y (- (* -1 (/ (* y z) (pow x 3))) (/ z (pow x 2))))) |
(/.f64 (fma.f64 y (/.f64 (fma.f64 (/.f64 y x) z z) x) z) (neg.f64 x)) |
(+ (* -1 (/ z x)) (* y (- (* y (- (* -1 (/ (* y z) (pow x 4))) (/ z (pow x 3)))) (/ z (pow x 2))))) |
(fma.f64 (*.f64 y y) (neg.f64 (fma.f64 (/.f64 z (pow.f64 x #s(literal 4 binary64))) y (/.f64 z (pow.f64 x #s(literal 3 binary64))))) (*.f64 (/.f64 z x) (-.f64 #s(literal -1 binary64) (/.f64 y x)))) |
(* -1 x) |
(neg.f64 x) |
(- y x) |
(-.f64 y x) |
(- y x) |
(-.f64 y x) |
(- y x) |
(-.f64 y x) |
(- x (/ x z)) |
(-.f64 x (/.f64 x z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (/ x z)) |
(/.f64 (neg.f64 x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(* -1 x) |
(neg.f64 x) |
(- y x) |
(-.f64 y x) |
(- y x) |
(-.f64 y x) |
(- y x) |
(-.f64 y x) |
(- x (/ x z)) |
(-.f64 x (/.f64 x z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- x (/ x z)) |
(-.f64 x (/.f64 x z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(- (+ x (/ y z)) (/ x z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (/ x z)) |
(/.f64 (neg.f64 x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(+ (* -1 (/ x z)) (/ y z)) |
(/.f64 (-.f64 y x) z) |
(/ y z) |
(/.f64 y z) |
(/ y z) |
(/.f64 y z) |
(/ y z) |
(/.f64 y z) |
(/ y z) |
(/.f64 y z) |
(+ x (* -1 (/ x z))) |
(-.f64 x (/.f64 x z)) |
(+ x (+ (* -1 (/ x z)) (/ y z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ x (+ (* -1 (/ x z)) (/ y z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ x (+ (* -1 (/ x z)) (/ y z))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
x |
(+ x (* -1 y)) |
(-.f64 x y) |
(+ x (* -1 y)) |
(-.f64 x y) |
(+ x (* -1 y)) |
(-.f64 x y) |
(* -1 y) |
(neg.f64 y) |
(* -1 y) |
(neg.f64 y) |
(* -1 y) |
(neg.f64 y) |
(* -1 y) |
(neg.f64 y) |
(/ y z) |
(/.f64 y z) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(/.f64 (-.f64 y x) z) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(/.f64 (-.f64 y x) z) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(/.f64 (-.f64 y x) z) |
(/ y z) |
(/.f64 y z) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(/ z y) |
(/.f64 z y) |
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(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (/ x z)) |
(/.f64 (neg.f64 x) z) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(/.f64 (-.f64 y x) z) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(/.f64 (-.f64 y x) z) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(/.f64 (-.f64 y x) z) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
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) |
| 5 250× | lower-*.f64 |
| 5 250× | lower-*.f32 |
| 3 980× | lower-/.f32 |
| 3 968× | lower-/.f64 |
| 2 330× | lower--.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 34 | 132 |
| 0 | 48 | 118 |
| 1 | 216 | 118 |
| 2 | 1799 | 118 |
| 0 | 8298 | 118 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) (/.f64 z (-.f64 y x))) |
(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z (-.f64 y x)))) |
(/.f64 z (-.f64 y x)) |
(-.f64 y x) |
#s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) |
(/.f64 #s(approx (- y x) (neg.f64 x)) z) |
#s(approx (- y x) (neg.f64 x)) |
(neg.f64 x) |
#s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) |
(-.f64 x (/.f64 x z)) |
(/.f64 x z) |
(+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) |
#s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z)) |
(/.f64 y z) |
(fma.f64 (/.f64 #s(literal -1 binary64) z) #s(approx (- x y) (neg.f64 y)) x) |
(/.f64 #s(literal -1 binary64) z) |
#s(approx (- x y) (neg.f64 y)) |
(neg.f64 y) |
| Outputs |
|---|
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Compiled 17 500 to 2 402 computations (86.3% saved)
11 alts after pruning (3 fresh and 8 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 101 | 1 | 1 102 |
| Fresh | 0 | 2 | 2 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 4 | 4 |
| Total | 1 102 | 11 | 1 113 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.8% | (fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) |
| ✓ | 74.5% | (fma.f64 (/.f64 #s(literal -1 binary64) z) #s(approx (- x y) (neg.f64 y)) x) |
| ▶ | 68.3% | (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) |
| ✓ | 100.0% | (+.f64 x (/.f64 (-.f64 y x) z)) |
| ✓ | 74.6% | (+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) |
| ✓ | 56.4% | #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) |
| ▶ | 56.4% | #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) |
| ✓ | 71.4% | #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) |
| ✓ | 28.6% | #s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) |
| ✓ | 46.1% | #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
| ▶ | 71.1% | #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) |
Compiled 77 to 75 computations (2.6% saved)
| 1× | egg-herbie |
Found 12 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (/.f64 x z) | |
| cost-diff | 0 | #s(approx (- (/ x z) x) (/.f64 x z)) | |
| cost-diff | 0 | (/.f64 y z) | |
| cost-diff | 0 | (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) | |
| cost-diff | 0 | (/.f64 z x) | |
| cost-diff | 0 | (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) | |
| cost-diff | 0 | #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) | |
| cost-diff | 704 | (/.f64 #s(literal 1 binary64) (/.f64 z x)) | |
| cost-diff | 0 | (/.f64 #s(literal -1 binary64) (-.f64 y x)) | |
| cost-diff | 0 | #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) | |
| cost-diff | 320 | (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) | |
| cost-diff | 704 | (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) |
| 800× | lower-fma.f64 |
| 800× | lower-fma.f32 |
| 384× | lower-*.f32 |
| 382× | lower-*.f64 |
| 268× | times-frac |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 111 |
| 0 | 35 | 111 |
