
Time bar (total: 7.7s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 0 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 1 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 2 |
| 75% | 74.9% | 25% | 0.1% | 0% | 0% | 0% | 3 |
| 87.5% | 87.4% | 12.5% | 0.1% | 0% | 0% | 0% | 4 |
| 93.8% | 93.7% | 6.2% | 0.1% | 0% | 0% | 0% | 5 |
| 96.9% | 96.8% | 3.1% | 0.1% | 0% | 0% | 0% | 6 |
| 98.4% | 98.3% | 1.6% | 0.1% | 0% | 0% | 0% | 7 |
| 99.2% | 99.1% | 0.8% | 0.1% | 0% | 0% | 0% | 8 |
| 99.6% | 99.5% | 0.4% | 0.1% | 0% | 0% | 0% | 9 |
| 99.8% | 99.7% | 0.2% | 0.1% | 0% | 0% | 0% | 10 |
| 99.9% | 99.8% | 0.1% | 0.1% | 0% | 0% | 0% | 11 |
| 100% | 99.9% | 0% | 0.1% | 0% | 0% | 0% | 12 |
Compiled 21 to 11 computations (47.6% saved)
| 690.0ms | 8 256× | 0 | valid |
ival-mult: 221.0ms (57% of total)ival-div: 58.0ms (14.9% of total)ival-sub: 57.0ms (14.7% of total)ival-add: 37.0ms (9.5% of total)ival-true: 6.0ms (1.5% of total)exact: 5.0ms (1.3% of total)ival-assert: 3.0ms (0.8% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 132 | 0 | - | 0 | - | (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
| 10 | 0 | - | 0 | - | (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) |
| 0 | 0 | - | 0 | - | (*.f64 (*.f64 y #s(literal 4 binary64)) y) |
| 0 | 0 | - | 0 | - | (*.f64 y #s(literal 4 binary64)) |
| 0 | 0 | - | 0 | - | #s(literal 4 binary64) |
| 0 | 0 | - | 0 | - | (*.f64 x x) |
| 0 | 0 | - | 0 | - | (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) |
| 0 | 0 | - | 0 | - | y |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
/.f64 | (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) | o/o | 111 | 0 |
| ↳ | (*.f64 (*.f64 y #s(literal 4 binary64)) y) | overflow | 66 | |
| ↳ | (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) | overflow | 111 | |
| ↳ | (*.f64 y #s(literal 4 binary64)) | overflow | 1 | |
| ↳ | (*.f64 x x) | overflow | 55 | |
| ↳ | (*.f64 (*.f64 y #s(literal 4 binary64)) y) | overflow | 66 | |
| ↳ | (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) | overflow | 111 | |
| ↳ | (*.f64 y #s(literal 4 binary64)) | overflow | 1 | |
| ↳ | (*.f64 x x) | overflow | 55 | |
/.f64 | (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) | u/u | 21 | 0 |
| ↳ | (*.f64 (*.f64 y #s(literal 4 binary64)) y) | underflow | 55 | |
| ↳ | (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) | underflow | 21 | |
| ↳ | (*.f64 x x) | underflow | 67 | |
| ↳ | (*.f64 (*.f64 y #s(literal 4 binary64)) y) | underflow | 55 | |
| ↳ | (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) | underflow | 21 | |
| ↳ | (*.f64 x x) | underflow | 67 | |
-.f64 | (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) | nan-rescue | 10 | 0 |
| ↳ | (*.f64 x x) | overflow | 55 | |
| ↳ | (*.f64 (*.f64 y #s(literal 4 binary64)) y) | overflow | 66 | |
| ↳ | (*.f64 y #s(literal 4 binary64)) | overflow | 1 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 132 | 0 |
| - | 0 | 124 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 132 | 0 | 0 |
| - | 0 | 0 | 124 |
| number | freq |
|---|---|
| 0 | 124 |
| 1 | 122 |
| 2 | 10 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 40.0ms | 512× | 0 | valid |
Compiled 125 to 31 computations (75.2% saved)
ival-mult: 12.0ms (58.5% of total)ival-div: 3.0ms (14.6% of total)ival-sub: 2.0ms (9.8% of total)ival-add: 2.0ms (9.8% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
| 984× | times-frac |
| 880× | lower-fma.f64 |
| 880× | lower-fma.f32 |
| 784× | distribute-lft-in |
| 762× | distribute-rgt-in |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 97 |
| 1 | 89 | 97 |
| 2 | 240 | 95 |
| 3 | 620 | 95 |
| 4 | 1743 | 95 |
| 5 | 2721 | 95 |
| 6 | 2962 | 95 |
| 7 | 2981 | 95 |
| 8 | 2996 | 95 |
| 9 | 3001 | 95 |
| 10 | 3001 | 95 |
| 11 | 3301 | 95 |
| 12 | 3437 | 95 |
| 13 | 3437 | 95 |
| 14 | 3581 | 95 |
| 15 | 4417 | 95 |
| 16 | 4417 | 95 |
| 0 | 9 | 19 |
| 0 | 15 | 19 |
| 1 | 27 | 19 |
| 2 | 56 | 19 |
| 3 | 112 | 19 |
| 4 | 215 | 19 |
| 5 | 344 | 19 |
| 6 | 511 | 19 |
| 7 | 724 | 19 |
| 8 | 1191 | 19 |
| 9 | 2211 | 19 |
| 10 | 2260 | 19 |
| 11 | 2298 | 19 |
| 12 | 2326 | 19 |
| 13 | 2326 | 19 |
| 0 | 2326 | 17 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
| Outputs |
|---|
