
Time bar (total: 26.5s)
| 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 |
| 50% | 50% | 50% | 0.1% | 0% | 0% | 0% | 3 |
| 50% | 50% | 50% | 0.1% | 0% | 0% | 0% | 4 |
| 62.5% | 62.4% | 37.5% | 0.1% | 0% | 0% | 0% | 5 |
| 68.8% | 68.7% | 31.2% | 0.1% | 0% | 0% | 0% | 6 |
| 78.1% | 78% | 21.9% | 0.1% | 0% | 0% | 0% | 7 |
| 82.8% | 82.7% | 17.2% | 0.1% | 0% | 0% | 0% | 8 |
| 88.3% | 88.2% | 11.7% | 0.1% | 0% | 0% | 0% | 9 |
| 91% | 90.9% | 9% | 0.1% | 0% | 0% | 0% | 10 |
| 93.9% | 93.9% | 6% | 0.1% | 0% | 0% | 0% | 11 |
| 95.4% | 95.3% | 4.6% | 0.1% | 0% | 0% | 0% | 12 |
Compiled 13 to 11 computations (15.4% saved)
| 1.2s | 8 254× | 0 | valid |
| 0.0ms | 1× | 3 | valid |
| 0.0ms | 1× | 2 | valid |
ival-sub: 288.0ms (40.1% of total)ival-mult: 159.0ms (22.1% of total)ival-div: 152.0ms (21.1% of total)ival-add: 102.0ms (14.2% of total)exact: 8.0ms (1.1% of total)ival-true: 6.0ms (0.8% of total)ival-assert: 3.0ms (0.4% of total)adjust: 0.0ms (0% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 34 | 0 | - | 0 | - | (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) |
| 0 | 0 | - | 0 | - | (/.f64 (*.f64 x y) #s(literal 2 binary64)) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (*.f64 x y) |
| 0 | 0 | - | 0 | - | (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
| 0 | 0 | - | 0 | - | (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) |
| 0 | 0 | - | 0 | - | #s(literal 2 binary64) |
| 0 | 0 | - | 0 | - | y |
| 0 | 0 | - | 0 | - | x |
| Predicted + | Predicted - | |
|---|---|---|
| + | 0 | 0 |
| - | 0 | 256 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 0 | 0 | 0 |
| - | 0 | 0 | 256 |
| number | freq |
|---|---|
| 0 | 256 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 0 | 0 | 0 |
| - | 0 | 0 | 1 |
| 9.1s | 512× | 0 | valid |
Compiled 95 to 31 computations (67.4% saved)
ival-sub: 9.0s (99.8% of total)ival-div: 7.0ms (0.1% of total)ival-mult: 4.0ms (0% of total)ival-add: 2.0ms (0% of total)ival-true: 1.0ms (0% of total)exact: 1.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
| 384× | lower-fma.f64 |
| 384× | lower-fma.f32 |
| 272× | lower-*.f32 |
| 270× | lower-*.f64 |
| 224× | associate-*l* |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 23 | 63 |
| 1 | 57 | 61 |
| 2 | 121 | 57 |
| 3 | 253 | 55 |
| 4 | 541 | 55 |
| 5 | 888 | 55 |
| 6 | 995 | 55 |
| 7 | 1019 | 55 |
| 8 | 1029 | 55 |
| 9 | 1033 | 55 |
| 0 | 9 | 11 |
| 0 | 14 | 11 |
| 1 | 22 | 11 |
| 2 | 33 | 11 |
| 3 | 48 | 11 |
| 4 | 90 | 11 |
| 5 | 163 | 11 |
| 6 | 284 | 11 |
| 7 | 379 | 11 |
| 8 | 589 | 11 |
| 9 | 679 | 11 |
| 10 | 801 | 11 |
| 11 | 837 | 11 |
| 12 | 1000 | 11 |
| 13 | 1009 | 11 |
| 0 | 1009 | 10 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
| Outputs |
|---|
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
(+.f64 x (/.f64 y (fma.f64 x (*.f64 y #s(literal -1/2 binary64)) #s(literal -1 binary64)))) |
Compiled 13 to 9 computations (30.8% saved)
Compiled 2 to 2 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.9% | (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
Compiled 13 to 9 computations (30.8% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) | |
| cost-diff | 0 | (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) | |
| cost-diff | 128 | (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) | |
| cost-diff | 384 | (/.f64 (*.f64 x y) #s(literal 2 binary64)) |
| 384× | lower-fma.f64 |
| 384× | lower-fma.f32 |
| 272× | lower-*.f32 |
| 270× | lower-*.f64 |
| 224× | associate-*l* |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 39 |
| 0 | 14 | 39 |
| 1 | 22 | 39 |
| 2 | 33 | 39 |
| 3 | 48 | 39 |
| 4 | 90 | 39 |
| 5 | 163 | 39 |
| 6 | 284 | 39 |
| 7 | 379 | 39 |
| 8 | 589 | 39 |
| 9 | 679 | 39 |
| 10 | 801 | 39 |
| 11 | 837 | 39 |
| 12 | 1000 | 39 |
| 13 | 1009 | 39 |
| 0 | 1009 | 36 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
x |
(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) |
y |
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) |
#s(literal 1 binary64) |
(/.f64 (*.f64 x y) #s(literal 2 binary64)) |
(*.f64 x y) |
#s(literal 2 binary64) |
| Outputs |
|---|
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
(+.f64 x (/.f64 y (fma.f64 x (*.f64 y #s(literal -1/2 binary64)) #s(literal -1 binary64)))) |
x |
(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) |
(/.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
y |
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) |
(fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(/.f64 (*.f64 x y) #s(literal 2 binary64)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(*.f64 x y) |
#s(literal 2 binary64) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (*.f64 x y) | |
| accuracy | 0.00390625 | (/.f64 (*.f64 x y) #s(literal 2 binary64)) | |
| accuracy | 0.00390625 | (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) | |
| accuracy | 8.019984185516416 | (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) |
| 15.0ms | 256× | 0 | valid |
Compiled 41 to 11 computations (73.2% saved)
ival-div: 3.0ms (37.2% of total)ival-mult: 2.0ms (24.8% of total)ival-sub: 1.0ms (12.4% of total)ival-add: 1.0ms (12.4% 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 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ()) |
#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ()) |
#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ()) |
#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (*.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (*.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (- (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor 0 x) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y) (taylor 0 x) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ()) |
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#s(alt (* x y) (taylor inf y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
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#s(alt (* x y) (taylor -inf y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor -inf y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor -inf y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
30 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | y | @ | 0 | (/ (* x y) 2) |
| 1.0ms | x | @ | -inf | (- x (/ y (+ 1 (/ (* x y) 2)))) |
| 1.0ms | x | @ | 0 | (/ (* x y) 2) |
| 1.0ms | x | @ | inf | (/ (* x y) 2) |
| 1.0ms | y | @ | inf | (- x (/ y (+ 1 (/ (* x y) 2)))) |
| 1× | egg-herbie |
| 13 558× | lower-fma.f64 |
| 13 558× | lower-fma.f32 |
| 4 930× | lower-*.f64 |
| 4 930× | lower-*.f32 |
| 1 854× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 231 | 1053 |
| 1 | 738 | 1018 |
| 2 | 1942 | 987 |
| 3 | 6081 | 981 |
| 0 | 8428 | 934 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
1 |
(+ 1 (* 1/2 (* x y))) |
(+ 1 (* 1/2 (* x y))) |
(+ 1 (* 1/2 (* x y))) |
(* 1/2 (* x y)) |
(* x (+ (* 1/2 y) (/ 1 x))) |
(* x (+ (* 1/2 y) (/ 1 x))) |
(* x (+ (* 1/2 y) (/ 1 x))) |
(* 1/2 (* x y)) |
(* -1 (* x (- (* -1/2 y) (/ 1 x)))) |
(* -1 (* x (- (* -1/2 y) (/ 1 x)))) |
(* -1 (* x (- (* -1/2 y) (/ 1 x)))) |
1 |
(+ 1 (* 1/2 (* x y))) |
(+ 1 (* 1/2 (* x y))) |
(+ 1 (* 1/2 (* x y))) |
(* 1/2 (* x y)) |
(* y (+ (* 1/2 x) (/ 1 y))) |
(* y (+ (* 1/2 x) (/ 1 y))) |
(* y (+ (* 1/2 x) (/ 1 y))) |
(* 1/2 (* x y)) |
(* -1 (* y (- (* -1/2 x) (/ 1 y)))) |
(* -1 (* y (- (* -1/2 x) (/ 1 y)))) |
(* -1 (* y (- (* -1/2 x) (/ 1 y)))) |
(* -1 y) |
(- (* x (+ 1 (* 1/2 (pow y 2)))) y) |
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) |
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) |
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) |
x |
(+ x (* -1 y)) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) |
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
y |
(* y (+ 1 (* -1/2 (* x y)))) |
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x))))) |
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x))))) |
(/ 2 x) |
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) |
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y))) |
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) |
(/ 2 x) |
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) |
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x))) |
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x))) |
y |
(+ y (* -1/2 (* x (pow y 2)))) |
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) |
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2))))) |
(/ 2 x) |
(/ (- 2 (* 4 (/ 1 (* x y)))) x) |
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x) |
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x) |
(/ 2 x) |
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x)) |
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x)) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
| Outputs |
|---|
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 (* x y))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(+ 1 (* 1/2 (* x y))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(+ 1 (* 1/2 (* x y))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* x (+ (* 1/2 y) (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(* x (+ (* 1/2 y) (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(* x (+ (* 1/2 y) (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* -1 (* x (- (* -1/2 y) (/ 1 x)))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(* -1 (* x (- (* -1/2 y) (/ 1 x)))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(* -1 (* x (- (* -1/2 y) (/ 1 x)))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 (* x y))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(+ 1 (* 1/2 (* x y))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(+ 1 (* 1/2 (* x y))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* y (+ (* 1/2 x) (/ 1 y))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(* y (+ (* 1/2 x) (/ 1 y))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(* y (+ (* 1/2 x) (/ 1 y))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(* -1 (* y (- (* -1/2 x) (/ 1 y)))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(* -1 (* y (- (* -1/2 x) (/ 1 y)))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(* -1 (* y (- (* -1/2 x) (/ 1 y)))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(* -1 y) |
(neg.f64 y) |
(- (* x (+ 1 (* 1/2 (pow y 2)))) y) |
(fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) |
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) |
(fma.f64 x (*.f64 (*.f64 y y) (fma.f64 x (*.f64 y #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) (-.f64 x y)) |
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) |
(fma.f64 x (fma.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x (pow.f64 y #s(literal 4 binary64)))) (*.f64 (*.f64 y y) (fma.f64 x (*.f64 y #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))) (-.f64 x y)) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) |
(fma.f64 x (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 x (*.f64 x (*.f64 x y)))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) x) |
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) |
(+.f64 (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 x (*.f64 y y)))) (*.f64 x x))) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) |
(fma.f64 x (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 x (*.f64 x (*.f64 x y)))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) x) |
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) |
(+.f64 (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 x (*.f64 y y)))) (*.f64 x x))) |
x |
(+ x (* -1 y)) |
(-.f64 x y) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) |
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) |
(fma.f64 x (*.f64 (*.f64 y y) (fma.f64 x (*.f64 y #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) (-.f64 x y)) |
(- x (* 2 (/ 1 x))) |
(+.f64 x (/.f64 #s(literal -2 binary64) x)) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(+.f64 x (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 x y)) #s(literal -2 binary64)) x)) |
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) |
(-.f64 x (/.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 x y))) (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x (*.f64 y y))))) x)) |
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) |
(+.f64 (-.f64 x (/.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 x y))) (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x (*.f64 y y))))) x)) (/.f64 #s(literal 16 binary64) (*.f64 (*.f64 y y) (*.f64 y (*.f64 (*.f64 x (*.f64 x x)) x))))) |
(- x (* 2 (/ 1 x))) |
(+.f64 x (/.f64 #s(literal -2 binary64) x)) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(+.f64 x (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 x y)) #s(literal -2 binary64)) x)) |
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(-.f64 x (/.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 x y))) (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x (*.f64 y y))))) x)) |
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(+.f64 (-.f64 x (/.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 x y))) (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x (*.f64 y y))))) x)) (/.f64 #s(literal 16 binary64) (*.f64 (*.f64 y y) (*.f64 y (*.f64 (*.f64 x (*.f64 x x)) x))))) |
y |
(* y (+ 1 (* -1/2 (* x y)))) |
(fma.f64 x (*.f64 y (*.f64 y #s(literal -1/2 binary64))) y) |
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x))))) |
(fma.f64 x (*.f64 (*.f64 y y) (fma.f64 x (*.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) y) |
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x))))) |
(fma.f64 (*.f64 y y) (fma.f64 x #s(literal -1/2 binary64) (*.f64 y (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) (*.f64 x (*.f64 (*.f64 x (*.f64 x y)) #s(literal -1/8 binary64)))))) y) |
(/ 2 x) |
(/.f64 #s(literal 2 binary64) x) |
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) |
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 x y)) #s(literal -2 binary64)) x) |
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y))) |
(/.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 x y))) (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x (*.f64 y y))))) x) |
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) |
(+.f64 (/.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 x y))) (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x (*.f64 y y))))) x) (/.f64 #s(literal -16 binary64) (*.f64 (*.f64 y y) (*.f64 y (*.f64 (*.f64 x (*.f64 x x)) x))))) |
(/ 2 x) |
(/.f64 #s(literal 2 binary64) x) |
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) |
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 x y)) #s(literal -2 binary64)) x) |
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x))) |
(/.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 x y))) (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x (*.f64 y y))))) x) |
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x))) |
(+.f64 (/.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 x y))) (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x (*.f64 y y))))) x) (/.f64 #s(literal -16 binary64) (*.f64 (*.f64 y y) (*.f64 y (*.f64 (*.f64 x (*.f64 x x)) x))))) |
y |
(+ y (* -1/2 (* x (pow y 2)))) |
(fma.f64 x (*.f64 y (*.f64 y #s(literal -1/2 binary64))) y) |
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) |
(fma.f64 x (*.f64 (*.f64 y y) (fma.f64 x (*.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) y) |
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2))))) |
(fma.f64 x (fma.f64 x (*.f64 x (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1/8 binary64))) (*.f64 (*.f64 y y) (fma.f64 x (*.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))) y) |
(/ 2 x) |
(/.f64 #s(literal 2 binary64) x) |
(/ (- 2 (* 4 (/ 1 (* x y)))) x) |
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 x y)) #s(literal -2 binary64)) x) |
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x) |
(/.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 x y))) (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x (*.f64 y y))))) x) |
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x) |
(/.f64 (+.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 x y))) (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x (*.f64 y y))))) (/.f64 #s(literal -16 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 y (*.f64 y y))))))) x) |
(/ 2 x) |
(/.f64 #s(literal 2 binary64) x) |
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x)) |
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 x y)) #s(literal -2 binary64)) x) |
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x)) |
(/.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 x y))) (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x (*.f64 y y))))) x) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x)) |