| 1 | 56 | 106 |
| 2 | 98 | 94 |
| 3 | 214 | 94 |
| 4 | 552 | 93 |
| 5 | 1192 | 93 |
| 6 | 1792 | 93 |
| 7 | 1931 | 93 |
| 8 | 1987 | 93 |
| 9 | 2020 | 93 |
| 0 | 2020 | 93 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) |
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) |
#s(literal -1 binary64) |
(*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) |
(/.f64 #s(literal -1 binary64) (-.f64 y x)) |
(-.f64 y x) |
y |
x |
z |
#s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) |
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) |
x |
(/.f64 #s(literal 1 binary64) (/.f64 z x)) |
#s(literal 1 binary64) |
(/.f64 z x) |
z |
(-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) |
(/.f64 y z) |
y |
z |
#s(approx (- (/ x z) x) (/.f64 x z)) |
(/.f64 x z) |
x |
| Outputs |
|---|
#s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) |
#s(approx (- (/ y z) (- (/ x z) x)) (/.f64 (-.f64 y x) z)) |
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) |
(/.f64 (-.f64 y x) z) |
#s(literal -1 binary64) |
(*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) |
(/.f64 z (-.f64 x y)) |
(/.f64 #s(literal -1 binary64) (-.f64 y x)) |
(-.f64 y x) |
y |
x |
z |
#s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) |
#s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) |
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) |
(-.f64 x (/.f64 x z)) |
x |
(/.f64 #s(literal 1 binary64) (/.f64 z x)) |
(/.f64 x z) |
#s(literal 1 binary64) |
(/.f64 z x) |
z |
(-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) |
(/.f64 y z) |
y |
z |
#s(approx (- (/ x z) x) (/.f64 x z)) |
(/.f64 x z) |
x |
Found 12 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (/.f64 y z) | |
| accuracy | 0 | (/.f64 x z) | |
| accuracy | 1.7695250574906176 | (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) | |
| accuracy | 27.32129191731023 | #s(approx (- (/ x z) x) (/.f64 x z)) | |
| accuracy | 0 | (/.f64 z x) | |
| accuracy | 0.0078125 | (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) | |
| accuracy | 0.4432400800562817 | (/.f64 #s(literal 1 binary64) (/.f64 z x)) | |
| accuracy | 27.884221081691866 | #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) | |
| accuracy | 0.015625 | (/.f64 #s(literal -1 binary64) (-.f64 y x)) | |
| accuracy | 0.2109375 | (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) | |
| accuracy | 0.2265625 | (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) | |
| accuracy | 18.29859788591886 | #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) |
| 39.0ms | 256× | 0 | valid |
Compiled 87 to 20 computations (77% saved)
ival-div: 15.0ms (66.3% of total)ival-sub: 4.0ms (17.7% of total)ival-mult: 2.0ms (8.8% of total)ival-add: 1.0ms (4.4% 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 (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) (patch (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) #<representation binary64>) () ()) |
#s(alt (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) (patch (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) #<representation binary64>) () ()) |
#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal -1 binary64) (-.f64 y x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 y x)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 z x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 z x)) #<representation binary64>) () ()) |
#s(alt #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) (patch #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) #<representation binary64>) () ()) |
#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) #<representation binary64>) () ()) |
#s(alt (/.f64 z x) (patch (/.f64 z x) #<representation binary64>) () ()) |
#s(alt (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) (patch (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) #<representation binary64>) () ()) |
#s(alt (/.f64 y z) (patch (/.f64 y z) #<representation binary64>) () ()) |
#s(alt #s(approx (- (/ x z) x) (/.f64 x z)) (patch #s(approx (- (/ x z) x) (/.f64 x z)) #<representation binary64>) () ()) |
#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) (patch (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) (patch (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) (patch (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) (patch (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ z (- y x))) (taylor 0 z) (#s(alt (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) (patch (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ z (- y x))) (taylor 0 z) (#s(alt (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) (patch (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ z (- y x))) (taylor 0 z) (#s(alt (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) (patch (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ z (- y x))) (taylor 0 z) (#s(alt (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) (patch (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor 0 z) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 z x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 z x)) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor 0 z) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 z x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 z x)) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor 0 z) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 z x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 z x)) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor 0 z) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 z x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 z x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) (patch #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) (patch #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) (patch #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) (patch #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ x z)) (taylor 0 z) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (* x z) x) z) (taylor 0 z) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (* x z) x) z) (taylor 0 z) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (* x z) x) z) (taylor 0 z) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) #<representation binary64>) () ())) ()) |