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
(/.f64 (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) (fma.f64 y (*.f64 y #s(literal 4 binary64)) (*.f64 x x))) |
(abs y)
(abs x)
Compiled 19 to 9 computations (52.6% saved)
Compiled 0 to 2 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 48.4% | (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
Compiled 19 to 9 computations (52.6% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) | |
| cost-diff | 128 | (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) | |
| cost-diff | 128 | (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) |
| 880× | lower-fma.f64 |
| 880× | lower-fma.f32 |
| 738× | times-frac |
| 592× | lower-*.f32 |
| 586× | lower-*.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 51 |
| 0 | 15 | 51 |
| 1 | 27 | 51 |
| 2 | 56 | 51 |
| 3 | 112 | 51 |
| 4 | 215 | 51 |
| 5 | 344 | 51 |
| 6 | 511 | 51 |
| 7 | 724 | 51 |
| 8 | 1191 | 51 |
| 9 | 2211 | 51 |
| 10 | 2260 | 51 |
| 11 | 2298 | 51 |
| 12 | 2326 | 51 |
| 13 | 2326 | 51 |
| 0 | 2326 | 47 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) |
(*.f64 x x) |
x |
(*.f64 (*.f64 y #s(literal 4 binary64)) y) |
(*.f64 y #s(literal 4 binary64)) |
y |
#s(literal 4 binary64) |
(+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) |
| Outputs |
|---|
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
(/.f64 (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) (fma.f64 y (*.f64 y #s(literal 4 binary64)) (*.f64 x x))) |
(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(*.f64 x x) |
x |
(*.f64 (*.f64 y #s(literal 4 binary64)) y) |
(*.f64 y (*.f64 y #s(literal 4 binary64))) |
(*.f64 y #s(literal 4 binary64)) |
y |
#s(literal 4 binary64) |
(+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) |
(fma.f64 y (*.f64 y #s(literal 4 binary64)) (*.f64 x x)) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (*.f64 x x) | |
| accuracy | 0.00390625 | (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) | |
| accuracy | 2.2578021791510294 | (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) | |
| accuracy | 32.43239088951576 | (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
| 28.0ms | 256× | 0 | valid |
Compiled 53 to 11 computations (79.2% saved)
ival-mult: 8.0ms (66.5% of total)ival-div: 2.0ms (16.6% of total)ival-sub: 1.0ms (8.3% of total)ival-add: 1.0ms (8.3% 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 x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ()) |
#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ()) |
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (pow x 2) (taylor 0 y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ()) |
#s(alt (* -4 (pow y 2)) (taylor inf y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) (taylor inf y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) (taylor inf y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) (taylor inf y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (* 4 (pow y 2)) (taylor inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt -1 (taylor inf y) (#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ()) |
#s(alt (- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) (taylor inf y) (#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ()) |
#s(alt (* -4 (pow y 2)) (taylor -inf y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) (taylor -inf y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) (taylor -inf y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
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#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | y | @ | 0 | ((- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x x)) |
| 1.0ms | y | @ | inf | ((- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x x)) |
| 1.0ms | x | @ | -inf | ((- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x x)) |
| 1.0ms | x | @ | inf | ((- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x x)) |
| 1.0ms | x | @ | 0 | ((- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x x)) |
| 1× | egg-herbie |
| 18 822× | lower-fma.f64 |
| 18 822× | lower-fma.f32 |
| 7 268× | lower-*.f64 |
| 7 268× | lower-*.f32 |
| 2 750× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 115 | 954 |
| 1 | 319 | 954 |
| 2 | 956 | 808 |