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (+.f64 (/.f64 #s(literal 16 binary64) (*.f64 x (*.f64 x (*.f64 y (*.f64 y y))))) (/.f64 #s(literal -8 binary64) (*.f64 x (*.f64 y y))))) x)) x) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
| 5 754× | lower-fma.f64 |
| 5 754× | lower-fma.f32 |
| 4 124× | lower-*.f32 |
| 4 122× | lower-*.f64 |
| 2 962× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 35 |
| 0 | 14 | 35 |
| 1 | 63 | 35 |
| 2 | 500 | 35 |
| 3 | 6873 | 35 |
| 0 | 8527 | 32 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (*.f64 x y) #s(literal 2 binary64)) |
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) |
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) |
(*.f64 x y) |
| Outputs |
|---|
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 (*.f64 (*.f64 x y) #s(literal 1/2 binary64)))) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x y) #s(literal -1/2 binary64))) |
(neg.f64 (*.f64 (*.f64 x y) #s(literal -1/2 binary64))) |
(/.f64 x (/.f64 #s(literal 2 binary64) y)) |
(/.f64 (*.f64 x y) #s(literal 2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x y))) |
(/.f64 (*.f64 x (neg.f64 y)) #s(literal -2 binary64)) |
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x y))) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x y))) |
(pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal -1 binary64)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(*.f64 x (*.f64 (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 y (*.f64 x #s(literal 1/2 binary64))) |
(*.f64 y (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 y (*.f64 (neg.f64 x) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 x y) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 (*.f64 x y) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 x y) #s(literal 1/2 binary64))) |
(*.f64 (*.f64 x (neg.f64 y)) #s(literal -1/2 binary64)) |
(*.f64 (neg.f64 y) (*.f64 x #s(literal -1/2 binary64))) |
(*.f64 (neg.f64 y) (/.f64 x #s(literal -2 binary64))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y)) #s(literal -1 binary64))) |
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x) |
(*.f64 #s(literal -1 binary64) (*.f64 (*.f64 x y) #s(literal -1/2 binary64))) |
(*.f64 #s(literal -1/2 binary64) (*.f64 x (neg.f64 y))) |
(*.f64 (neg.f64 x) (/.f64 y #s(literal -2 binary64))) |
(*.f64 (neg.f64 x) (*.f64 y #s(literal -1/2 binary64))) |
(*.f64 (*.f64 x #s(literal 1/2 binary64)) y) |
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal -1/2 binary64))) |
(+.f64 (*.f64 (*.f64 x y) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x y) #s(literal 1/2 binary64))) |
(+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) (neg.f64 (/.f64 (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x y) #s(literal -1/2 binary64))) |
(-.f64 #s(literal 0 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))) |
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) (/.f64 (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64)))) |
(-.f64 (/.f64 (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)))) |
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 x (*.f64 (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 y (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(fma.f64 y (*.f64 (neg.f64 x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 (*.f64 x y) #s(literal 1/2 binary64) #s(literal 1 binary64)) |
(fma.f64 (*.f64 (*.f64 x y) #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1 binary64) (*.f64 (*.f64 x y) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) (neg.f64 (/.f64 (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
(fma.f64 (*.f64 x (neg.f64 y)) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(fma.f64 (neg.f64 y) (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 (neg.f64 y) (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y)) #s(literal -1 binary64)) #s(literal 1 binary64)) |
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)) |
(fma.f64 #s(literal -1 binary64) (*.f64 (*.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 x (neg.f64 y)) #s(literal 1 binary64)) |
(fma.f64 (neg.f64 x) (/.f64 y #s(literal -2 binary64)) #s(literal 1 binary64)) |
(fma.f64 (neg.f64 x) (*.f64 y #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x (*.f64 y (*.f64 x y))) #s(literal -1/4 binary64) #s(literal 1 binary64))) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (neg.f64 (/.f64 (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) y #s(literal 1 binary64)) |
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64))))) (fma.f64 (*.f64 x y) (fma.f64 #s(literal 1/4 binary64) (*.f64 x y) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (neg.f64 (/.f64 (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(neg.f64 (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) (fma.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y))) #s(literal -1 binary64)))) |
(/.f64 (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(/.f64 (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64)) #s(literal -1 binary64)) |
(/.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64)) (fma.f64 (*.f64 x y) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(/.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64)) (neg.f64 (neg.f64 (fma.f64 (*.f64 x y) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64))))) |
(/.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64)) (*.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 y (*.f64 x y))) #s(literal -1/4 binary64) #s(literal 1 binary64)) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 y (*.f64 x y))) #s(literal -1/4 binary64) #s(literal 1 binary64)) (*.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64)))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 y (*.f64 x y))) #s(literal -1/4 binary64) #s(literal 1 binary64)) (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 x y) #s(literal 1/2 binary64))))) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64)))) |
(/.f64 (neg.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64))) (neg.f64 (fma.f64 (*.f64 x y) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
(/.f64 (neg.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64))) (*.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 x y) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64))))) |
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y))))) (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 x y) #s(literal 1/2 binary64)))) |
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y))))) (*.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 x y) #s(literal 1/2 binary64))))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64))) (*.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 y (*.f64 y y))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 y (*.f64 y y)))) #s(literal 1/64 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x y) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64))) (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 y (*.f64 y y))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 y (*.f64 y y)))) #s(literal 1/64 binary64))) (*.f64 (fma.f64 (*.f64 x y) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)))))) |
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 y (*.f64 y y))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 y (*.f64 y y)))) #s(literal 1/64 binary64))) (*.f64 (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))) (fma.f64 (*.f64 x y) (*.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (fma.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y))) #s(literal -1 binary64)) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))) |
(/.f64 (fma.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y))) #s(literal -1 binary64)) (*.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)))) |
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x (*.f64 y (*.f64 x y))) (*.f64 x (*.f64 y (*.f64 x y)))) #s(literal 1/16 binary64))) (*.f64 (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 (*.f64 x y) (*.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))))) (*.f64 (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64)))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64)))) (fma.f64 (*.f64 x y) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 (*.f64 x y) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))))) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))))) (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 x y) #s(literal 1/2 binary64))))) |
(/.f64 (neg.f64 (fma.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y))) #s(literal -1 binary64))) (neg.f64 (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)))) |
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) (fma.f64 (/.f64 (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) (/.f64 (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) (/.f64 (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))))))) |
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (*.f64 (/.f64 (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) (/.f64 (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))))) (+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) (/.f64 (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
(/.f64 (*.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 (*.f64 x y) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 y (*.f64 x y))) #s(literal -1/4 binary64) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
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(*.f64 (/.f64 (neg.f64 y) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64))) (neg.f64 (fma.f64 (*.f64 x y) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
(*.f64 (/.f64 (neg.f64 y) (fma.f64 (*.f64 x (*.f64 y (*.f64 x y))) #s(literal -1/4 binary64) #s(literal 1 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 x y) #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 y (neg.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64)))) (neg.f64 (fma.f64 (*.f64 x y) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))) |
(*.f64 (/.f64 y (+.f64 #s(literal -1 binary64) (*.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y)))))) (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 x y) #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 y (fma.f64 y (*.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x y))) #s(literal -1 binary64))) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (neg.f64 y))) |
(neg.f64 (*.f64 x (neg.f64 y))) |
(*.f64 x y) |
(*.f64 y x) |
(*.f64 y (neg.f64 (neg.f64 x))) |
(*.f64 (*.f64 x y) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 x y)) |
(*.f64 (neg.f64 y) (neg.f64 x)) |
(*.f64 #s(literal -1 binary64) (*.f64 x (neg.f64 y))) |
(*.f64 (neg.f64 x) (neg.f64 y)) |
(*.f64 (neg.f64 (neg.f64 x)) y) |
Compiled 11 052 to 1 049 computations (90.5% saved)
7 alts after pruning (7 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 387 | 7 | 394 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 388 | 7 | 395 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.9% | (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) |
| 63.3% | (-.f64 x (/.f64 y #s(approx (+ 1 (/ (* x y) 2)) (*.f64 #s(literal 1/2 binary64) (*.f64 x y))))) | |
| ▶ | 63.4% | (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) |
| ▶ | 64.0% | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x)) |
| 60.2% | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x)) | |
| ▶ | 74.7% | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) |
| ▶ | 28.0% | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) |
Compiled 132 to 78 computations (40.9% saved)
| 1× | egg-herbie |
Found 15 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 x y) | |
| cost-diff | 0 | (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) | |
| cost-diff | 0 | (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) | |
| cost-diff | 0 | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x)) | |
| cost-diff | 0 | (/.f64 #s(literal 2 binary64) x) | |
| cost-diff | 0 | #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)) | |
| cost-diff | 0 | (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) | |
| cost-diff | 0 | (-.f64 x y) | |
| cost-diff | 0 | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) | |
| cost-diff | 0 | (neg.f64 y) | |
| cost-diff | 0 | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) | |
| cost-diff | 0 | (*.f64 y #s(literal 1/2 binary64)) | |
| cost-diff | 0 | (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)) | |
| cost-diff | 0 | (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) | |
| cost-diff | 0 | (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) |
| 1 384× | lower-fma.f32 |
| 1 378× | lower-fma.f64 |
| 664× | lower-*.f32 |
| 660× | lower-*.f64 |
| 274× | distribute-lft-neg-in |
Useful iterations: 6 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 26 | 144 |
| 0 | 40 | 144 |
| 1 | 70 | 144 |
| 2 | 120 | 144 |
| 3 | 187 | 144 |
| 4 | 377 | 144 |
| 5 | 713 | 141 |
| 6 | 1097 | 139 |
| 7 | 1431 | 139 |
| 8 | 1610 | 139 |
| 9 | 1736 | 139 |
| 10 | 1823 | 139 |
| 11 | 1935 | 139 |
| 12 | 1952 | 139 |
| 13 | 1961 | 139 |
| 14 | 1968 | 139 |
| 15 | 1969 | 139 |
| 0 | 1969 | 139 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) |
x |
(/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) |
y |
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)) |
(*.f64 y #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
#s(literal 1 binary64) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) |
(neg.f64 y) |
y |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) |
(-.f64 x y) |
x |
y |
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) |
x |
#s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)) |
(/.f64 #s(literal 2 binary64) x) |
#s(literal 2 binary64) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x)) |
(fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) |
y |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) |
#s(literal 1/2 binary64) |
(*.f64 x y) |
x |
#s(literal -1 binary64) |
| Outputs |
|---|
(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) |
(+.f64 x (/.f64 y (fma.f64 x (*.f64 y #s(literal -1/2 binary64)) #s(literal -1 binary64)))) |
x |
(/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) |
(/.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
y |
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)) |
(fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(*.f64 y #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
#s(literal 1 binary64) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) |
(neg.f64 y) |
y |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) |
(-.f64 x y) |
x |
y |
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) |
x |
#s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)) |
(/.f64 #s(literal 2 binary64) x) |
#s(literal 2 binary64) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x)) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) x)) |
(fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) |
(fma.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) x) |
y |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) |
(fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
#s(literal 1/2 binary64) |
(*.f64 x y) |
x |
#s(literal -1 binary64) |
Found 15 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) | |
| accuracy | 0 | (*.f64 x y) | |
| accuracy | 0.02734375 | (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) | |
| accuracy | 23.029317657867953 | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x)) | |
| accuracy | 0 | (/.f64 #s(literal 2 binary64) x) | |
| accuracy | 0 | (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) | |
| accuracy | 30.201998629908275 | #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)) | |
| accuracy | 0 | (-.f64 x y) | |
| accuracy | 16.214899226745544 | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) | |
| accuracy | 0 | (neg.f64 y) | |
| accuracy | 46.06567019735219 | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) | |
| accuracy | 0 | (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)) | |
| accuracy | 0 | (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) | |
| accuracy | 0 | (*.f64 y #s(literal 1/2 binary64)) | |
| accuracy | 8.019984185516416 | (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) |
| 41.0ms | 256× | 0 | valid |
Compiled 127 to 25 computations (80.3% saved)
ival-mult: 8.0ms (32.1% of total)ival-div: 7.0ms (28.1% of total)ival-add: 4.0ms (16% of total)ival-sub: 3.0ms (12% of total)exact: 1.0ms (4% of total)ival-neg: 1.0ms (4% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ()) |