#s(alt (/ z x) (taylor 0 z) (#s(alt (/.f64 z x) (patch (/.f64 z x) #<representation binary64>) () ())) ()) |
#s(alt (/ z x) (taylor 0 z) (#s(alt (/.f64 z x) (patch (/.f64 z x) #<representation binary64>) () ())) ()) |
#s(alt (/ z x) (taylor 0 z) (#s(alt (/.f64 z x) (patch (/.f64 z x) #<representation binary64>) () ())) ()) |
#s(alt (/ z x) (taylor 0 z) (#s(alt (/.f64 z x) (patch (/.f64 z x) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor 0 z) (#s(alt (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) (patch (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) (patch (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) (patch (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* x z)) x) z) (taylor 0 z) (#s(alt (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) (patch (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) #<representation binary64>) () ())) ()) |
#s(alt (/ y z) (taylor 0 z) (#s(alt (/.f64 y z) (patch (/.f64 y z) #<representation binary64>) () ())) ()) |
#s(alt (/ y z) (taylor 0 z) (#s(alt (/.f64 y z) (patch (/.f64 y z) #<representation binary64>) () ())) ()) |
#s(alt (/ y z) (taylor 0 z) (#s(alt (/.f64 y z) (patch (/.f64 y z) #<representation binary64>) () ())) ()) |
#s(alt (/ y z) (taylor 0 z) (#s(alt (/.f64 y z) (patch (/.f64 y z) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor 0 z) (#s(alt #s(approx (- (/ x z) x) (/.f64 x z)) (patch #s(approx (- (/ x z) x) (/.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ x (* -1 (* x z))) z) (taylor 0 z) (#s(alt #s(approx (- (/ x z) x) (/.f64 x z)) (patch #s(approx (- (/ x z) x) (/.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ x (* -1 (* x z))) z) (taylor 0 z) (#s(alt #s(approx (- (/ x z) x) (/.f64 x z)) (patch #s(approx (- (/ x z) x) (/.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ x (* -1 (* x z))) z) (taylor 0 z) (#s(alt #s(approx (- (/ x z) x) (/.f64 x z)) (patch #s(approx (- (/ x z) x) (/.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor 0 z) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor 0 z) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor 0 z) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor 0 z) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor inf z) (#s(alt (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) (patch (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor inf z) (#s(alt (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) (patch (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor inf z) (#s(alt (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) (patch (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- y x) z) (taylor inf z) (#s(alt (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) (patch (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ z (- y x))) (taylor inf z) (#s(alt (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) (patch (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ z (- y x))) (taylor inf z) (#s(alt (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) (patch (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ z (- y x))) (taylor inf z) (#s(alt (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) (patch (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ z (- y x))) (taylor inf z) (#s(alt (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) (patch (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf z) (#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (/ y z)) (/ x z)) (taylor inf z) (#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (/ y z)) (/ x z)) (taylor inf z) (#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (/ y z)) (/ x z)) (taylor inf z) (#s(alt #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) (patch #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor inf z) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 z x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 z x)) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor inf z) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 z x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 z x)) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor inf z) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 z x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 z x)) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor inf z) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 z x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 z x)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf z) (#s(alt #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) (patch #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (/ y z)) (/ x z)) (taylor inf z) (#s(alt #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) (patch #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (/ y z)) (/ x z)) (taylor inf z) (#s(alt #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) (patch #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (/ y z)) (/ x z)) (taylor inf z) (#s(alt #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) (patch #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf z) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* -1 (/ x z))) (taylor inf z) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* -1 (/ x z))) (taylor inf z) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* -1 (/ x z))) (taylor inf z) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) #<representation binary64>) () ())) ()) |