| 3 | 4078 | 800 |
| 0 | 8264 | 730 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(pow x 2) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(pow x 2) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(* -4 (pow y 2)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* 4 (pow y 2)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
(* -4 (pow y 2)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* 4 (pow y 2)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
(* -4 (pow y 2)) |
(- (pow x 2) (* 4 (pow y 2))) |
(- (pow x 2) (* 4 (pow y 2))) |
(- (pow x 2) (* 4 (pow y 2))) |
(* 4 (pow y 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
| Outputs |
|---|
(pow x 2) |
(*.f64 x x) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(pow x 2) |
(*.f64 x x) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64)) |
(* -4 (pow y 2)) |
(*.f64 (*.f64 y y) #s(literal -4 binary64)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(* 4 (pow y 2)) |
(*.f64 #s(literal 4 binary64) (*.f64 y y)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
-1 |
#s(literal -1 binary64) |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64)) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
(+.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64)) (/.f64 (*.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/32 binary64)) (pow.f64 y #s(literal 6 binary64)))) |
(* -4 (pow y 2)) |
(*.f64 (*.f64 y y) #s(literal -4 binary64)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(* 4 (pow y 2)) |
(*.f64 #s(literal 4 binary64) (*.f64 y y)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
-1 |
#s(literal -1 binary64) |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64)) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
(+.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64)) (/.f64 (*.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/32 binary64)) (pow.f64 y #s(literal 6 binary64)))) |
(* -4 (pow y 2)) |
(*.f64 (*.f64 y y) #s(literal -4 binary64)) |
(- (pow x 2) (* 4 (pow y 2))) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(- (pow x 2) (* 4 (pow y 2))) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(- (pow x 2) (* 4 (pow y 2))) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(* 4 (pow y 2)) |
(*.f64 #s(literal 4 binary64) (*.f64 y y)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
-1 |
#s(literal -1 binary64) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) |
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64)) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/32 binary64) x) (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64)))) (*.f64 x x) (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64)) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 #s(literal -8 binary64) (*.f64 y y)) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 16 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 #s(literal -8 binary64) (*.f64 y y)) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 16 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
| 4 732× | lower-fma.f64 |
| 4 732× | lower-fma.f32 |
| 4 522× | lower-*.f32 |
| 4 516× | lower-*.f64 |
| 2 930× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 40 |
| 0 | 15 | 40 |
| 1 | 54 | 40 |
| 2 | 397 | 40 |
| 3 | 6323 | 40 |
| 0 | 8488 | 36 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) |
(+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) |
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
(*.f64 x x) |
| Outputs |
|---|
#<batchref> |
#<batchref> |
#<batchref> |
#<batchref> |
#<batchref> |
#<batchref> |
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#<batchref> |
#<batchref> |
#<batchref> |
#<batchref> |
#<batchref> |
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Compiled 25 742 to 1 555 computations (94% saved)
9 alts after pruning (9 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 698 | 9 | 707 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 699 | 9 | 708 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 49.6% | (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) |
| ▶ | 48.4% | (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
| 48.4% | (/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) | |