#s(alt (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 y #s(literal 1/2 binary64)) (patch (*.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) #<representation binary64>) () ()) |
#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ()) |
#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) #<representation binary64>) () ()) |
#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ()) |
#s(alt (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) (patch (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ()) |
#s(alt #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)) (patch #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ()) |
#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x)) #<representation binary64>) () ()) |
#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ()) |
#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* -1 y) (taylor 0 x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y) (taylor 0 x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) (taylor 0 x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) (taylor 0 x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1 (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- x (* 2 (/ 1 x))) (taylor inf y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) (taylor inf y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) (taylor inf y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) (taylor inf y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- x (* 2 (/ 1 x))) (taylor -inf y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
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#s(alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) (taylor -inf y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x (pow y 2))) (taylor inf y) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (- (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y))) (taylor inf y) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y))) (taylor inf y) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x (pow y 2))) (taylor -inf y) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (- (* 1/2 x) (/ 1 y))) (taylor -inf y) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x))) (taylor -inf y) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x))) (taylor -inf y) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor 0 x) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2))))) (taylor 0 x) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2))))) (taylor 0 x) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2))))) (taylor 0 x) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/2 (pow y 2)))) (taylor inf x) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) (taylor inf x) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) (taylor inf x) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) (taylor inf x) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1/2 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) (taylor -inf x) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) (taylor -inf x) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) (taylor -inf x) (#s(alt (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) (patch (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) #<representation binary64>) () ())) ()) |
#s(alt -1 (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (* 1/2 (* x y)) 1) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (* 1/2 (* x y)) 1) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (* 1/2 (* x y)) 1) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt -1 (taylor 0 y) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (* 1/2 (* x y)) 1) (taylor 0 y) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (* 1/2 (* x y)) 1) (taylor 0 y) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (* 1/2 (* x y)) 1) (taylor 0 y) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* y (- (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* y (- (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* y (- (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (+ (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (+ (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (+ (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor 0 x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor 0 x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor 0 x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor 0 x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor inf y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor inf y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor inf y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor inf y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor -inf y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor -inf y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor -inf y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor -inf y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
81 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | y | @ | -inf | (- x y) |
| 0.0ms | x | @ | -inf | (+ (* y (+ (* 1/2 (* x y)) -1)) x) |
| 0.0ms | y | @ | -inf | (* y 1/2) |
| 0.0ms | y | @ | inf | (+ (* y (+ (* 1/2 (* x y)) -1)) x) |
| 0.0ms | y | @ | inf | (* y 1/2) |
| 1× | egg-herbie |
| 12 856× | lower-fma.f64 |
| 12 856× | lower-fma.f32 |
| 4 554× | lower-*.f64 |
| 4 554× | lower-*.f32 |
| 2 528× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 278 | 3213 |
| 1 | 875 | 3109 |
| 2 | 2370 | 3007 |
| 3 | 7087 | 2993 |
| 0 | 8319 | 2814 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* -1 y) |
(- (* x (+ 1 (* 1/2 (pow y 2)))) y) |
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) |
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) |
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) |
x |
(+ x (* -1 y)) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) |
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
y |
(* y (+ 1 (* -1/2 (* x y)))) |
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x))))) |
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x))))) |
(/ 2 x) |
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) |
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y))) |
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) |
(/ 2 x) |
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) |
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x))) |
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x))) |
y |
(+ y (* -1/2 (* x (pow y 2)))) |
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) |
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2))))) |
(/ 2 x) |
(/ (- 2 (* 4 (/ 1 (* x y)))) x) |
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x) |
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x) |
(/ 2 x) |
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x)) |
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x)) |
1 |
(+ 1 (* 1/2 (* x y))) |
(+ 1 (* 1/2 (* x y))) |
(+ 1 (* 1/2 (* x y))) |
(* 1/2 (* x y)) |
(* y (+ (* 1/2 x) (/ 1 y))) |
(* y (+ (* 1/2 x) (/ 1 y))) |
(* y (+ (* 1/2 x) (/ 1 y))) |
(* 1/2 (* x y)) |
(* -1 (* y (- (* -1/2 x) (/ 1 y)))) |
(* -1 (* y (- (* -1/2 x) (/ 1 y)))) |
(* -1 (* y (- (* -1/2 x) (/ 1 y)))) |
1 |
(+ 1 (* 1/2 (* x y))) |
(+ 1 (* 1/2 (* x y))) |
(+ 1 (* 1/2 (* x y))) |
(* 1/2 (* x y)) |
(* x (+ (* 1/2 y) (/ 1 x))) |
(* x (+ (* 1/2 y) (/ 1 x))) |
(* x (+ (* 1/2 y) (/ 1 x))) |
(* 1/2 (* x y)) |
(* -1 (* x (- (* -1/2 y) (/ 1 x)))) |
(* -1 (* x (- (* -1/2 y) (/ 1 x)))) |
(* -1 (* x (- (* -1/2 y) (/ 1 x)))) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* 1/2 y) |
(* -1 y) |
(- (* x (+ 1 (* 1/2 (pow y 2)))) y) |
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) |
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) |
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) |
x |
(+ x (* -1 y)) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) |
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(- (* x (+ 1 (* 1/2 (pow y 2)))) y) |
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) |
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) |
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) |
x |
(+ x (* -1 y)) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) |
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(* -1 y) |
(- x y) |
(- x y) |
(- x y) |
x |
(* x (+ 1 (* -1 (/ y x)))) |
(* x (+ 1 (* -1 (/ y x)))) |
(* x (+ 1 (* -1 (/ y x)))) |
x |
(* -1 (* x (- (/ y x) 1))) |
(* -1 (* x (- (/ y x) 1))) |
(* -1 (* x (- (/ y x) 1))) |
x |
(+ x (* -1 y)) |
(+ x (* -1 y)) |
(+ x (* -1 y)) |
(* -1 y) |
(* y (- (/ x y) 1)) |
(* y (- (/ x y) 1)) |
(* y (- (/ x y) 1)) |
(* -1 y) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
(* -1 (* y (+ 1 (* -1 (/ x y))))) |
(* -1 y) |
(- (* x (+ 1 (* 1/2 (pow y 2)))) y) |
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) |
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) |
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) |
x |
(+ x (* -1 y)) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) |
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
y |
(* y (+ 1 (* -1/2 (* x y)))) |
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x))))) |
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x))))) |
(/ 2 x) |
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) |
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y))) |
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) |
(/ 2 x) |
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) |
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x))) |
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x))) |
y |
(+ y (* -1/2 (* x (pow y 2)))) |
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) |
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2))))) |
(/ 2 x) |
(/ (- 2 (* 4 (/ 1 (* x y)))) x) |
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x) |
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x) |
(/ 2 x) |
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x)) |
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x)) |
(/ 2 x) |
(/ 2 x) |
(/ 2 x) |
(/ 2 x) |
(/ 2 x) |
(/ 2 x) |
(/ 2 x) |
(/ 2 x) |
(/ 2 x) |
(/ 2 x) |
(/ 2 x) |
(/ 2 x) |
(* -1 y) |
(- (* x (+ 1 (* 1/2 (pow y 2)))) y) |
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) |
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) |
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) |
x |
(+ x (* -1 y)) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) |
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
x |
(+ x (* -1 y)) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(* 1/2 (* x (pow y 2))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y))) |
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y))) |
(* 1/2 (* x (pow y 2))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x))) |
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x))) |
(* -1 y) |
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2))))) |
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2))))) |
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2))))) |
(* x (+ 1 (* 1/2 (pow y 2)))) |
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) |
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) |
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) |
(* -1 (* x (- (* -1/2 (pow y 2)) 1))) |
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) |
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) |
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) |
-1 |
(- (* 1/2 (* x y)) 1) |
(- (* 1/2 (* x y)) 1) |
(- (* 1/2 (* x y)) 1) |
(* 1/2 (* x y)) |
(* x (- (* 1/2 y) (/ 1 x))) |
(* x (- (* 1/2 y) (/ 1 x))) |
(* x (- (* 1/2 y) (/ 1 x))) |
(* 1/2 (* x y)) |
(* -1 (* x (+ (* -1/2 y) (/ 1 x)))) |
(* -1 (* x (+ (* -1/2 y) (/ 1 x)))) |
(* -1 (* x (+ (* -1/2 y) (/ 1 x)))) |
-1 |
(- (* 1/2 (* x y)) 1) |
(- (* 1/2 (* x y)) 1) |
(- (* 1/2 (* x y)) 1) |
(* 1/2 (* x y)) |
(* y (- (* 1/2 x) (/ 1 y))) |
(* y (- (* 1/2 x) (/ 1 y))) |
(* y (- (* 1/2 x) (/ 1 y))) |
(* 1/2 (* x y)) |
(* -1 (* y (+ (* -1/2 x) (/ 1 y)))) |
(* -1 (* y (+ (* -1/2 x) (/ 1 y)))) |
(* -1 (* y (+ (* -1/2 x) (/ 1 y)))) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
| Outputs |
|---|
(* -1 y) |
(neg.f64 y) |
(- (* x (+ 1 (* 1/2 (pow y 2)))) y) |
(fma.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) x) |
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) |
(fma.f64 x (*.f64 (*.f64 y y) (fma.f64 y (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) (-.f64 x y)) |
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) |
(fma.f64 x (fma.f64 (*.f64 y y) (fma.f64 y (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) (*.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))) (-.f64 x y)) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) |
(fma.f64 x (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 x (*.f64 y (*.f64 x x)))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) x) |
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) |
(fma.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 y (*.f64 y x)))) (*.f64 x (*.f64 x x))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) x) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) |
(fma.f64 x (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 x (*.f64 y (*.f64 x x)))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) x) |
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) |
(+.f64 (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 y (*.f64 y x)))) (*.f64 x x))) |
x |
(+ x (* -1 y)) |
(-.f64 x y) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(fma.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) x) |
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) |
(fma.f64 x (*.f64 (*.f64 y y) (fma.f64 y (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) (-.f64 x y)) |
(- x (* 2 (/ 1 x))) |
(+.f64 x (/.f64 #s(literal -2 binary64) x)) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(+.f64 x (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)) |
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) |
(+.f64 x (/.f64 (+.f64 #s(literal -2 binary64) (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y (*.f64 x x)))))) x)) |
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) |
(+.f64 x (+.f64 (/.f64 #s(literal 16 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 x (*.f64 x x)) x))) (/.f64 (+.f64 #s(literal -2 binary64) (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y (*.f64 x x)))))) x))) |
(- x (* 2 (/ 1 x))) |
(+.f64 x (/.f64 #s(literal -2 binary64) x)) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(+.f64 x (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)) |
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(+.f64 x (/.f64 (+.f64 #s(literal -2 binary64) (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y (*.f64 x x)))))) x)) |
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(-.f64 x (+.f64 (/.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y (*.f64 x x)))) (/.f64 #s(literal -4 binary64) (*.f64 y x)))) x) (/.f64 #s(literal -16 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 x (*.f64 x x)) x))))) |
y |
(* y (+ 1 (* -1/2 (* x y)))) |
(fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y) |
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x))))) |
(fma.f64 x (*.f64 (*.f64 y y) (fma.f64 y (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) y) |
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x))))) |
(fma.f64 (*.f64 y y) (fma.f64 y (fma.f64 y (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/8 binary64))) (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) (*.f64 x #s(literal -1/2 binary64))) y) |
(/ 2 x) |
(/.f64 #s(literal 2 binary64) x) |
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) |
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(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
| 4 694× | lower-*.f32 |
| 4 690× | lower-*.f64 |
| 4 434× | lower-/.f32 |
| 4 430× | lower-/.f64 |
| 4 348× | lower-fma.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 26 | 131 |
| 0 | 40 | 131 |
| 1 | 188 | 126 |
| 2 | 1578 | 126 |
| 0 | 8121 | 126 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) |
(/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) |
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)) |
(*.f64 y #s(literal 1/2 binary64)) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) |
(neg.f64 y) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) |
(-.f64 x y) |
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) |
#s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)) |
(/.f64 #s(literal 2 binary64) x) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x)) |
(fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) |
(*.f64 x y) |
| Outputs |
|---|
(+.f64 x (neg.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))) |
(+.f64 (neg.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) x) |
(-.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) |
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x x (*.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))))) (/.f64 (/.f64 (*.f64 y (*.f64 y y)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))) (fma.f64 x x (*.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))))) |
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))) (/.f64 (/.f64 (*.f64 y y) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) |
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (neg.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) (/.f64 (/.f64 (*.f64 y y) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) (-.f64 x (neg.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))))) |
(fma.f64 y (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) x) |
(fma.f64 (neg.f64 y) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))) x) |
(fma.f64 #s(literal -1 binary64) (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))) x) |
(fma.f64 (/.f64 y (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x (*.f64 y #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #s(literal 1 binary64)))) x) |
(fma.f64 (/.f64 y (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x y)))))) x) |
(fma.f64 (/.f64 y (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x y))))) x) |
(fma.f64 (/.f64 y (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)))) x) |
(fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) #s(literal -1 binary64))) (/.f64 y (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)))) x) |
(fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 y (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x (*.f64 y #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #s(literal 1 binary64)))) x) |
(fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 y (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x y)))))) x) |
(fma.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)))) (/.f64 y (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x y))))) x) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (*.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) (-.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) (-.f64 (*.f64 x x) (/.f64 (*.f64 y y) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x x (*.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) (-.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) (-.f64 (*.f64 x x) (/.f64 (*.f64 y y) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))))) |
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) (fma.f64 x x (*.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))))) |
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) (fma.f64 x x (-.f64 (/.f64 (*.f64 y y) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) (*.f64 x (neg.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))))) |
(/.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 y y) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))) |
(/.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 y y) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))) (-.f64 x (neg.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))))) (neg.f64 (fma.f64 x x (*.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))))) (neg.f64 (fma.f64 x x (-.f64 (/.f64 (*.f64 y y) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) (*.f64 x (neg.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 y y) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) (neg.f64 (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 y y) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) (neg.f64 (-.f64 x (neg.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 x x (*.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))))) (*.f64 (fma.f64 x x (*.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))))) (*.f64 (fma.f64 x x (*.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) (fma.f64 x x (*.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))) (*.f64 (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) (/.f64 (*.f64 y y) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) (*.f64 (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))))) (neg.f64 (neg.f64 (fma.f64 x x (*.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 y y) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))))) (neg.f64 (neg.f64 (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))))) |
(/.f64 (+.f64 (/.f64 (*.f64 y (*.f64 y y)) (neg.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) (*.f64 x (*.f64 x x))) (+.f64 (/.f64 (*.f64 y y) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) (-.f64 (*.f64 x x) (*.f64 (neg.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) x)))) |
(pow.f64 (/.f64 (fma.f64 x x (*.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) (-.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) (-.f64 (*.f64 x x) (/.f64 (*.f64 y y) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) #s(literal -1 binary64)) |
(*.f64 (-.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))))) |
(*.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 y y) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) y)) #s(literal -1 binary64))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) (neg.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))) |
(neg.f64 (neg.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))) |
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(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) y)) |
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(fma.f64 (*.f64 #s(literal 1 binary64) (*.f64 x y)) #s(literal 1/2 binary64) #s(literal -1 binary64)) |
(fma.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(fma.f64 (*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) y #s(literal -1 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x y) #s(literal -1/2 binary64)))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) #s(literal -1 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x y) #s(literal -1/2 binary64)))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal -1 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) #s(literal -1 binary64))))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal -1 binary64)) (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x y) #s(literal -1/2 binary64))))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) (*.f64 (*.f64 x y) #s(literal -1/2 binary64))))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64))) (-.f64 #s(literal -1 binary64) (*.f64 x (*.f64 y #s(literal 1/2 binary64))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x y) #s(literal -1/2 binary64)))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal -1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) (*.f64 (*.f64 x y) #s(literal -1/2 binary64)))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 #s(literal -1 binary64) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) #s(literal -1 binary64))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64)) (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) (neg.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (neg.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64))) (neg.f64 (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x y) #s(literal -1/2 binary64))))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64))))) |
(pow.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x y) #s(literal -1/2 binary64)))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x y) #s(literal -1/2 binary64)))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)))) |
(*.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) #s(literal -1 binary64))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64))))) |
(*.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x (*.f64 y #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) #s(literal 1 binary64))))) |
(*.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x y))))))) |
(*.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x y)))))) |
(*.f64 x y) |
(*.f64 y x) |
Compiled 14 670 to 1 246 computations (91.5% saved)
8 alts after pruning (4 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 684 | 4 | 688 |
| Fresh | 2 | 0 | 2 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 0 | 0 |
| Total | 687 | 8 | 695 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.9% | (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) |
| ▶ | 63.3% | (-.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))))) |
| ▶ | 64.0% | (-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y))) |
| ✓ | 63.4% | (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) |
| ▶ | 60.2% | #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x)) |
| ✓ | 74.7% | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) |
| ✓ | 28.0% | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) |
| ▶ | 29.0% | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
Compiled 79 to 46 computations (41.8% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 y (*.f64 x #s(literal 1/2 binary64))) | |
| cost-diff | 0 | #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))) | |
| cost-diff | 0 | (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))) | |
| cost-diff | 0 | (-.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))))) | |
| cost-diff | 0 | (*.f64 y (*.f64 x #s(literal -1/2 binary64))) | |
| cost-diff | 0 | (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y) | |
| cost-diff | 0 | #s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y)) | |
| cost-diff | 0 | (-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y))) | |
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | (/.f64 #s(literal -2 binary64) (*.f64 x x)) | |
| cost-diff | 0 | #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x)) | |
| cost-diff | 512 | (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) | |
| cost-diff | 0 | (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) | |
| cost-diff | 0 | (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))) | |
| cost-diff | 0 | #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) | |
| cost-diff | 0 | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
| 6 154× | lower-fma.f32 |
| 6 148× | lower-fma.f64 |
| 2 934× | lower-*.f32 |
| 2 922× | lower-*.f64 |
| 2 664× | lower--.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 40 | 224 |
| 0 | 55 | 222 |
| 1 | 110 | 222 |
| 2 | 188 | 216 |
| 3 | 274 | 216 |
| 4 | 414 | 216 |
| 5 | 738 | 216 |
| 6 | 1492 | 216 |
| 7 | 2725 | 216 |
| 8 | 6062 | 216 |
| 0 | 8262 | 207 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) |
(*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))) |
y |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(*.f64 x #s(literal 1/2 binary64)) |
x |
#s(literal 1/2 binary64) |
#s(literal -1 binary64) |
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x)) |
(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
x |
(/.f64 #s(literal -2 binary64) (*.f64 x x)) |
#s(literal -2 binary64) |
(*.f64 x x) |
(-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y))) |
x |
#s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y)) |
(fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y) |
y |
(*.f64 y (*.f64 x #s(literal -1/2 binary64))) |
(*.f64 x #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
(-.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))))) |
x |
(/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))) |
y |
#s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))) |
(*.f64 y (*.f64 x #s(literal 1/2 binary64))) |
(*.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
| Outputs |
|---|
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) |
#s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)))) |
(*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))) |
y |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(*.f64 x #s(literal 1/2 binary64)) |
x |
#s(literal 1/2 binary64) |
#s(literal -1 binary64) |
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x)) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (+.f64 x (/.f64 #s(literal -2 binary64) x))) |
(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
(+.f64 x (/.f64 #s(literal -2 binary64) x)) |
x |
(/.f64 #s(literal -2 binary64) (*.f64 x x)) |
#s(literal -2 binary64) |
(*.f64 x x) |
(-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y))) |
(-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 x (*.f64 y (*.f64 y #s(literal -1/2 binary64))) y))) |
x |
#s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y)) |
#s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 x (*.f64 y (*.f64 y #s(literal -1/2 binary64))) y)) |
(fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y) |
(fma.f64 x (*.f64 y (*.f64 y #s(literal -1/2 binary64))) y) |
y |
(*.f64 y (*.f64 x #s(literal -1/2 binary64))) |
(*.f64 x #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
(-.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))))) |
x |
(/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))) |
y |
#s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))) |
(*.f64 y (*.f64 x #s(literal 1/2 binary64))) |
(*.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (*.f64 y (*.f64 x #s(literal 1/2 binary64))) | |
| accuracy | 0 | (*.f64 x #s(literal 1/2 binary64)) | |
| accuracy | 8.019984185516416 | (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))) | |
| accuracy | 30.049528026168918 | #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))) | |
| accuracy | 0 | (*.f64 y (*.f64 x #s(literal -1/2 binary64))) | |
| accuracy | 0 | (*.f64 x #s(literal -1/2 binary64)) | |
| accuracy | 0.05859375 | (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y) | |
| accuracy | 33.50735254118063 | #s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y)) | |
| accuracy | 0 | (*.f64 x x) | |
| accuracy | 0.6225930682932458 | (/.f64 #s(literal -2 binary64) (*.f64 x x)) | |
| accuracy | 14.505241114106104 | (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) | |
| accuracy | 23.44864922201512 | #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x)) | |
| accuracy | 0 | (*.f64 x #s(literal 1/2 binary64)) | |
| accuracy | 0.0625 | (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))) | |
| accuracy | 22.987462061139045 | #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) | |
| accuracy | 23.029317657867953 | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
| 234.0ms | 256× | 0 | valid |
Compiled 155 to 36 computations (76.8% saved)
ival-mult: 19.0ms (51.8% of total)ival-add: 8.0ms (21.8% of total)ival-div: 6.0ms (16.4% of total)ival-sub: 2.0ms (5.5% of total)exact: 1.0ms (2.7% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (patch #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) #<representation binary64>) () ()) |
#s(alt (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))) (patch (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) (patch (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) (patch (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) #<representation binary64>) () ()) |
#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x)) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal -2 binary64) (*.f64 x x)) (patch (/.f64 #s(literal -2 binary64) (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ()) |
#s(alt (-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y))) (patch (-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y))) #<representation binary64>) () ()) |
#s(alt #s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y)) (patch #s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y)) #<representation binary64>) () ()) |
#s(alt (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y) (patch (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y) #<representation binary64>) () ()) |
#s(alt (*.f64 y (*.f64 x #s(literal -1/2 binary64))) (patch (*.f64 y (*.f64 x #s(literal -1/2 binary64))) #<representation binary64>) () ()) |
#s(alt (-.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))))) (patch (-.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))))) #<representation binary64>) () ()) |
#s(alt (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))) (patch (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ()) |
#s(alt (*.f64 y (*.f64 x #s(literal 1/2 binary64))) (patch (*.f64 y (*.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ()) |