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#s(alt (/ x z) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 z x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 z x)) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 z x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 z x)) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 z x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 z x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ 1 z) 1))) (taylor -inf x) (#s(alt #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) (patch #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) (patch #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) (patch #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) (patch #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ 1 z) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ 1 z) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ 1 z) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ 1 z) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) #<representation binary64>) () ())) ()) |
#s(alt (/ z x) (taylor -inf x) (#s(alt (/.f64 z x) (patch (/.f64 z x) #<representation binary64>) () ())) ()) |
#s(alt (/ z x) (taylor -inf x) (#s(alt (/.f64 z x) (patch (/.f64 z x) #<representation binary64>) () ())) ()) |
#s(alt (/ z x) (taylor -inf x) (#s(alt (/.f64 z x) (patch (/.f64 z x) #<representation binary64>) () ())) ()) |
#s(alt (/ z x) (taylor -inf x) (#s(alt (/.f64 z x) (patch (/.f64 z x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (/ 1 z) 1))) (taylor -inf x) (#s(alt (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) (patch (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) (patch (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) (patch (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) (taylor -inf x) (#s(alt (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) (patch (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- 1 (/ 1 z)))) (taylor -inf x) (#s(alt #s(approx (- (/ x z) x) (/.f64 x z)) (patch #s(approx (- (/ x z) x) (/.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- 1 (/ 1 z)))) (taylor -inf x) (#s(alt #s(approx (- (/ x z) x) (/.f64 x z)) (patch #s(approx (- (/ x z) x) (/.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- 1 (/ 1 z)))) (taylor -inf x) (#s(alt #s(approx (- (/ x z) x) (/.f64 x z)) (patch #s(approx (- (/ x z) x) (/.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- 1 (/ 1 z)))) (taylor -inf x) (#s(alt #s(approx (- (/ x z) x) (/.f64 x z)) (patch #s(approx (- (/ x z) x) (/.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor -inf x) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor -inf x) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor -inf x) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
#s(alt (/ x z) (taylor -inf x) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ()) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | z | @ | 0 | ((/ -1 (* (/ -1 (- y x)) z)) (* (/ -1 (- y x)) z) (+ x (/ (- y x) z)) (/ -1 (- y x)) (/ 1 (/ z x)) (- (/ y z) (- (/ x z) x)) (- x (/ 1 (/ z x))) (/ z x) (- (/ y z) (- (/ x z) x)) (/ y z) (- (/ x z) x) (/ x z)) |
| 3.0ms | y | @ | inf | ((/ -1 (* (/ -1 (- y x)) z)) (* (/ -1 (- y x)) z) (+ x (/ (- y x) z)) (/ -1 (- y x)) (/ 1 (/ z x)) (- (/ y z) (- (/ x z) x)) (- x (/ 1 (/ z x))) (/ z x) (- (/ y z) (- (/ x z) x)) (/ y z) (- (/ x z) x) (/ x z)) |
| 2.0ms | x | @ | -inf | ((/ -1 (* (/ -1 (- y x)) z)) (* (/ -1 (- y x)) z) (+ x (/ (- y x) z)) (/ -1 (- y x)) (/ 1 (/ z x)) (- (/ y z) (- (/ x z) x)) (- x (/ 1 (/ z x))) (/ z x) (- (/ y z) (- (/ x z) x)) (/ y z) (- (/ x z) x) (/ x z)) |
| 1.0ms | z | @ | -inf | ((/ -1 (* (/ -1 (- y x)) z)) (* (/ -1 (- y x)) z) (+ x (/ (- y x) z)) (/ -1 (- y x)) (/ 1 (/ z x)) (- (/ y z) (- (/ x z) x)) (- x (/ 1 (/ z x))) (/ z x) (- (/ y z) (- (/ x z) x)) (/ y z) (- (/ x z) x) (/ x z)) |
| 1.0ms | x | @ | inf | ((/ -1 (* (/ -1 (- y x)) z)) (* (/ -1 (- y x)) z) (+ x (/ (- y x) z)) (/ -1 (- y x)) (/ 1 (/ z x)) (- (/ y z) (- (/ x z) x)) (- x (/ 1 (/ z x))) (/ z x) (- (/ y z) (- (/ x z) x)) (/ y z) (- (/ x z) x) (/ x z)) |
| 1× | egg-herbie |
| 9 884× | lower-fma.f64 |
| 9 884× | lower-fma.f32 |
| 3 624× | lower-*.f64 |
| 3 624× | lower-*.f32 |
| 3 198× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 302 | 2592 |
| 1 | 875 | 2487 |
| 2 | 2422 | 2287 |
| 3 | 7588 | 2281 |
| 0 | 8315 | 2202 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(* -1 (/ z (- y x))) |
(* -1 (/ z (- y x))) |
(* -1 (/ z (- y x))) |
(* -1 (/ z (- y x))) |
(/ (- y x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ (- y x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(* -1 (/ x z)) |
(/ (- (* x z) x) z) |
(/ (- (* x z) x) z) |
(/ (- (* x z) x) z) |
(/ z x) |
(/ z x) |
(/ z x) |
(/ z x) |
(/ (- y x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ (- (+ y (* x z)) x) z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ x z) |
(/ (+ x (* -1 (* x z))) z) |
(/ (+ x (* -1 (* x z))) z) |
(/ (+ x (* -1 (* x z))) z) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(* -1 (/ z (- y x))) |
(* -1 (/ z (- y x))) |
(* -1 (/ z (- y x))) |
(* -1 (/ z (- y x))) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
x |
(+ x (* -1 (/ x z))) |
(+ x (* -1 (/ x z))) |
(+ x (* -1 (/ x z))) |
(/ z x) |
(/ z x) |
(/ z x) |
(/ z x) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(* -1 x) |
(- (/ x z) x) |
(- (/ x z) x) |
(- (/ x z) x) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(/ (- y x) z) |
(* -1 (/ z (- y x))) |
(* -1 (/ z (- y x))) |
(* -1 (/ z (- y x))) |
(* -1 (/ z (- y x))) |
x |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
x |