| 32.3% | (/.f64 (-.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (/.f64 (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) x) x) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (*.f64 (/.f64 (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) x) x) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) | |
| 48.4% | (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)))) | |
| ▶ | 53.5% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
| 48.1% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) | |
| ▶ | 46.3% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) |
| ▶ | 53.5% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
Compiled 310 to 166 computations (46.5% saved)
| 1× | egg-herbie |
Found 14 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 #s(literal 4 binary64) y) | |
| cost-diff | 0 | (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) | |
| cost-diff | 0 | (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) | |
| cost-diff | 1728 | (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) | |
| cost-diff | 0 | (*.f64 #s(literal -4 binary64) y) | |
| cost-diff | 0 | (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) | |
| cost-diff | 0 | (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) | |
| cost-diff | 128 | (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) | |
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | (/.f64 (*.f64 x x) y) | |
| cost-diff | 0 | (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) | |
| cost-diff | 0 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) | |
| cost-diff | 0 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
| 1 840× | lower-fma.f32 |
| 1 832× | lower-fma.f64 |
| 1 408× | lower-*.f32 |
| 1 396× | lower-*.f64 |
| 594× | unsub-neg |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 32 | 233 |
| 0 | 54 | 219 |
| 1 | 95 | 216 |
| 2 | 143 | 216 |
| 3 | 236 | 216 |
| 4 | 355 | 216 |
| 5 | 488 | 216 |
| 6 | 651 | 216 |
| 7 | 932 | 216 |
| 8 | 1843 | 216 |
| 9 | 3174 | 216 |
| 10 | 3455 | 216 |
| 11 | 3520 | 216 |
| 12 | 3542 | 216 |
| 13 | 3554 | 216 |
| 14 | 3558 | 216 |
| 15 | 3866 | 216 |
| 16 | 3994 | 216 |
| 17 | 3994 | 216 |
| 18 | 3994 | 216 |
| 19 | 4002 | 216 |
| 20 | 4002 | 216 |
| 0 | 4002 | 216 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
#s(literal -1 binary64) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
(fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) |
(/.f64 (*.f64 x x) y) |
(*.f64 x x) |
x |
y |
(/.f64 #s(literal 1/2 binary64) y) |
#s(literal 1/2 binary64) |
#s(literal -1 binary64) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
(fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) |
(*.f64 #s(literal -4 binary64) y) |
#s(literal -4 binary64) |
y |
(*.f64 x x) |
x |
(+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) |
(*.f64 (*.f64 y #s(literal 4 binary64)) y) |
(*.f64 y #s(literal 4 binary64)) |
#s(literal 4 binary64) |
(fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) |
(/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
x |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(*.f64 #s(literal 4 binary64) y) |
#s(literal 4 binary64) |
y |
(*.f64 x x) |
(*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) |
(*.f64 #s(literal -4 binary64) y) |
#s(literal -4 binary64) |
(/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
| Outputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
#s(literal -1 binary64) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))) |
(fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)) |
(/.f64 (*.f64 x x) y) |
(*.f64 x x) |
x |
y |
(/.f64 #s(literal 1/2 binary64) y) |
#s(literal 1/2 binary64) |
#s(literal -1 binary64) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
(fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) |
(*.f64 #s(literal -4 binary64) y) |
#s(literal -4 binary64) |
y |
(*.f64 x x) |
x |
(+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(*.f64 (*.f64 y #s(literal 4 binary64)) y) |
(*.f64 (*.f64 #s(literal 4 binary64) y) y) |
(*.f64 y #s(literal 4 binary64)) |
(*.f64 #s(literal 4 binary64) y) |
#s(literal 4 binary64) |
(fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
(/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