#s(alt (*.f64 x #s(literal 1/2 binary64)) (patch (*.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 x #s(literal -1/2 binary64)) (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* -1 y) (taylor 0 x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y) (taylor 0 x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) (taylor 0 x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) (taylor 0 x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1 (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- x (* 2 (/ 1 x))) (taylor inf y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) (taylor inf y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) (taylor inf y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- x (* 2 (/ 1 x))) (taylor -inf y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) (taylor -inf y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) (taylor -inf y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) (taylor -inf y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (patch #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (patch #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (patch #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (patch #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* x (pow y 2))) (taylor inf y) (#s(alt #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (patch #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (- (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (patch #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) #<representation binary64>) () ())) ()) |
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#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal -1/2 binary64)) (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal -1/2 binary64)) (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal -1/2 binary64)) (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ()) |
93 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | 0 | (/ -2 (* x x)) |
| 1.0ms | x | @ | 0 | (+ (* y (* y (* x -1/2))) y) |
| 1.0ms | x | @ | inf | (+ (* y (* y (* x -1/2))) y) |
| 1.0ms | y | @ | 0 | (+ (* y (* y (* x -1/2))) y) |
| 1.0ms | x | @ | 0 | (+ (* x (/ -2 (* x x))) x) |
| 1× | egg-herbie |
| 10 996× | lower-fma.f64 |
| 10 996× | lower-fma.f32 |
| 3 750× | lower-*.f64 |
| 3 750× | lower-*.f32 |
| 3 456× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 279 | 3677 |
| 1 | 887 | 3612 |
| 2 | 2407 | 3282 |
| 3 | 7254 | 3186 |
| 0 | 8263 | 3014 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* -1 y) |
(- (* x (+ 1 (* 1/2 (pow y 2)))) y) |
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) |
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) |
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) |
x |
(+ x (* -1 y)) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) |
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
x |
(+ x (* -1 y)) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(* 1/2 (* x (pow y 2))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y))) |
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y))) |
(* 1/2 (* x (pow y 2))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x))) |
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x))) |
(* -1 y) |
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2))))) |
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2))))) |
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2))))) |
(* x (+ 1 (* 1/2 (pow y 2)))) |
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) |
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) |
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) |
(* -1 (* x (- (* -1/2 (pow y 2)) 1))) |
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) |
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) |
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) |
(* -1 y) |
(* y (- (* 1/2 (* x y)) 1)) |
(* y (- (* 1/2 (* x y)) 1)) |
(* y (- (* 1/2 (* x y)) 1)) |
(* 1/2 (* x (pow y 2))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* 1/2 (* x (pow y 2))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* -1 y) |
(+ (* -1 y) (* 1/2 (* x (pow y 2)))) |
(+ (* -1 y) (* 1/2 (* x (pow y 2)))) |
(+ (* -1 y) (* 1/2 (* x (pow y 2)))) |
(* 1/2 (* x (pow y 2))) |
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))) |
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))) |
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))) |
(* 1/2 (* x (pow y 2))) |
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x)))) |
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x)))) |
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x)))) |
-1 |
(- (* 1/2 (* x y)) 1) |
(- (* 1/2 (* x y)) 1) |
(- (* 1/2 (* x y)) 1) |
(* 1/2 (* x y)) |
(* y (- (* 1/2 x) (/ 1 y))) |
(* y (- (* 1/2 x) (/ 1 y))) |
(* y (- (* 1/2 x) (/ 1 y))) |
(* 1/2 (* x y)) |
(* -1 (* y (+ (* -1/2 x) (/ 1 y)))) |
(* -1 (* y (+ (* -1/2 x) (/ 1 y)))) |
(* -1 (* y (+ (* -1/2 x) (/ 1 y)))) |
-1 |
(- (* 1/2 (* x y)) 1) |
(- (* 1/2 (* x y)) 1) |
(- (* 1/2 (* x y)) 1) |
(* 1/2 (* x y)) |
(* x (- (* 1/2 y) (/ 1 x))) |
(* x (- (* 1/2 y) (/ 1 x))) |
(* x (- (* 1/2 y) (/ 1 x))) |
(* 1/2 (* x y)) |
(* -1 (* x (+ (* -1/2 y) (/ 1 x)))) |
(* -1 (* x (+ (* -1/2 y) (/ 1 x)))) |
(* -1 (* x (+ (* -1/2 y) (/ 1 x)))) |
(/ -2 x) |
(/ (- (pow x 2) 2) x) |
(/ (- (pow x 2) 2) x) |
(/ (- (pow x 2) 2) x) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(* -1 y) |
(- (* x (+ 1 (* 1/2 (pow y 2)))) y) |
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) |
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) |
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) |
x |
(+ x (* -1 y)) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) |
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(/ -2 (pow x 2)) |
(/ -2 (pow x 2)) |
(/ -2 (pow x 2)) |
(/ -2 (pow x 2)) |
(/ -2 (pow x 2)) |
(/ -2 (pow x 2)) |
(/ -2 (pow x 2)) |
(/ -2 (pow x 2)) |
(/ -2 (pow x 2)) |
(/ -2 (pow x 2)) |
(/ -2 (pow x 2)) |
(/ -2 (pow x 2)) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* -1 y) |
(- (* x (+ 1 (* 1/2 (pow y 2)))) y) |
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) |
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) |
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) |
x |
(+ x (* -1 y)) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) |
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
y |
(* y (+ 1 (* -1/2 (* x y)))) |
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x))))) |
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x))))) |
(/ 2 x) |
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) |
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y))) |
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) |
(/ 2 x) |
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) |
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x))) |
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x))) |
y |
(+ y (* -1/2 (* x (pow y 2)))) |
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) |
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2))))) |
(/ 2 x) |
(/ (- 2 (* 4 (/ 1 (* x y)))) x) |
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x) |
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x) |
(/ 2 x) |
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x)) |
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x)) |
y |
(* y (+ 1 (* -1/2 (* x y)))) |
(* y (+ 1 (* -1/2 (* x y)))) |
(* y (+ 1 (* -1/2 (* x y)))) |
(* -1/2 (* x (pow y 2))) |
(* (pow y 2) (+ (* -1/2 x) (/ 1 y))) |
(* (pow y 2) (+ (* -1/2 x) (/ 1 y))) |
(* (pow y 2) (+ (* -1/2 x) (/ 1 y))) |
(* -1/2 (* x (pow y 2))) |
(* (pow y 2) (+ (* -1/2 x) (/ 1 y))) |
(* (pow y 2) (+ (* -1/2 x) (/ 1 y))) |
(* (pow y 2) (+ (* -1/2 x) (/ 1 y))) |
y |
(+ y (* -1/2 (* x (pow y 2)))) |
(+ y (* -1/2 (* x (pow y 2)))) |
(+ y (* -1/2 (* x (pow y 2)))) |
(* -1/2 (* x (pow y 2))) |
(* x (+ (* -1/2 (pow y 2)) (/ y x))) |
(* x (+ (* -1/2 (pow y 2)) (/ y x))) |
(* x (+ (* -1/2 (pow y 2)) (/ y x))) |
(* -1/2 (* x (pow y 2))) |
(* -1 (* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) |
(* -1 (* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) |
(* -1 (* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1/2 (* x y)) |
(* -1 y) |
(- (* x (+ 1 (* 1/2 (pow y 2)))) y) |
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) |
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) |
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) |
x |
(+ x (* -1 y)) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) |
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
y |
(* y (+ 1 (* -1/2 (* x y)))) |
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x))))) |
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x))))) |
(/ 2 x) |
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) |
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y))) |
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) |
(/ 2 x) |
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) |
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x))) |
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x))) |
y |
(+ y (* -1/2 (* x (pow y 2)))) |
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) |
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2))))) |
(/ 2 x) |
(/ (- 2 (* 4 (/ 1 (* x y)))) x) |
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x) |
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x) |
(/ 2 x) |
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x)) |
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x)) |
1 |
(+ 1 (* 1/2 (* x y))) |
(+ 1 (* 1/2 (* x y))) |
(+ 1 (* 1/2 (* x y))) |
(* 1/2 (* x y)) |
(* y (+ (* 1/2 x) (/ 1 y))) |
(* y (+ (* 1/2 x) (/ 1 y))) |
(* y (+ (* 1/2 x) (/ 1 y))) |
(* 1/2 (* x y)) |
(* -1 (* y (- (* -1/2 x) (/ 1 y)))) |
(* -1 (* y (- (* -1/2 x) (/ 1 y)))) |
(* -1 (* y (- (* -1/2 x) (/ 1 y)))) |
1 |
(+ 1 (* 1/2 (* x y))) |
(+ 1 (* 1/2 (* x y))) |
(+ 1 (* 1/2 (* x y))) |
(* 1/2 (* x y)) |
(* x (+ (* 1/2 y) (/ 1 x))) |
(* x (+ (* 1/2 y) (/ 1 x))) |
(* x (+ (* 1/2 y) (/ 1 x))) |
(* 1/2 (* x y)) |
(* -1 (* x (- (* -1/2 y) (/ 1 x)))) |
(* -1 (* x (- (* -1/2 y) (/ 1 x)))) |
(* -1 (* x (- (* -1/2 y) (/ 1 x)))) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 (* x y)) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
| Outputs |
|---|
(* -1 y) |
(neg.f64 y) |
(- (* x (+ 1 (* 1/2 (pow y 2)))) y) |
(fma.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) x) |
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) |
(fma.f64 x (*.f64 (*.f64 y y) (fma.f64 y (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) (-.f64 x y)) |
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) |
(fma.f64 x (fma.f64 (*.f64 y y) (fma.f64 y (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) (fma.f64 (*.f64 x (pow.f64 y #s(literal 4 binary64))) (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))) (neg.f64 y)) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(+.f64 x (/.f64 #s(literal -2 binary64) x)) |
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) |
(+.f64 x (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 4 binary64) (*.f64 y x))) x)) |
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) |
(+.f64 x (/.f64 (+.f64 #s(literal -2 binary64) (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y (*.f64 x x)))))) x)) |
x |
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(/.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y (*.f64 x x)))) (/.f64 #s(literal -4 binary64) (*.f64 y x)))) x) |
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) |
(+.f64 (/.f64 #s(literal -16 binary64) (*.f64 (*.f64 y y) (*.f64 y (*.f64 (*.f64 x (*.f64 x x)) x)))) (/.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y (*.f64 x x)))) (/.f64 #s(literal -4 binary64) (*.f64 y x)))) x)) |
(/ 2 x) |
(/.f64 #s(literal 2 binary64) x) |
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) |
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x) |
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x))) |
(/.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y (*.f64 x x)))) (/.f64 #s(literal -4 binary64) (*.f64 y x)))) x) |
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x))) |
(+.f64 (/.f64 #s(literal -16 binary64) (*.f64 (*.f64 y y) (*.f64 y (*.f64 (*.f64 x (*.f64 x x)) x)))) (/.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y (*.f64 x x)))) (/.f64 #s(literal -4 binary64) (*.f64 y x)))) x)) |
y |
(+ y (* -1/2 (* x (pow y 2)))) |
(fma.f64 y (*.f64 (*.f64 y x) #s(literal -1/2 binary64)) y) |
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) |
(fma.f64 x (*.f64 (*.f64 y y) (fma.f64 y (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) y) |
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2))))) |
(fma.f64 x (fma.f64 x (*.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 x #s(literal -1/8 binary64))) (*.f64 (*.f64 y y) (fma.f64 y (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))) y) |
(/ 2 x) |
(/.f64 #s(literal 2 binary64) x) |
(/ (- 2 (* 4 (/ 1 (* x y)))) x) |
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x) |
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x) |
(/.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y (*.f64 x x)))) (/.f64 #s(literal -4 binary64) (*.f64 y x)))) x) |
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x) |
(/.f64 (+.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y (*.f64 x x)))) (/.f64 #s(literal -4 binary64) (*.f64 y x)))) (/.f64 #s(literal -16 binary64) (*.f64 y (*.f64 x (*.f64 y (*.f64 y (*.f64 x x))))))) x) |
(/ 2 x) |
(/.f64 #s(literal 2 binary64) x) |
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x)) |
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x) |
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x)) |
(/.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y (*.f64 x x)))) (/.f64 #s(literal -4 binary64) (*.f64 y x)))) x) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x)) |
(/.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y y)) (/.f64 #s(literal -16 binary64) (*.f64 y (*.f64 y (*.f64 y x))))) (*.f64 x x)) (/.f64 #s(literal -4 binary64) (*.f64 y x)))) x) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 (* x y))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* 1/2 (* x y))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* 1/2 (* x y))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* y (+ (* 1/2 x) (/ 1 y))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* y (+ (* 1/2 x) (/ 1 y))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* y (+ (* 1/2 x) (/ 1 y))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* -1 (* y (- (* -1/2 x) (/ 1 y)))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* -1 (* y (- (* -1/2 x) (/ 1 y)))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* -1 (* y (- (* -1/2 x) (/ 1 y)))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 (* x y))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* 1/2 (* x y))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* 1/2 (* x y))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* x (+ (* 1/2 y) (/ 1 x))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* x (+ (* 1/2 y) (/ 1 x))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* x (+ (* 1/2 y) (/ 1 x))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* -1 (* x (- (* -1/2 y) (/ 1 x)))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* -1 (* x (- (* -1/2 y) (/ 1 x)))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* -1 (* x (- (* -1/2 y) (/ 1 x)))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 (* x y)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
| 4 650× | lower-*.f32 |
| 4 638× | lower-*.f64 |
| 4 560× | lower-/.f32 |
| 4 556× | lower-/.f64 |
| 3 532× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 40 | 209 |
| 0 | 55 | 207 |
| 1 | 278 | 207 |
| 2 | 1745 | 201 |
| 0 | 8119 | 192 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)))) |
(*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))) |
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x)) |
(/.f64 #s(literal -2 binary64) (*.f64 x x)) |
(*.f64 x x) |
(-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y))) |
#s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y)) |
(fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y) |
(*.f64 y (*.f64 x #s(literal -1/2 binary64))) |
(-.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))))) |
(/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))) |
#s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))) |
(*.f64 y (*.f64 x #s(literal 1/2 binary64))) |
(*.f64 x #s(literal 1/2 binary64)) |
(*.f64 x #s(literal -1/2 binary64)) |
| Outputs |
|---|
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 (*.f64 x y) #s(literal 1/2 binary64) #s(literal -1 binary64))))) |