(+ x (* -1 (/ (- (* -1 y) (* -1 x)) z))) |
(+ x (* -1 (/ (- (* -1 y) (* -1 x)) z))) |
(+ x (* -1 (/ (- (* -1 y) (* -1 x)) z))) |
x |
(+ x (* -1 (/ x z))) |
(+ x (* -1 (/ x z))) |
(+ x (* -1 (/ x z))) |
(/ z x) |
(/ z x) |
(/ z x) |
(/ z x) |
x |
(+ x (* -1 (/ (- (* -1 y) (* -1 x)) z))) |
(+ x (* -1 (/ (- (* -1 y) (* -1 x)) z))) |
(+ x (* -1 (/ (- (* -1 y) (* -1 x)) z))) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(* -1 x) |
(- (/ x z) x) |
(- (/ x z) x) |
(- (/ x z) x) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
(* -1 (/ x z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(/ z x) |
(+ (/ z x) (/ (* y z) (pow x 2))) |
(+ (* y (+ (/ z (pow x 2)) (/ (* y z) (pow x 3)))) (/ z x)) |
(+ (* y (+ (* y (+ (/ z (pow x 3)) (/ (* y z) (pow x 4)))) (/ z (pow x 2)))) (/ z x)) |
(- x (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ 1 x) |
(+ (/ 1 x) (/ y (pow x 2))) |
(+ (* y (+ (/ 1 (pow x 2)) (/ y (pow x 3)))) (/ 1 x)) |
(+ (* y (+ (* y (+ (/ 1 (pow x 3)) (/ y (pow x 4)))) (/ 1 (pow x 2)))) (/ 1 x)) |
(- x (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- x (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(- (+ x (/ y z)) (/ x z)) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(* y (+ (* -1 (/ x (* y z))) (/ 1 z))) |
(* -1 (/ z y)) |
(/ (+ (* -1 z) (* -1 (/ (* x z) y))) y) |
(/ (+ (* -1 z) (+ (* -1 (/ (* x z) y)) (* -1 (/ (* (pow x 2) z) (pow y 2))))) y) |
(/ (+ (* -1 z) (+ (* -1 (/ (* x z) y)) (+ (* -1 (/ (* (pow x 2) z) (pow y 2))) (* -1 (/ (* (pow x 3) z) (pow y 3)))))) y) |
(/ y z) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(/ -1 y) |
(/ (- (* -1 (/ x y)) 1) y) |
(/ (- (* -1 (/ (pow x 2) (pow y 2))) (+ 1 (/ x y))) y) |
(/ (- (* -1 (/ (pow x 3) (pow y 3))) (+ 1 (+ (/ x y) (/ (pow x 2) (pow y 2))))) y) |
(/ y z) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(/ y z) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(* y (- (+ (/ 1 z) (/ x y)) (/ x (* y z)))) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(* -1 (* y (- (/ x (* y z)) (/ 1 z)))) |
(* -1 (/ z y)) |
(* -1 (/ (+ z (/ (* x z) y)) y)) |
(* -1 (/ (+ z (* -1 (/ (- (* -1 (/ (* (pow x 2) z) y)) (* x z)) y))) y)) |
(* -1 (/ (+ z (* -1 (/ (- (* -1 (/ (- (/ (* (pow x 3) z) y) (* -1 (* (pow x 2) z))) y)) (* x z)) y))) y)) |
(/ y z) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ x z))) y)) (/ 1 z)))) |
(/ -1 y) |
(* -1 (/ (+ 1 (/ x y)) y)) |
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow x 2) y)) x) y))) y)) |
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (* -1 (pow x 2))) y)) x) y))) y)) |
(/ y z) |
(* -1 (* y (- (* -1 (/ (- x (/ x z)) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (- x (/ x z)) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (- x (/ x z)) y)) (/ 1 z)))) |
(/ y z) |
(* -1 (* y (- (* -1 (/ (- x (/ x z)) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (- x (/ x z)) y)) (/ 1 z)))) |
(* -1 (* y (- (* -1 (/ (- x (/ x z)) y)) (/ 1 z)))) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(/ y z) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(+ (* -1 (/ x z)) (/ y z)) |
(* -1 (/ z y)) |
(+ (* -1 (/ z y)) (* -1 (/ (* x z) (pow y 2)))) |
(+ (* -1 (/ z y)) (* x (+ (* -1 (/ z (pow y 2))) (* -1 (/ (* x z) (pow y 3)))))) |
(+ (* -1 (/ z y)) (* x (+ (* -1 (/ z (pow y 2))) (* x (+ (* -1 (/ z (pow y 3))) (* -1 (/ (* x z) (pow y 4)))))))) |
(/ y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(/ -1 y) |
(- (* -1 (/ x (pow y 2))) (/ 1 y)) |
(- (* x (- (* -1 (/ 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)) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(* x (- 1 (/ 1 z))) |
(* x (- 1 (/ 1 z))) |
(* x (- 1 (/ 1 z))) |
(* x (- 1 (/ 1 z))) |
(/ z x) |
(/ z x) |
(/ z x) |
(/ z x) |
(/ y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(* x (- (/ 1 z) 1)) |
(* x (- (/ 1 z) 1)) |
(* x (- (/ 1 z) 1)) |
(* x (- (/ 1 z) 1)) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
(* -1 (/ x z)) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(/ z x) |
(/ (+ z (/ (* y z) x)) x) |
(/ (+ z (+ (/ (* y z) x) (/ (* (pow y 2) z) (pow x 2)))) x) |
(/ (+ z (+ (/ (* y z) x) (+ (/ (* (pow y 2) z) (pow x 2)) (/ (* (pow y 3) z) (pow x 3))))) x) |
(* x (- 1 (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(/ 1 x) |
(/ (+ 1 (/ y x)) x) |
(/ (- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ y x))) x) |
(/ (- (+ 1 (/ (pow y 3) (pow x 3))) (+ (* -1 (/ y x)) (* -1 (/ (pow y 2) (pow x 2))))) x) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
(* x (- 1 (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- 1 (/ 1 z))) |
(* x (- 1 (/ 1 z))) |
(* x (- 1 (/ 1 z))) |
(* x (- 1 (/ 1 z))) |
(/ z x) |
(/ z x) |
(/ z x) |
(/ z x) |
(* x (- 1 (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(* x (- (/ 1 z) 1)) |
(* x (- (/ 1 z) 1)) |
(* x (- (/ 1 z) 1)) |
(* x (- (/ 1 z) 1)) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
(* -1 (/ x z)) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(/ z x) |
(* -1 (/ (+ (* -1 z) (* -1 (/ (* y z) x))) x)) |
(* -1 (/ (+ (* -1 z) (* -1 (/ (+ (* y z) (/ (* (pow y 2) z) x)) x))) x)) |
(* -1 (/ (+ (* -1 z) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow y 2) z)) (* -1 (/ (* (pow y 3) z) x))) x)) (* y z)) x))) x)) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(/ 1 x) |
(* -1 (/ (- (* -1 (/ y x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (/ (pow y 2) x) (* -1 y)) x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow y 3) x)) (pow y 2)) x)) (* -1 y)) x)) 1) x)) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (/ 1 z) 1))) |
(/ z x) |
(/ z x) |
(/ z x) |
(/ z x) |
(* -1 (* x (- (/ 1 z) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(* -1 (* x (- 1 (/ 1 z)))) |
(* -1 (* x (- 1 (/ 1 z)))) |
(* -1 (* x (- 1 (/ 1 z)))) |
(* -1 (* x (- 1 (/ 1 z)))) |
(/ x z) |
(/ x z) |
(/ x z) |
(/ x z) |
| Outputs |
|---|