x |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(*.f64 #s(literal 4 binary64) y) |
#s(literal 4 binary64) |
y |
(*.f64 x x) |
(*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) |
(*.f64 (/.f64 #s(literal -4 binary64) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (*.f64 y y)) |
(*.f64 #s(literal -4 binary64) y) |
#s(literal -4 binary64) |
(/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
Found 14 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.09212875976844201 | (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) | |
| accuracy | 1.30736202688408 | (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) | |
| accuracy | 18.022584524566945 | (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) | |
| accuracy | 20.267217752802186 | (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) | |
| accuracy | 0 | (*.f64 #s(literal -4 binary64) y) | |
| accuracy | 0.00390625 | (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) | |
| accuracy | 1.2499869262524468 | (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) | |
| accuracy | 32.43239088951576 | (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) | |
| accuracy | 0 | (*.f64 x x) | |
| accuracy | 1.2393679828089452 | (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) | |
| accuracy | 6.614303267020626 | (/.f64 (*.f64 x x) y) | |
| accuracy | 28.559047546275004 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) | |
| accuracy | 34.348505192988924 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) | |
| accuracy | 29.75186949592177 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
| 86.0ms | 256× | 0 | valid |
Compiled 230 to 31 computations (86.5% saved)
ival-div: 26.0ms (51.3% of total)ival-mult: 17.0ms (33.5% of total)ival-add: 5.0ms (9.9% of total)ival-sub: 1.0ms (2% of total)exact: 1.0ms (2% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 x x) y) (patch (/.f64 (*.f64 x x) y) #<representation binary64>) () ()) |
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ()) |
#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ()) |
#s(alt (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal -4 binary64) y) (patch (*.f64 #s(literal -4 binary64) y) #<representation binary64>) () ()) |
#s(alt (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) (patch (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) #<representation binary64>) () ()) |
#s(alt (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 4 binary64) y) (patch (*.f64 #s(literal 4 binary64) y) #<representation binary64>) () ()) |
#s(alt (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ()) |
#s(alt (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) (patch (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (/ (pow x 2) (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (/ (pow x 2) y) (taylor 0 y) (#s(alt (/.f64 (*.f64 x x) y) (patch (/.f64 (*.f64 x x) y) #<representation binary64>) () ())) ()) |
#s(alt (/ (pow x 2) y) (taylor 0 y) (#s(alt (/.f64 (*.f64 x x) y) (patch (/.f64 (*.f64 x x) y) #<representation binary64>) () ())) ()) |
#s(alt (/ (pow x 2) y) (taylor 0 y) (#s(alt (/.f64 (*.f64 x x) y) (patch (/.f64 (*.f64 x x) y) #<representation binary64>) () ())) ()) |
#s(alt (/ (pow x 2) y) (taylor 0 y) (#s(alt (/.f64 (*.f64 x x) y) (patch (/.f64 (*.f64 x x) y) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 y) (#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -4 y) (taylor 0 y) (#s(alt (*.f64 #s(literal -4 binary64) y) (patch (*.f64 #s(literal -4 binary64) y) #<representation binary64>) () ())) ()) |
#s(alt (* -4 y) (taylor 0 y) (#s(alt (*.f64 #s(literal -4 binary64) y) (patch (*.f64 #s(literal -4 binary64) y) #<representation binary64>) () ())) ()) |
#s(alt (* -4 y) (taylor 0 y) (#s(alt (*.f64 #s(literal -4 binary64) y) (patch (*.f64 #s(literal -4 binary64) y) #<representation binary64>) () ())) ()) |
#s(alt (* -4 y) (taylor 0 y) (#s(alt (*.f64 #s(literal -4 binary64) y) (patch (*.f64 #s(literal -4 binary64) y) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 y) (#s(alt (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) (patch (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) (patch (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) (patch (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) (patch (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 x) (taylor 0 y) (#s(alt (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())) ()) |