#s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 (*.f64 x y) #s(literal 1/2 binary64) #s(literal -1 binary64)))) |
(+.f64 (neg.f64 y) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y)) (neg.f64 y)) |
(-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y)) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y))) (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y)) (neg.f64 y))) (/.f64 (*.f64 y y) (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y)) (neg.f64 y)))) |
(fma.f64 x (*.f64 (*.f64 y #s(literal 1/2 binary64)) y) (neg.f64 y)) |
(fma.f64 y (*.f64 x (*.f64 y #s(literal 1/2 binary64))) (neg.f64 y)) |
(fma.f64 y #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y))) |
(fma.f64 (*.f64 x y) (*.f64 y #s(literal 1/2 binary64)) (neg.f64 y)) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y) (neg.f64 y)) |
(fma.f64 (*.f64 x (*.f64 y #s(literal 1/2 binary64))) y (neg.f64 y)) |
(fma.f64 #s(literal -1 binary64) y (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y))) |
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 y y) (neg.f64 y)) |
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) (*.f64 x y) (neg.f64 y)) |
(fma.f64 (*.f64 y y) (*.f64 x #s(literal 1/2 binary64)) (neg.f64 y)) |
(fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)) |
(fma.f64 (*.f64 y (*.f64 y #s(literal 1/2 binary64))) x (neg.f64 y)) |
(/.f64 (fma.f64 (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (*.f64 y (*.f64 y y)) (neg.f64 (*.f64 y (*.f64 y y)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y)) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y)) (-.f64 (*.f64 y y) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y)) (neg.f64 y))))) |
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y)) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y))) (*.f64 y y)) (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y)) (neg.f64 y))) |
(/.f64 (*.f64 y (fma.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) #s(literal -1 binary64))) (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x y) #s(literal -1/2 binary64))))) |
(/.f64 (*.f64 y (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) #s(literal -1 binary64))) (fma.f64 (*.f64 x y) #s(literal 1/2 binary64) #s(literal 1 binary64))) |
(/.f64 (*.f64 (fma.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) #s(literal -1 binary64)) y) (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x y) #s(literal -1/2 binary64))))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) #s(literal -1 binary64)) y) (fma.f64 (*.f64 x y) #s(literal 1/2 binary64) #s(literal 1 binary64))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (*.f64 y (*.f64 y y)) (neg.f64 (*.f64 y (*.f64 y y))))) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y)) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y)) (-.f64 (*.f64 y y) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y)) (neg.f64 y)))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y)) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y))) (*.f64 y y))) (neg.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) y)) (neg.f64 y)))) |
(/.f64 (neg.f64 (*.f64 y (fma.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) #s(literal -1 binary64)))) (neg.f64 (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x y) #s(literal -1/2 binary64)))))) |
(/.f64 (neg.f64 (*.f64 y (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) #s(literal -1 binary64)))) (neg.f64 (fma.f64 (*.f64 x y) #s(literal 1/2 binary64) #s(literal 1 binary64)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) #s(literal -1 binary64)) y)) (neg.f64 (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x y) #s(literal -1/2 binary64)))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) #s(literal -1 binary64)) y)) (neg.f64 (fma.f64 (*.f64 x y) #s(literal 1/2 binary64) #s(literal 1 binary64)))) |
(*.f64 y (fma.f64 (*.f64 x y) #s(literal 1/2 binary64) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (*.f64 x y) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) |
(+.f64 (*.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) |
(+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) |
(-.f64 (*.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal 1 binary64)) |
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) (fma.f64 (*.f64 x y) #s(literal 1/2 binary64) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal 1/2 binary64) #s(literal 1 binary64)))) |
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (*.f64 x (*.f64 y #s(literal 1/2 binary64))))) (/.f64 (*.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) (-.f64 #s(literal -1 binary64) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))) |
(-.f64 (/.f64 (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (fma.f64 (*.f64 x y) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64) (fma.f64 (*.f64 x y) #s(literal 1/2 binary64) #s(literal 1 binary64))))) |
(expm1.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y))) #s(literal -1 binary64))) |
(fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
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(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64))))))) (*.f64 (+.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))) (/.f64 (*.f64 y y) (*.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))))) (*.f64 (+.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))) (+.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) (*.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))))))) (neg.f64 (neg.f64 (fma.f64 (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64))))) (+.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))) (*.f64 x x))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 y y) (*.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64))))))))) (neg.f64 (neg.f64 (+.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64))))))))) |
(pow.f64 (/.f64 (fma.f64 (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64))))) (+.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))) (*.f64 x x)) (-.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) (*.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64))))))))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (+.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))) (-.f64 (*.f64 x x) (/.f64 (*.f64 y y) (*.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))))) #s(literal -1 binary64)) |
(*.f64 (-.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 y (*.f64 y y)) (*.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) (*.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))))) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64))))) (+.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))) (*.f64 x x)))) |
(*.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 y y) (*.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) y)) #s(literal -1 binary64))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))) (/.f64 (neg.f64 y) #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))) |
(neg.f64 (/.f64 (neg.f64 y) #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))) |
(/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) y)) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) y) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) y)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) y))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) y) #s(literal 1 binary64)))) |
(/.f64 (neg.f64 y) (neg.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))) |
(/.f64 (*.f64 y #s(literal 1 binary64)) #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64))))) |
(/.f64 (neg.f64 (neg.f64 y)) (neg.f64 (neg.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64))))))) |
(/.f64 (neg.f64 (*.f64 y #s(literal 1 binary64))) (neg.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))) |
(/.f64 (neg.f64 (neg.f64 (neg.f64 y))) (neg.f64 (neg.f64 (neg.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))))) |
(pow.f64 (/.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) y) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) y) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(*.f64 y (/.f64 #s(literal 1 binary64) #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))) |
(*.f64 #s(literal 1 binary64) (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))))) |
(*.f64 (neg.f64 y) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64))))))) |
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64))))) y) |
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1 binary64))) |
#s(approx (+ (* (* y 1/2) x) 1) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y))) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 x y) #s(literal -2 binary64))) |
(neg.f64 (/.f64 (*.f64 x y) #s(literal -2 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x y))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y))))) |
(/.f64 (*.f64 x y) #s(literal 2 binary64)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal 1 binary64)))) |
(/.f64 (neg.f64 (*.f64 x y)) #s(literal -2 binary64)) |
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 x y)) #s(literal 2 binary64)) |
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x y))) #s(literal -2 binary64)) |
(/.f64 (*.f64 (*.f64 x y) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(/.f64 (*.f64 (neg.f64 (*.f64 x y)) #s(literal 1 binary64)) #s(literal -2 binary64)) |
(/.f64 (neg.f64 (neg.f64 (*.f64 x y))) #s(literal 2 binary64)) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (*.f64 x y))) #s(literal -2 binary64)) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x y)))) #s(literal 2 binary64)) |
(/.f64 (neg.f64 (*.f64 (*.f64 x y) #s(literal 1 binary64))) #s(literal -2 binary64)) |
(/.f64 (neg.f64 (*.f64 (neg.f64 (*.f64 x y)) #s(literal 1 binary64))) #s(literal 2 binary64)) |
(/.f64 (neg.f64 (neg.f64 (neg.f64 (*.f64 x y)))) #s(literal -2 binary64)) |
(pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(*.f64 x (*.f64 y #s(literal 1/2 binary64))) |
(*.f64 x (*.f64 (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 y (*.f64 x #s(literal 1/2 binary64))) |
(*.f64 y (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 y (/.f64 x #s(literal 2 binary64))) |
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 y #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 x y) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x y) #s(literal 1 binary64))) |
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y)) #s(literal -1 binary64))) |
(*.f64 (*.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal 1 binary64)) |
(*.f64 (*.f64 x #s(literal 1/2 binary64)) y) |
(*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 y #s(literal 1 binary64))) |
(*.f64 (*.f64 y #s(literal 1/2 binary64)) x) |
(*.f64 (*.f64 y #s(literal 1/2 binary64)) (*.f64 x #s(literal 1 binary64))) |
(*.f64 (neg.f64 (*.f64 x y)) #s(literal -1/2 binary64)) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 x y)) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 y #s(literal 1/2 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) y) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 y #s(literal 1/2 binary64))) x) |
(*.f64 x #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
(*.f64 x #s(literal -1/2 binary64)) |
(*.f64 #s(literal -1/2 binary64) x) |
Compiled 12 263 to 1 033 computations (91.6% saved)
9 alts after pruning (2 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 684 | 2 | 686 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 3 | 4 |
| Done | 0 | 4 | 4 |
| Total | 685 | 9 | 694 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.9% | (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) |
| ✓ | 63.3% | (-.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))))) |
| ✓ | 63.4% | (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) |
| ✓ | 60.2% | #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x)) |
| ▶ | 13.8% | #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) |
| ✓ | 74.7% | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) |
| ✓ | 28.0% | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) |
| ▶ | 29.0% | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)))) |
| ✓ | 29.0% | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
Compiled 86 to 50 computations (41.9% saved)
| 1× | egg-herbie |
Found 7 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (/.f64 #s(literal -2 binary64) x) | |
| cost-diff | 0 | #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) | |
| cost-diff | 0 | #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) | |
| cost-diff | 0 | (*.f64 y (*.f64 x y)) | |
| cost-diff | 0 | #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y))) | |
| cost-diff | 0 | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)))) | |
| cost-diff | 128 | (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)) |
| 5 824× | lower-fma.f32 |
| 5 822× | lower-fma.f64 |
| 2 824× | lower-*.f32 |
| 2 820× | lower-*.f64 |
| 2 638× | lower--.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 34 | 119 |
| 0 | 41 | 119 |
| 1 | 80 | 119 |
| 2 | 140 | 111 |
| 3 | 240 | 111 |
| 4 | 457 | 111 |
| 5 | 912 | 111 |
| 6 | 1690 | 111 |
| 7 | 2744 | 111 |
| 8 | 5938 | 111 |
| 0 | 8150 | 102 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)))) |
#s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y))) |
(fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)) |
(*.f64 y (*.f64 x y)) |
y |
(*.f64 x y) |
x |
#s(literal 1/2 binary64) |
(neg.f64 y) |
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) |
#s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) |
(/.f64 #s(literal -2 binary64) x) |
#s(literal -2 binary64) |
x |
| Outputs |
|---|
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)))) |
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64))))) |
#s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y))) |
#s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)))) |
(fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)) |
(*.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64))) |
(*.f64 y (*.f64 x y)) |
y |
(*.f64 x y) |
x |
#s(literal 1/2 binary64) |
(neg.f64 y) |
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) |
#s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) |
(/.f64 #s(literal -2 binary64) x) |
#s(literal -2 binary64) |
x |
Found 7 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (/.f64 #s(literal -2 binary64) x) | |
| accuracy | 23.44864922201512 | #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) | |
| accuracy | 32.033027077017344 | #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) | |
| accuracy | 0 | (neg.f64 y) | |
| accuracy | 0.140625 | (*.f64 y (*.f64 x y)) | |
| accuracy | 22.987462061139045 | #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y))) | |
| accuracy | 23.029317657867953 | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)))) |
| 92.0ms | 256× | 0 | valid |
Compiled 72 to 32 computations (55.6% saved)
ival-div: 48.0ms (59.3% of total)ival-mult: 18.0ms (22.2% of total)ival-add: 10.0ms (12.4% of total)ival-sub: 2.0ms (2.5% of total)exact: 1.0ms (1.2% of total)ival-neg: 1.0ms (1.2% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)) (patch (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)) #<representation binary64>) () ()) |
#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y))) (patch #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y))) #<representation binary64>) () ()) |
#s(alt (*.f64 y (*.f64 x y)) (patch (*.f64 y (*.f64 x y)) #<representation binary64>) () ()) |
#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ()) |
#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* -1 y) (taylor 0 y) (#s(alt (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)) (patch (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)) #<representation binary64>) () ())) ()) |