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(/ (- y x) z) |
(/.f64 (-.f64 y x) z) |
(* -1 (/ z (- y x))) |
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(/.f64 y z) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(+ (* x (- 1 (/ 1 z))) (/ y z)) |
(-.f64 x (/.f64 (-.f64 x y) z)) |
(* x (- (/ 1 z) 1)) |
(-.f64 (/.f64 x z) x) |
(* x (- (/ 1 z) 1)) |
(-.f64 (/.f64 x z) x) |
(* x (- (/ 1 z) 1)) |
(-.f64 (/.f64 x z) x) |
(* x (- (/ 1 z) 1)) |
(-.f64 (/.f64 x z) x) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(* -1 (/ x z)) |
(/.f64 (neg.f64 x) z) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (/.f64 (neg.f64 x) z)) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (/.f64 (neg.f64 x) z)) |
(* x (- (/ y (* x z)) (/ 1 z))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (/.f64 (neg.f64 x) z)) |
(/ z x) |
(/.f64 z x) |
(/ (+ z (/ (* y z) x)) x) |
(/.f64 (fma.f64 (/.f64 z x) y z) x) |
(/ (+ z (+ (/ (* y z) x) (/ (* (pow y 2) z) (pow x 2)))) x) |
(/.f64 (fma.f64 (/.f64 z x) (fma.f64 (/.f64 y x) y y) z) x) |
(/ (+ z (+ (/ (* y z) x) (+ (/ (* (pow y 2) z) (pow x 2)) (/ (* (pow y 3) z) (pow x 3))))) x) |
(/.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) z (fma.f64 (/.f64 z x) (fma.f64 (/.f64 y x) y y) z)) x) |
(* x (- 1 (/ 1 z))) |
(-.f64 x (/.f64 x z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ (+ 1 (/ y x)) x) |
(/.f64 (-.f64 (/.f64 y x) #s(literal -1 binary64)) x) |
(/ (- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ y x))) x) |
(/.f64 (fma.f64 (-.f64 (/.f64 y x) #s(literal -1 binary64)) (/.f64 y x) #s(literal 1 binary64)) x) |
(/ (- (+ 1 (/ (pow y 3) (pow x 3))) (+ (* -1 (/ y x)) (* -1 (/ (pow y 2) (pow x 2))))) x) |
(/.f64 (fma.f64 (-.f64 (/.f64 y x) #s(literal -1 binary64)) (/.f64 y x) (+.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) #s(literal 1 binary64))) x) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(* x (- 1 (/ 1 z))) |
(-.f64 x (/.f64 x z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(* x (- 1 (/ 1 z))) |
(-.f64 x (/.f64 x z)) |
(* x (- 1 (/ 1 z))) |
(-.f64 x (/.f64 x z)) |
(* x (- 1 (/ 1 z))) |
(-.f64 x (/.f64 x z)) |
(* x (- 1 (/ 1 z))) |
(-.f64 x (/.f64 x z)) |
(/ z x) |
(/.f64 z x) |
(/ z x) |
(/.f64 z x) |
(/ z x) |
(/.f64 z x) |
(/ z x) |
(/.f64 z x) |
(* x (- 1 (/ 1 z))) |
(-.f64 x (/.f64 x z)) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(* x (- (+ 1 (/ y (* x z))) (/ 1 z))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(* x (- (/ 1 z) 1)) |
(-.f64 (/.f64 x z) x) |
(* x (- (/ 1 z) 1)) |
(-.f64 (/.f64 x z) x) |
(* x (- (/ 1 z) 1)) |
(-.f64 (/.f64 x z) x) |
(* x (- (/ 1 z) 1)) |
(-.f64 (/.f64 x z) x) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(* -1 (/ x z)) |
(/.f64 (neg.f64 x) z) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (/.f64 (neg.f64 x) z)) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (/.f64 (neg.f64 x) z)) |
(* -1 (* x (+ (* -1 (/ y (* x z))) (/ 1 z)))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (/.f64 (neg.f64 x) z)) |
(/ z x) |
(/.f64 z x) |
(* -1 (/ (+ (* -1 z) (* -1 (/ (* y z) x))) x)) |
(/.f64 (fma.f64 (/.f64 z x) y z) x) |
(* -1 (/ (+ (* -1 z) (* -1 (/ (+ (* y z) (/ (* (pow y 2) z) x)) x))) x)) |
(/.f64 (+.f64 (/.f64 (*.f64 y (fma.f64 (/.f64 z x) y z)) x) z) x) |
(* -1 (/ (+ (* -1 z) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow y 2) z)) (* -1 (/ (* (pow y 3) z) x))) x)) (* y z)) x))) x)) |
(/.f64 (+.f64 (/.f64 (fma.f64 z y (/.f64 (*.f64 y (*.f64 y (fma.f64 (/.f64 z x) y z))) x)) x) z) x) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(* -1 (/ (- (* -1 (/ y x)) 1) x)) |
(/.f64 (-.f64 (/.f64 y x) #s(literal -1 binary64)) x) |
(* -1 (/ (- (* -1 (/ (- (/ (pow y 2) x) (* -1 y)) x)) 1) x)) |
(/.f64 (fma.f64 (-.f64 (/.f64 y x) #s(literal -1 binary64)) (/.f64 y x) #s(literal 1 binary64)) x) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow y 3) x)) (pow y 2)) x)) (* -1 y)) x)) 1) x)) |
(/.f64 (-.f64 (/.f64 (+.f64 (/.f64 (*.f64 y (fma.f64 (/.f64 y x) y y)) x) y) x) #s(literal -1 binary64)) x) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(/ z x) |
(/.f64 z x) |
(/ z x) |
(/.f64 z x) |
(/ z x) |
(/.f64 z x) |
(/ z x) |
(/.f64 z x) |
(* -1 (* x (- (/ 1 z) 1))) |
(-.f64 x (/.f64 x z)) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(* -1 (* x (- (+ (* -1 (/ y (* x z))) (/ 1 z)) 1))) |
(fma.f64 (/.f64 (/.f64 y z) x) x (-.f64 x (/.f64 x z))) |
(* -1 (* x (- 1 (/ 1 z)))) |
(-.f64 (/.f64 x z) x) |
(* -1 (* x (- 1 (/ 1 z)))) |
(-.f64 (/.f64 x z) x) |
(* -1 (* x (- 1 (/ 1 z)))) |
(-.f64 (/.f64 x z) x) |
(* -1 (* x (- 1 (/ 1 z)))) |
(-.f64 (/.f64 x z) x) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
(/ x z) |
(/.f64 x z) |
| 8 646× | lower-fma.f64 |
| 8 646× | lower-fma.f32 |
| 4 710× | lower-/.f32 |
| 4 698× | lower-/.f64 |
| 3 246× | lower-*.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 98 |
| 0 | 35 | 90 |
| 1 | 162 | 81 |
| 2 | 1454 | 81 |
| 0 | 8593 | 81 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z)) |
(*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z) |
#s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) |
(/.f64 #s(literal -1 binary64) (-.f64 y x)) |
(/.f64 #s(literal 1 binary64) (/.f64 z x)) |
#s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) |
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x))) |
(/.f64 z x) |
(-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) |
(/.f64 y z) |
#s(approx (- (/ x z) x) (/.f64 x z)) |
(/.f64 x z) |
| Outputs |
|---|
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Compiled 10 522 to 1 509 computations (85.7% saved)
11 alts after pruning (0 fresh and 11 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 737 | 0 | 737 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 3 | 3 |
| Done | 0 | 8 | 8 |