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#s(alt 1 (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) (patch (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) (patch (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4))))) (+ (* -16 (/ (pow y 4) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) (patch (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -64 (/ (pow y 6) (pow x 6))) (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4)))))) (+ (* -16 (/ (pow y 4) (pow x 4))) (+ (* 4 (/ (pow y 2) (pow x 2))) (* 64 (/ (pow y 6) (pow x 6)))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) (patch (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (- (* 4 (/ (pow y 2) (pow x 2))) 1) x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (- (* -16 (/ (pow y 4) (pow x 4))) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (- (* 64 (/ (pow y 6) (pow x 6))) (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4)))))) x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (/ y (pow x 2)) (taylor -inf x) (#s(alt (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ y (* -4 (/ (pow y 3) (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* 16 (/ (pow y 5) (pow x 4)))) (* 4 (/ (pow y 3) (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ y (* -64 (/ (pow y 7) (pow x 6)))) (+ (* -16 (/ (pow y 5) (pow x 4))) (* 4 (/ (pow y 3) (pow x 2))))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* -4 (/ (pow y 2) (pow x 2))) (taylor -inf x) (#s(alt (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) (patch (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -4 (pow y 2)) (* 16 (/ (pow y 4) (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) (patch (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -64 (/ (pow y 6) (pow x 4))) (+ (* -4 (pow y 2)) (* 16 (/ (pow y 4) (pow x 2))))) (pow x 2)) (taylor -inf x) (#s(alt (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) (patch (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -64 (/ (pow y 6) (pow x 4))) (+ (* -4 (pow y 2)) (+ (* 16 (/ (pow y 4) (pow x 2))) (* 256 (/ (pow y 8) (pow x 6)))))) (pow x 2)) (taylor -inf x) (#s(alt (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) (patch (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) #<representation binary64>) () ())) ()) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 5.0ms | x | @ | 0 | ((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/ (* x x) y) (* x x) (+ (* x x) (* (* y 4) y)) (/ (+ (* (* -4 y) y) (* x x)) (+ (* x x) (* (* y 4) y))) (+ (* (* -4 y) y) (* x x)) (* -4 y) (+ (* (/ x (+ (* (* 4 y) y) (* x x))) x) (* (* -4 y) (/ y (+ (* (* 4 y) y) (* x x))))) (/ x (+ (* (* 4 y) y) (* x x))) (+ (* (* 4 y) y) (* x x)) (* 4 y) (/ y (+ (* (* 4 y) y) (* x x))) (* (* -4 y) (/ y (+ (* (* 4 y) y) (* x x))))) |
| 5.0ms | y | @ | inf | ((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/ (* x x) y) (* x x) (+ (* x x) (* (* y 4) y)) (/ (+ (* (* -4 y) y) (* x x)) (+ (* x x) (* (* y 4) y))) (+ (* (* -4 y) y) (* x x)) (* -4 y) (+ (* (/ x (+ (* (* 4 y) y) (* x x))) x) (* (* -4 y) (/ y (+ (* (* 4 y) y) (* x x))))) (/ x (+ (* (* 4 y) y) (* x x))) (+ (* (* 4 y) y) (* x x)) (* 4 y) (/ y (+ (* (* 4 y) y) (* x x))) (* (* -4 y) (/ y (+ (* (* 4 y) y) (* x x))))) |
| 3.0ms | x | @ | inf | ((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/ (* x x) y) (* x x) (+ (* x x) (* (* y 4) y)) (/ (+ (* (* -4 y) y) (* x x)) (+ (* x x) (* (* y 4) y))) (+ (* (* -4 y) y) (* x x)) (* -4 y) (+ (* (/ x (+ (* (* 4 y) y) (* x x))) x) (* (* -4 y) (/ y (+ (* (* 4 y) y) (* x x))))) (/ x (+ (* (* 4 y) y) (* x x))) (+ (* (* 4 y) y) (* x x)) (* 4 y) (/ y (+ (* (* 4 y) y) (* x x))) (* (* -4 y) (/ y (+ (* (* 4 y) y) (* x x))))) |
| 3.0ms | y | @ | 0 | ((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/ (* x x) y) (* x x) (+ (* x x) (* (* y 4) y)) (/ (+ (* (* -4 y) y) (* x x)) (+ (* x x) (* (* y 4) y))) (+ (* (* -4 y) y) (* x x)) (* -4 y) (+ (* (/ x (+ (* (* 4 y) y) (* x x))) x) (* (* -4 y) (/ y (+ (* (* 4 y) y) (* x x))))) (/ x (+ (* (* 4 y) y) (* x x))) (+ (* (* 4 y) y) (* x x)) (* 4 y) (/ y (+ (* (* 4 y) y) (* x x))) (* (* -4 y) (/ y (+ (* (* 4 y) y) (* x x))))) |