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#s(alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) (taylor inf y) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (- x (* 2 (/ 1 x))) (taylor -inf y) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) (taylor -inf y) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) (taylor -inf y) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) (taylor -inf y) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (/ -2 x) (taylor 0 x) (#s(alt #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (pow x 2) 2) x) (taylor 0 x) (#s(alt #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (pow x 2) 2) x) (taylor 0 x) (#s(alt #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (pow x 2) 2) x) (taylor 0 x) (#s(alt #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1 (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1 (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1 (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (/ -2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (/ -2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (/ -2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (/ -2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (/ -2 x) (taylor inf x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (/ -2 x) (taylor inf x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (/ -2 x) (taylor inf x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (/ -2 x) (taylor inf x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (/ -2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (/ -2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (/ -2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (/ -2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor inf y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor inf y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor inf y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor inf y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor -inf y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor -inf y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor -inf y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 y) (taylor -inf y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ()) |
39 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | 0 | (* y (* x y)) |
| 0.0ms | y | @ | 0 | (* y (* x y)) |
| 0.0ms | x | @ | -inf | (* y (* x y)) |
| 0.0ms | x | @ | 0 | (/ -2 x) |
| 0.0ms | y | @ | 0 | (+ (* (* y (* x y)) 1/2) (neg y)) |
| 1× | egg-herbie |
| 20 400× | lower-fma.f64 |
| 20 400× | lower-fma.f32 |
| 4 062× | lower-*.f64 |
| 4 062× | lower-*.f32 |
| 3 590× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 167 | 1410 |
| 1 | 498 | 1403 |
| 2 | 1383 | 1379 |
| 3 | 4128 | 1363 |
| 0 | 8250 | 1271 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* -1 y) |
(* y (- (* 1/2 (* x y)) 1)) |
(* y (- (* 1/2 (* x y)) 1)) |
(* y (- (* 1/2 (* x y)) 1)) |
(* 1/2 (* x (pow y 2))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* 1/2 (* x (pow y 2))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* -1 y) |
(- (* 1/2 (* x (pow y 2))) y) |
(- (* 1/2 (* x (pow y 2))) y) |
(- (* 1/2 (* x (pow y 2))) y) |
(* 1/2 (* x (pow y 2))) |
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))) |
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))) |
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))) |
(* 1/2 (* x (pow y 2))) |
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x)))) |
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x)))) |
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x)))) |
(* -1 y) |
(- (* x (+ 1 (* 1/2 (pow y 2)))) y) |
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) |
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) |
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) |
x |
(+ x (* -1 y)) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) |
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
x |
(+ x (* -1 y)) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(* 1/2 (* x (pow y 2))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y))) |
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y))) |
(* 1/2 (* x (pow y 2))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x))) |
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x))) |
(* -1 y) |
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2))))) |
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2))))) |
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2))))) |
(* x (+ 1 (* 1/2 (pow y 2)))) |
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) |
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) |
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) |
(* -1 (* x (- (* -1/2 (pow y 2)) 1))) |
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) |
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) |
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* x (pow y 2)) |
(* -1 y) |
(- (* x (+ 1 (* 1/2 (pow y 2)))) y) |
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) |
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) |
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) |
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) |
x |
(+ x (* -1 y)) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) |
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) |
(- x (* 2 (/ 1 x))) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(/ -2 x) |
(/ (- (pow x 2) 2) x) |
(/ (- (pow x 2) 2) x) |
(/ (- (pow x 2) 2) x) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(/ -2 x) |
(/ -2 x) |
(/ -2 x) |
(/ -2 x) |
(/ -2 x) |
(/ -2 x) |
(/ -2 x) |
(/ -2 x) |
(/ -2 x) |
(/ -2 x) |
(/ -2 x) |
(/ -2 x) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
(* -1 y) |
| Outputs |
|---|
(* -1 y) |
(neg.f64 y) |
(* y (- (* 1/2 (* x y)) 1)) |
(*.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) |
(* y (- (* 1/2 (* x y)) 1)) |
(*.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) |
(* y (- (* 1/2 (* x y)) 1)) |
(*.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) |
(* 1/2 (* x (pow y 2))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y (*.f64 y x))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(*.f64 (*.f64 y y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal -1 binary64) y))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(*.f64 (*.f64 y y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal -1 binary64) y))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(*.f64 (*.f64 y y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal -1 binary64) y))) |
(* 1/2 (* x (pow y 2))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y (*.f64 y x))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(*.f64 (*.f64 y y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal -1 binary64) y))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(*.f64 (*.f64 y y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal -1 binary64) y))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(*.f64 (*.f64 y y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal -1 binary64) y))) |
(* -1 y) |
(neg.f64 y) |
(- (* 1/2 (* x (pow y 2))) y) |
(*.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) |
(- (* 1/2 (* x (pow y 2))) y) |
(*.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) |
(- (* 1/2 (* x (pow y 2))) y) |
(*.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) |
(* 1/2 (* x (pow y 2))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y (*.f64 y x))) |
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))) |
(*.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) |
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))) |
(*.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) |
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))) |
(*.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) |
(* 1/2 (* x (pow y 2))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y (*.f64 y x))) |
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x)))) |
(*.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) |
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x)))) |
(*.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) |
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x)))) |
(*.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) |
(* -1 y) |
(neg.f64 y) |
(- (* x (+ 1 (* 1/2 (pow y 2)))) y) |
(fma.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) x) |
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) |
(fma.f64 y (fma.f64 y (*.f64 x (fma.f64 y (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64)) x) |
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) |
(-.f64 (fma.f64 x (fma.f64 y (*.f64 y (fma.f64 y (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) (*.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))) x) y) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal -2 binary64))) x) |
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) |
(+.f64 x (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 y (*.f64 y x)))) (*.f64 x x)))) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) |
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal -2 binary64))) x) |
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) |
(+.f64 x (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 y (*.f64 y x)))) (*.f64 x x)))) |
x |
(+ x (* -1 y)) |
(-.f64 x y) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(fma.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) x) |
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) |
(fma.f64 y (fma.f64 y (*.f64 x (fma.f64 y (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64)) x) |
(- x (* 2 (/ 1 x))) |
(+.f64 x (/.f64 #s(literal -2 binary64) x)) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(+.f64 (+.f64 x (/.f64 #s(literal -2 binary64) x)) (/.f64 #s(literal 4 binary64) (*.f64 y (*.f64 x x)))) |
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) |
(-.f64 (+.f64 x (/.f64 #s(literal -2 binary64) x)) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y x))) (/.f64 #s(literal -4 binary64) y)) (*.f64 x x))) |
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) |
(+.f64 x (+.f64 (/.f64 #s(literal 16 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 x (*.f64 x x)) x))) (-.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y x))) (/.f64 #s(literal -4 binary64) y)) (*.f64 x x))))) |
(- x (* 2 (/ 1 x))) |
(+.f64 x (/.f64 #s(literal -2 binary64) x)) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(+.f64 (+.f64 x (/.f64 #s(literal -2 binary64) x)) (/.f64 #s(literal 4 binary64) (*.f64 y (*.f64 x x)))) |
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(-.f64 (+.f64 x (/.f64 #s(literal -2 binary64) x)) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y x))) (/.f64 #s(literal -4 binary64) y)) (*.f64 x x))) |
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(+.f64 x (+.f64 (/.f64 #s(literal 16 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 x (*.f64 x x)) x))) (-.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y x))) (/.f64 #s(literal -4 binary64) y)) (*.f64 x x))))) |
x |
(+ x (* -1 y)) |
(-.f64 x y) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(fma.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) x) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(fma.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) x) |
(* 1/2 (* x (pow y 2))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y (*.f64 y x))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(*.f64 (*.f64 y y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal -1 binary64) y))) |
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y))) |
(*.f64 (*.f64 y y) (fma.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) (/.f64 #s(literal -1 binary64) y))) |
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y))) |
(*.f64 (*.f64 y y) (fma.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) (/.f64 #s(literal -1 binary64) y))) |
(* 1/2 (* x (pow y 2))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y (*.f64 y x))) |
(* (pow y 2) (- (* 1/2 x) (/ 1 y))) |
(*.f64 (*.f64 y y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal -1 binary64) y))) |
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x))) |
(*.f64 (*.f64 y y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 x y)) y))) |
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x))) |
(*.f64 (*.f64 y y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 x y)) y))) |
(* -1 y) |
(neg.f64 y) |
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2))))) |
(fma.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) x) |
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2))))) |
(fma.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) x) |
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2))))) |
(fma.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) x) |
(* x (+ 1 (* 1/2 (pow y 2)))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 y (*.f64 y x)) x) |
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) |
(fma.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) x) |
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) |
(fma.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) x) |
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) |
(fma.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) x) |
(* -1 (* x (- (* -1/2 (pow y 2)) 1))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 y (*.f64 y x)) x) |
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) |
(fma.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) x) |
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) |
(fma.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) x) |
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) |
(fma.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) x) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* x (pow y 2)) |
(*.f64 y (*.f64 y x)) |
(* -1 y) |
(neg.f64 y) |
(- (* x (+ 1 (* 1/2 (pow y 2)))) y) |
(fma.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) x) |
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) |
(fma.f64 y (fma.f64 y (*.f64 x (fma.f64 y (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64)) x) |
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) |
(-.f64 (fma.f64 x (fma.f64 y (*.f64 y (fma.f64 y (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) (*.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))) x) y) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal -2 binary64))) x) |
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) |
(+.f64 x (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 y (*.f64 y x)))) (*.f64 x x)))) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) |
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal -2 binary64))) x) |
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) |
(+.f64 x (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 y (*.f64 y x)))) (*.f64 x x)))) |
x |
(+ x (* -1 y)) |
(-.f64 x y) |
(+ x (* y (- (* 1/2 (* x y)) 1))) |
(fma.f64 y (fma.f64 y (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) x) |
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) |
(fma.f64 y (fma.f64 y (*.f64 x (fma.f64 y (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64)) x) |
(- x (* 2 (/ 1 x))) |
(+.f64 x (/.f64 #s(literal -2 binary64) x)) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(+.f64 (+.f64 x (/.f64 #s(literal -2 binary64) x)) (/.f64 #s(literal 4 binary64) (*.f64 y (*.f64 x x)))) |
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) |
(-.f64 (+.f64 x (/.f64 #s(literal -2 binary64) x)) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y x))) (/.f64 #s(literal -4 binary64) y)) (*.f64 x x))) |
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) |
(+.f64 x (+.f64 (/.f64 #s(literal 16 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 x (*.f64 x x)) x))) (-.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y x))) (/.f64 #s(literal -4 binary64) y)) (*.f64 x x))))) |
(- x (* 2 (/ 1 x))) |
(+.f64 x (/.f64 #s(literal -2 binary64) x)) |
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) |
(+.f64 (+.f64 x (/.f64 #s(literal -2 binary64) x)) (/.f64 #s(literal 4 binary64) (*.f64 y (*.f64 x x)))) |
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(-.f64 (+.f64 x (/.f64 #s(literal -2 binary64) x)) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y x))) (/.f64 #s(literal -4 binary64) y)) (*.f64 x x))) |
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) |
(+.f64 x (+.f64 (/.f64 #s(literal 16 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 x (*.f64 x x)) x))) (-.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y x))) (/.f64 #s(literal -4 binary64) y)) (*.f64 x x))))) |
(/ -2 x) |
(/.f64 #s(literal -2 binary64) x) |
(/ (- (pow x 2) 2) x) |
(+.f64 x (/.f64 #s(literal -2 binary64) x)) |
(/ (- (pow x 2) 2) x) |
(+.f64 x (/.f64 #s(literal -2 binary64) x)) |
(/ (- (pow x 2) 2) x) |
(+.f64 x (/.f64 #s(literal -2 binary64) x)) |
x |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
(* x (- 1 (* 2 (/ 1 (pow x 2))))) |
(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
x |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) |
(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
(/ -2 x) |
(/.f64 #s(literal -2 binary64) x) |
(/ -2 x) |
(/.f64 #s(literal -2 binary64) x) |
(/ -2 x) |
(/.f64 #s(literal -2 binary64) x) |
(/ -2 x) |
(/.f64 #s(literal -2 binary64) x) |
(/ -2 x) |
(/.f64 #s(literal -2 binary64) x) |
(/ -2 x) |
(/.f64 #s(literal -2 binary64) x) |
(/ -2 x) |