| Total | 737 | 11 | 748 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.8% | (fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) |
| ✓ | 74.5% | (fma.f64 (/.f64 #s(literal -1 binary64) z) #s(approx (- x y) (neg.f64 y)) x) |
| ✓ | 68.3% | (-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) |
| ✓ | 100.0% | (+.f64 x (/.f64 (-.f64 y x) z)) |
| ✓ | 74.6% | (+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) |
| ✓ | 56.4% | #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) |
| ✓ | 56.4% | #s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) |
| ✓ | 71.4% | #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) |
| ✓ | 28.6% | #s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) |
| ✓ | 46.1% | #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
| ✓ | 71.1% | #s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) |
Compiled 195 to 123 computations (36.9% saved)
| Inputs |
|---|
#s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
#s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) |
#s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))) |
#s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) |
#s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) |
(+.f64 x #s(approx (/ (- y x) z) (/.f64 y z))) |
(+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) |
(+.f64 x (/.f64 (-.f64 y x) z)) |
(fma.f64 (/.f64 #s(literal -1 binary64) z) #s(approx (- x y) (neg.f64 y)) x) |
(fma.f64 (/.f64 #s(literal -1 binary64) z) (-.f64 x y) x) |
#s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z x)))) |
(-.f64 (/.f64 y z) #s(approx (- (/ x z) x) (/.f64 x z))) |
(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 z (-.f64 y x)))) |
(-.f64 (/.f64 y z) (-.f64 (/.f64 x z) x)) |
#s(approx (+ x (/ (- y x) z)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 y x)) z))) |
(+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) z)) |
| Outputs |
|---|
(+.f64 x (/.f64 (-.f64 y x) z)) |
4 calls:
| 6.0ms | y |
| 5.0ms | x |
| 5.0ms | z |
| 5.0ms | (+.f64 x (/.f64 (-.f64 y x) z)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | y |
| 100.0% | 1 | z |
| 100.0% | 1 | (+.f64 x (/.f64 (-.f64 y x) z)) |
Compiled 10 to 15 computations (-50% saved)
| Inputs |
|---|
#s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
#s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) |
#s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))) |
#s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) |
#s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) |
(+.f64 x #s(approx (/ (- y x) z) (/.f64 y z))) |
(+.f64 x #s(approx (/ (/ 1 (pow (- y x) -1)) z) (/.f64 y z))) |
| Outputs |
|---|
(+.f64 x #s(approx (/ (- y x) z) (/.f64 y z))) |
#s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) |
(+.f64 x #s(approx (/ (- y x) z) (/.f64 y z))) |
4 calls:
| 4.0ms | y |
| 3.0ms | (+.f64 x (/.f64 (-.f64 y x) z)) |
| 3.0ms | z |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 86.1% | 3 | x |
| 87.7% | 3 | y |
| 99.6% | 3 | z |
| 86.4% | 3 | (+.f64 x (/.f64 (-.f64 y x) z)) |
Compiled 10 to 15 computations (-50% saved)
| Inputs |
|---|
#s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
#s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) |
#s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))) |
#s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) |
#s(approx (- (/ y z) (- (/ x z) x)) (-.f64 x (/.f64 x z))) |
| Outputs |
|---|
#s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))) |
#s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) |
#s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))) |
3 calls:
| 2.0ms | z |
| 2.0ms | y |
| 2.0ms | (+.f64 x (/.f64 (-.f64 y x) z)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 74.5% | 3 | (+.f64 x (/.f64 (-.f64 y x) z)) |
| 80.7% | 3 | y |
| 86.1% | 3 | z |
Compiled 9 to 12 computations (-33.3% saved)
| Inputs |
|---|
#s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
#s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) |
#s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))) |
| Outputs |
|---|
#s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))) |
#s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
#s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))) |
3 calls:
| 3.0ms | z |
| 2.0ms | y |
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 76.3% | 3 | y |
| 77.2% | 3 | x |
| 65.2% | 5 | z |
Compiled 3 to 9 computations (-200% saved)
| Inputs |
|---|
#s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
#s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) |
| Outputs |
|---|
#s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
#s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) |
#s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
4 calls:
| 2.0ms | z |
| 2.0ms | y |
| 2.0ms | x |
| 2.0ms | (+.f64 x (/.f64 (-.f64 y x) z)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 49.8% | 3 | z |
| 46.1% | 1 | (+.f64 x (/.f64 (-.f64 y x) z)) |
| 59.4% | 3 | y |
| 57.4% | 3 | x |
Compiled 10 to 15 computations (-50% saved)
Total -0.0b remaining (-0%)
Threshold costs -0b (-0%)
| Inputs |
|---|
#s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
| Outputs |
|---|
#s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
4 calls:
| 3.0ms | y |
| 1.0ms | z |
| 1.0ms | x |
| 1.0ms | (+.f64 x (/.f64 (-.f64 y x) z)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 46.1% | 1 | (+.f64 x (/.f64 (-.f64 y x) z)) |
| 46.1% | 1 | z |
| 46.1% | 1 | x |
| 46.1% | 1 | y |
Compiled 10 to 15 computations (-50% saved)
| 2× | binary-search |
| 1× | narrow-enough |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 12.0ms | 0.0897097620357995 | 15748079426.595211 |
| 12.0ms | -1373613270035820500.0 | -8176599965388.96 |
| 13.0ms | 304× | 0 | valid |
Compiled 238 to 278 computations (-16.8% saved)
ival-sub: 3.0ms (47.9% of total)ival-div: 2.0ms (32% of total)ival-add: 1.0ms (16% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 2× | binary-search |
| 1× | narrow-enough |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 11.0ms | 6.226365386232782e+24 | 4.703401593332687e+32 |
| 30.0ms | -1373613270035820500.0 | -8176599965388.96 |
| 31.0ms | 272× | 0 | valid |
Compiled 226 to 264 computations (-16.8% saved)
ival-add: 22.0ms (87.2% of total)ival-div: 2.0ms (7.9% of total)ival-sub: 1.0ms (4% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 2× | binary-search |
| 1× | narrow-enough |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 8.0ms | 5.844551379533868e+28 | 1.4271228541751245e+29 |
| 13.0ms | -6.185626678412788e-124 | -7.711708362465303e-135 |
| 11.0ms | 240× | 0 | valid |
Compiled 160 to 207 computations (-29.4% saved)
ival-div: 3.0ms (57.1% of total)ival-sub: 1.0ms (19% of total)ival-add: 1.0ms (19% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 2× | binary-search |
| 1× | narrow-enough |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 45.0ms | 7.218533023990081e-78 | 1.8930378106486523e-75 |
| 7.0ms | -3.2830446626368773e-83 | -6.59675409101009e-84 |
| 45.0ms | 224× | 0 | valid |
Compiled 150 to 208 computations (-38.7% saved)
ival-div: 2.0ms (49.9% of total)ival-sub: 1.0ms (24.9% of total)ival-add: 1.0ms (24.9% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
| 14× | +-commutative-binary64-+.f64 |
| 10× | sub-neg-binary64-neg.f64-+.f64--.f64 |
| 6× | *-commutative-binary64-*.f64 |
| 6× | neg-sub0-binary64--.f64-neg.f64 |
| 6× | neg-mul-1-binary64-*.f64-neg.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 45 | 199 |
| 1 | 56 | 199 |
| 2 | 65 | 199 |
| 3 | 70 | 199 |
| 4 | 73 | 199 |
| 5 | 74 | 199 |
| 1× | saturated |
| Inputs |
|---|
(+.f64 x (/.f64 (-.f64 y x) z)) |
(if (<=.f64 z #s(literal -8200000000000 binary64)) (+.f64 x #s(approx (/ (- y x) z) (/.f64 y z))) (if (<=.f64 z #s(literal 1 binary64)) #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) (+.f64 x #s(approx (/ (- y x) z) (/.f64 y z))))) |
(if (<=.f64 z #s(literal -440000000000000000 binary64)) #s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))) (if (<=.f64 z #s(literal 110000000000000006409433382912 binary64)) #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) #s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))))) |
(if (<=.f64 x #s(literal -6118627158619345/6243497100631984462763194459586332611497196285329942301718313919250743477639531240240612206126983942319653862242813245790895951358576570612580352 binary64)) #s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))) (if (<=.f64 x #s(literal 60000000000000001896764932096 binary64)) #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) #s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))))) |
(if (<=.f64 y #s(literal -8202190217936295/273406340597876490546562778389702670669146178861651554553221325801244124899921990402939147127881728 binary64)) #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) (if (<=.f64 y #s(literal 8311106783444703/8148143905337944345073782753637512644205873574663745002544561797417525199053346824733589504 binary64)) #s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) #s(approx (+ x (/ (- y x) z)) (/.f64 y z)))) |
#s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
| Outputs |
|---|
(+.f64 x (/.f64 (-.f64 y x) z)) |
(+.f64 (/.f64 (-.f64 y x) z) x) |
(if (<=.f64 z #s(literal -8200000000000 binary64)) (+.f64 x #s(approx (/ (- y x) z) (/.f64 y z))) (if (<=.f64 z #s(literal 1 binary64)) #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) (+.f64 x #s(approx (/ (- y x) z) (/.f64 y z))))) |
(if (<=.f64 z #s(literal -8200000000000 binary64)) (+.f64 #s(approx (/ (- y x) z) (/.f64 y z)) x) (if (<=.f64 z #s(literal 1 binary64)) #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) (+.f64 #s(approx (/ (- y x) z) (/.f64 y z)) x))) |
(if (<=.f64 z #s(literal -440000000000000000 binary64)) #s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))) (if (<=.f64 z #s(literal 110000000000000006409433382912 binary64)) #s(approx (+ x (/ (- y x) z)) (/.f64 (-.f64 y x) z)) #s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))))) |
(if (<=.f64 x #s(literal -6118627158619345/6243497100631984462763194459586332611497196285329942301718313919250743477639531240240612206126983942319653862242813245790895951358576570612580352 binary64)) #s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))) (if (<=.f64 x #s(literal 60000000000000001896764932096 binary64)) #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) #s(approx (+ x (/ (- y x) z)) (-.f64 x (/.f64 x z))))) |
(if (<=.f64 y #s(literal -8202190217936295/273406340597876490546562778389702670669146178861651554553221325801244124899921990402939147127881728 binary64)) #s(approx (+ x (/ (- y x) z)) (/.f64 y z)) (if (<=.f64 y #s(literal 8311106783444703/8148143905337944345073782753637512644205873574663745002544561797417525199053346824733589504 binary64)) #s(approx (+ x (/ (- y x) z)) (/.f64 #s(approx (- y x) (neg.f64 x)) z)) #s(approx (+ x (/ (- y x) z)) (/.f64 y z)))) |
#s(approx (+ x (/ (- y x) z)) (/.f64 y z)) |
| 9 568× | lower-fma.f64 |
| 9 568× | lower-fma.f32 |
| 6 368× | lower-fma.f64 |
| 6 368× | lower-fma.f32 |
| 3 486× | lower-*.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 71 | 460 |
| 1 | 198 | 460 |
| 2 | 553 | 460 |
| 3 | 1590 | 460 |
| 4 | 3540 | 460 |
| 5 | 5031 | 460 |
| 6 | 6478 | 460 |
| 7 | 6764 | 460 |
| 8 | 6864 | 460 |
| 9 | 6864 | 460 |
| 0 | 8148 | 457 |
| 0 | 210 | 2282 |
| 1 | 601 | 2256 |
| 2 | 1611 | 2219 |
| 3 | 5866 | 2219 |
| 0 | 8380 | 2187 |
| 1× | done |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 148 to 87 computations (41.2% saved)
Compiled 232 to 96 computations (58.6% saved)
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