(/.f64 #s(literal -2 binary64) x) |
(/ -2 x) |
(/.f64 #s(literal -2 binary64) x) |
(/ -2 x) |
(/.f64 #s(literal -2 binary64) x) |
(/ -2 x) |
(/.f64 #s(literal -2 binary64) x) |
(/ -2 x) |
(/.f64 #s(literal -2 binary64) x) |
(/ -2 x) |
(/.f64 #s(literal -2 binary64) x) |
(* -1 y) |
(neg.f64 y) |
(* -1 y) |
(neg.f64 y) |
(* -1 y) |
(neg.f64 y) |
(* -1 y) |
(neg.f64 y) |
(* -1 y) |
(neg.f64 y) |
(* -1 y) |
(neg.f64 y) |
(* -1 y) |
(neg.f64 y) |
(* -1 y) |
(neg.f64 y) |
(* -1 y) |
(neg.f64 y) |
(* -1 y) |
(neg.f64 y) |
(* -1 y) |
(neg.f64 y) |
(* -1 y) |
(neg.f64 y) |
| 5 456× | lower-fma.f32 |
| 5 454× | lower-fma.f64 |
| 4 986× | lower-*.f32 |
| 4 982× | lower-*.f64 |
| 4 634× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 34 | 111 |
| 0 | 41 | 111 |
| 1 | 207 | 111 |
| 2 | 1733 | 103 |
| 0 | 8641 | 94 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)))) |
#s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y))) |
(*.f64 y (*.f64 x y)) |
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) |
#s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) |
(/.f64 #s(literal -2 binary64) x) |
(neg.f64 y) |
| Outputs |
|---|
(+.f64 (neg.f64 y) (*.f64 x (*.f64 (*.f64 y #s(literal 1/2 binary64)) y))) |
(+.f64 (*.f64 x (*.f64 (*.f64 y #s(literal 1/2 binary64)) y)) (neg.f64 y)) |
(-.f64 (*.f64 x (*.f64 (*.f64 y #s(literal 1/2 binary64)) y)) y) |
(-.f64 #s(literal 0 binary64) (-.f64 y (*.f64 x (*.f64 (*.f64 y #s(literal 1/2 binary64)) y)))) |
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64)) (*.f64 y y)) (-.f64 (*.f64 x (*.f64 (*.f64 y #s(literal 1/2 binary64)) y)) (neg.f64 y))) (/.f64 (*.f64 y y) (-.f64 (*.f64 x (*.f64 (*.f64 y #s(literal 1/2 binary64)) y)) (neg.f64 y)))) |
(-.f64 (fma.f64 x (*.f64 (*.f64 y #s(literal 1/2 binary64)) y) #s(literal 0 binary64)) y) |
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(pow.f64 (/.f64 (-.f64 (*.f64 x (*.f64 (*.f64 y #s(literal 1/2 binary64)) y)) (neg.f64 y)) (fma.f64 (*.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64)) (*.f64 y y) (*.f64 y (neg.f64 y)))) #s(literal -1 binary64)) |
(*.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) y) |
(*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 y (*.f64 y y))) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) (neg.f64 (*.f64 y (*.f64 y y)))) (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 y) (-.f64 (neg.f64 y) (*.f64 x (*.f64 (*.f64 y #s(literal 1/2 binary64)) y))) (*.f64 (*.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64)) (*.f64 y y))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64)) (*.f64 y y) (*.f64 y (neg.f64 y))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 (*.f64 y #s(literal 1/2 binary64)) y)) (neg.f64 y)))) |
(*.f64 (/.f64 y (fma.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64) #s(literal -1 binary64))) (/.f64 (fma.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
(*.f64 (/.f64 y (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 (fma.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))))) |
(*.f64 (/.f64 y (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 (fma.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y (*.f64 x #s(literal 1/2 binary64))) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))) |
(*.f64 (/.f64 y (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64)))) (/.f64 (fma.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 y x)))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 y (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 y (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y (*.f64 x #s(literal 1/2 binary64))) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64) #s(literal -1 binary64))) (/.f64 y (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 y x) (*.f64 y x)) #s(literal 1/4 binary64)))) (/.f64 y (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 y x)))))) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)))) |
(*.f64 y (*.f64 y x)) |
(*.f64 x (*.f64 y y)) |
(*.f64 (*.f64 y x) y) |
(*.f64 (*.f64 y y) x) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) |
#s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)) |
(exp.f64 (*.f64 (log.f64 (*.f64 x #s(literal -1/2 binary64))) #s(literal -1 binary64))) |
(neg.f64 (/.f64 #s(literal 2 binary64) x)) |
(/.f64 x (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 x #s(literal -2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 x #s(literal -1/2 binary64))))) |
(/.f64 #s(literal 2 binary64) (neg.f64 x)) |
(/.f64 #s(literal 2 binary64) (neg.f64 (neg.f64 (neg.f64 x)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 x #s(literal -1/2 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x #s(literal -2 binary64))))) |
(/.f64 #s(literal -2 binary64) x) |
(/.f64 #s(literal -2 binary64) (neg.f64 (neg.f64 x))) |
(/.f64 (neg.f64 x) (neg.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) |
(/.f64 (*.f64 x (/.f64 #s(literal -2 binary64) x)) x) |
(/.f64 (*.f64 x #s(literal -2 binary64)) (*.f64 x x)) |
(/.f64 (neg.f64 (*.f64 x #s(literal -2 binary64))) (*.f64 x (neg.f64 x))) |
(/.f64 (neg.f64 (*.f64 x (/.f64 #s(literal -2 binary64) x))) (neg.f64 x)) |
(/.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) |
(/.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) |
(/.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x (neg.f64 x))) |
(/.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 x (neg.f64 x))) |
(/.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) x) x) |
(/.f64 (neg.f64 (neg.f64 (*.f64 x #s(literal -2 binary64)))) (neg.f64 (*.f64 x (neg.f64 x)))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) x)) (neg.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) |
(/.f64 (neg.f64 (*.f64 x #s(literal 1 binary64))) (neg.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) |
(/.f64 (neg.f64 (*.f64 x #s(literal 2 binary64))) (neg.f64 (*.f64 x (neg.f64 x)))) |
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) (neg.f64 (*.f64 x (neg.f64 x)))) |
(/.f64 (neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) x)) (neg.f64 x)) |
(pow.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (*.f64 x x) (*.f64 x #s(literal -2 binary64))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(*.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) |
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 x))) |
(*.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 #s(literal -2 binary64) (/.f64 x (*.f64 x x))) |
(*.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x) |
(*.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 x x)) |
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 x #s(literal -1/2 binary64))) |
(*.f64 (*.f64 x #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x))) |
(*.f64 (/.f64 x x) (/.f64 #s(literal -2 binary64) x)) |
(*.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 x (neg.f64 x))) |
(*.f64 (/.f64 x (*.f64 x x)) #s(literal -2 binary64)) |
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 2 binary64) (*.f64 x x))) |
(*.f64 (/.f64 x (neg.f64 x)) (/.f64 #s(literal 2 binary64) x)) |
(+.f64 #s(literal 0 binary64) (neg.f64 y)) |
(-.f64 #s(literal 0 binary64) y) |
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 #s(literal 0 binary64) y)))) (/.f64 (*.f64 y (*.f64 y y)) (+.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 #s(literal 0 binary64) y))))) |
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) y)) (/.f64 (*.f64 y y) (+.f64 #s(literal 0 binary64) y))) |
(neg.f64 y) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 y (*.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 #s(literal 0 binary64) y)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 y y)) (+.f64 #s(literal 0 binary64) y)) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 y (*.f64 y y)))) (neg.f64 (+.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 #s(literal 0 binary64) y))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 y y))) (neg.f64 (+.f64 #s(literal 0 binary64) y))) |
(/.f64 (+.f64 #s(literal 0 binary64) (neg.f64 (*.f64 y (*.f64 y y)))) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 y y) (*.f64 #s(literal 0 binary64) (neg.f64 y))))) |
(*.f64 y #s(literal -1 binary64)) |
(*.f64 #s(literal -1 binary64) y) |
Compiled 5 363 to 475 computations (91.1% saved)
9 alts after pruning (1 fresh and 8 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 301 | 1 | 302 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 2 | 2 |
| Done | 1 | 6 | 7 |
| Total | 302 | 9 | 311 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.9% | (-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) |
| ✓ | 63.3% | (-.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))))) |
| ✓ | 63.4% | (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) |
| 11.2% | #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 (*.f64 x #s(literal -2 binary64)) (*.f64 x x)))) | |
| ✓ | 13.8% | #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) |
| ✓ | 74.7% | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) |
| ✓ | 28.0% | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) |
| ✓ | 29.0% | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)))) |
| ✓ | 29.0% | #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
Compiled 216 to 94 computations (56.5% saved)
| Inputs |
|---|
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) |
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) |
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x)) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)))) |
(-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y))) |
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 (*.f64 x #s(literal -2 binary64)) (*.f64 x x)))) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x)) |
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x)) |
(-.f64 x (/.f64 y #s(approx (+ 1 (/ (* x y) 2)) (*.f64 #s(literal 1/2 binary64) (*.f64 x y))))) |
(-.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))))) |
(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) |
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
| Outputs |
|---|
(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) |
3 calls:
| 5.0ms | (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
| 5.0ms | x |
| 5.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | x |
| 99.9% | 1 | y |
| 99.9% | 1 | (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
Compiled 19 to 13 computations (31.6% saved)
| Inputs |
|---|
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) |
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) |
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (*.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x)) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* y (+ (* 1/2 (* x y)) -1)) x) (fma.f64 (*.f64 y (*.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y)))) |
(-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (fma.f64 y (*.f64 y (*.f64 x #s(literal -1/2 binary64))) y))) |
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 (*.f64 x #s(literal -2 binary64)) (*.f64 x x)))) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x)) |
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x)) |
(-.f64 x (/.f64 y #s(approx (+ 1 (/ (* x y) 2)) (*.f64 #s(literal 1/2 binary64) (*.f64 x y))))) |
(-.f64 x (/.f64 y #s(approx (+ (* (* y 1/2) x) 1) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))))) |
| Outputs |
|---|
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) |
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) |
3 calls:
| 11.0ms | y |
| 4.0ms | x |
| 4.0ms | (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 87.7% | 3 | x |
| 91.4% | 3 | y |
| 87.3% | 3 | (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
Compiled 19 to 13 computations (31.6% saved)
| Inputs |
|---|
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) |
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) |
| Outputs |
|---|
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) |
3 calls:
| 2.0ms | (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
| 2.0ms | x |
| 2.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 74.7% | 1 | (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
| 74.7% | 1 | x |
| 78.7% | 2 | y |
Compiled 19 to 13 computations (31.6% saved)
| Inputs |
|---|
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) |
| Outputs |
|---|
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) |
3 calls:
| 3.0ms | x |
| 2.0ms | (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
| 2.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 74.7% | 1 | x |
| 74.7% | 1 | (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
| 74.7% | 1 | y |
Compiled 19 to 13 computations (31.6% saved)
Total -0.0b remaining (-0%)
Threshold costs -0b (-0%)
| Inputs |
|---|
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) |
| Outputs |
|---|
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) |
3 calls:
| 1.0ms | (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
| 1.0ms | y |
| 1.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 28.0% | 1 | y |
| 28.0% | 1 | x |
| 28.0% | 1 | (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) |
Compiled 19 to 13 computations (31.6% saved)
| 2× | binary-search |
| 1× | narrow-enough |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 11.0ms | 1.3275538409007365e+192 | 8.565052948598522e+192 |
| 12.0ms | -6.169041083422649e+78 | -6.7212827242804386e+75 |
| 12.0ms | 224× | 0 | valid |
Compiled 240 to 154 computations (35.8% saved)
ival-div: 3.0ms (41.9% of total)ival-mult: 2.0ms (27.9% of total)ival-sub: 1.0ms (14% of total)ival-add: 1.0ms (14% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 4.0ms | -8.355387397921626e+181 | -5.980612559404355e+181 |
| 2.0ms | 48× | 0 | valid |
Compiled 61 to 41 computations (32.8% saved)
ival-div: 1.0ms (68.3% of total)ival-sub: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)ival-add: 0.0ms (0% of total)ival-mult: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
| 14× | +-commutative_binary64 |
| 14× | sub-neg_binary64 |
| 10× | *-commutative_binary64 |
| 8× | neg-sub0_binary64 |
| 8× | neg-mul-1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 43 | 136 |
| 1 | 55 | 136 |
| 2 | 67 | 136 |
| 3 | 74 | 136 |
| 4 | 78 | 136 |
| 5 | 79 | 136 |
| 1× | saturated |
| Inputs |
|---|
(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) |
(if (<=.f64 y #s(literal -199999999999999996556522545109171713495495289428031795107950240435622308216832 binary64)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) (if (<=.f64 y #s(literal 3499999999999999826570166845091089407057842178783636107891949147496176232221280247531818879523068212802478058076054760381690939451384316420862848740947671803354662565317048152384621575449608192 binary64)) #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))))) |
(if (<=.f64 y #s(literal -66000000000000003374536672680185354940164741671665330739438321134502408753840037507071033534967293155400001427157047916395198166925634625035834458274419003965028095124185986499608576 binary64)) #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) |
| Outputs |
|---|
(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) |
(if (<=.f64 y #s(literal -199999999999999996556522545109171713495495289428031795107950240435622308216832 binary64)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) (if (<=.f64 y #s(literal 3499999999999999826570166845091089407057842178783636107891949147496176232221280247531818879523068212802478058076054760381690939451384316420862848740947671803354662565317048152384621575449608192 binary64)) #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))))) |
(if (<=.f64 y #s(literal -66000000000000003374536672680185354940164741671665330739438321134502408753840037507071033534967293155400001427157047916395198166925634625035834458274419003965028095124185986499608576 binary64)) #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) |
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) |
| 13 558× | lower-fma.f64 |
| 13 558× | lower-fma.f32 |
| 12 856× | lower-fma.f64 |
| 12 856× | lower-fma.f32 |
| 10 996× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 35 |
| 0 | 14 | 35 |
| 1 | 63 | 35 |
| 2 | 500 | 35 |
| 3 | 6873 | 35 |
| 0 | 8527 | 32 |
| 0 | 278 | 3213 |
| 1 | 875 | 3109 |
| 2 | 2370 | 3007 |
| 3 | 7087 | 2993 |
| 0 | 8319 | 2814 |
| 0 | 279 | 3677 |
| 1 | 887 | 3612 |
| 2 | 2407 | 3282 |
| 3 | 7254 | 3186 |
| 0 | 8263 | 3014 |
| 0 | 231 | 1053 |
| 1 | 738 | 1018 |
| 2 | 1942 | 987 |
| 3 | 6081 | 981 |
| 0 | 8428 | 934 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 140 to 77 computations (45% saved)
Compiled 138 to 66 computations (52.2% saved)
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