| 3.0ms | y | @ | -inf | ((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/ (* x x) y) (* x x) (+ (* x x) (* (* y 4) y)) (/ (+ (* (* -4 y) y) (* x x)) (+ (* x x) (* (* y 4) y))) (+ (* (* -4 y) y) (* x x)) (* -4 y) (+ (* (/ x (+ (* (* 4 y) y) (* x x))) x) (* (* -4 y) (/ y (+ (* (* 4 y) y) (* x x))))) (/ x (+ (* (* 4 y) y) (* x x))) (+ (* (* 4 y) y) (* x x)) (* 4 y) (/ y (+ (* (* 4 y) y) (* x x))) (* (* -4 y) (/ y (+ (* (* 4 y) y) (* x x))))) |
| 1× | egg-herbie |
| 16 292× | lower-fma.f64 |
| 16 292× | lower-fma.f32 |
| 4 372× | lower-*.f64 |
| 4 372× | lower-*.f32 |
| 3 772× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 374 | 5576 |
| 1 | 1098 | 5019 |
| 2 | 3135 | 4781 |
| 0 | 8320 | 4424 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(pow x 2) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(pow x 2) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(* -4 y) |
(* -4 y) |
(* -4 y) |
(* -4 y) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(/ 1 x) |
(+ (* -4 (/ (pow y 2) (pow x 3))) (/ 1 x)) |
(+ (* (pow y 2) (- (* 16 (/ (pow y 2) (pow x 5))) (* 4 (/ 1 (pow x 3))))) (/ 1 x)) |
(+ (* (pow y 2) (- (* (pow y 2) (+ (* -64 (/ (pow y 2) (pow x 7))) (* 16 (/ 1 (pow x 5))))) (* 4 (/ 1 (pow x 3))))) (/ 1 x)) |
(pow x 2) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(/ y (pow x 2)) |
(* y (+ (* -4 (/ (pow y 2) (pow x 4))) (/ 1 (pow x 2)))) |
(* y (+ (* (pow y 2) (- (* 16 (/ (pow y 2) (pow x 6))) (* 4 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))) |
(* y (+ (* (pow y 2) (- (* (pow y 2) (+ (* -64 (/ (pow y 2) (pow x 8))) (* 16 (/ 1 (pow x 6))))) (* 4 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))) |
(* -4 (/ (pow y 2) (pow x 2))) |
(* (pow y 2) (- (* 16 (/ (pow y 2) (pow x 4))) (* 4 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (* (pow y 2) (+ (* -64 (/ (pow y 2) (pow x 6))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (* (pow y 2) (+ (* (pow y 2) (- (* 256 (/ (pow y 2) (pow x 8))) (* 64 (/ 1 (pow x 6))))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2))))) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(* 4 (pow y 2)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
(* -4 (pow y 2)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* -4 y) |
(* -4 y) |
(* -4 y) |
(* -4 y) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/32 (/ (pow x 6) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/8 (/ (pow x 4) (pow y 4)))))) |
(* 1/4 (/ x (pow y 2))) |
(/ (+ (* -1/16 (/ (pow x 3) (pow y 2))) (* 1/4 x)) (pow y 2)) |
(/ (- (+ (* 1/64 (/ (pow x 5) (pow y 4))) (* 1/4 x)) (* 1/16 (/ (pow x 3) (pow y 2)))) (pow y 2)) |
(/ (- (+ (* -1/256 (/ (pow x 7) (pow y 6))) (* 1/4 x)) (+ (* -1/64 (/ (pow x 5) (pow y 4))) (* 1/16 (/ (pow x 3) (pow y 2))))) (pow y 2)) |
(* 4 (pow y 2)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(/ 1/4 y) |
(/ (+ 1/4 (* -1/16 (/ (pow x 2) (pow y 2)))) y) |
(/ (- (+ 1/4 (* 1/64 (/ (pow x 4) (pow y 4)))) (* 1/16 (/ (pow x 2) (pow y 2)))) y) |
(/ (- (+ 1/4 (* -1/256 (/ (pow x 6) (pow y 6)))) (+ (* -1/64 (/ (pow x 4) (pow y 4))) (* 1/16 (/ (pow x 2) (pow y 2))))) y) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) 1) |
(- (* -1/16 (/ (pow x 4) (pow y 4))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (* 1/64 (/ (pow x 6) (pow y 6))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/16 (/ (pow x 4) (pow y 4)))))) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(* 4 (pow y 2)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
(* -4 (pow y 2)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* -4 y) |
(* -4 y) |
(* -4 y) |
(* -4 y) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/32 (/ (pow x 6) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/8 (/ (pow x 4) (pow y 4)))))) |
(* 1/4 (/ x (pow y 2))) |
(/ (+ (* -1/16 (/ (pow x 3) (pow y 2))) (* 1/4 x)) (pow y 2)) |
(/ (- (+ (* 1/64 (/ (pow x 5) (pow y 4))) (* 1/4 x)) (* 1/16 (/ (pow x 3) (pow y 2)))) (pow y 2)) |
(/ (- (+ (* -1/256 (/ (pow x 7) (pow y 6))) (* 1/4 x)) (+ (* -1/64 (/ (pow x 5) (pow y 4))) (* 1/16 (/ (pow x 3) (pow y 2))))) (pow y 2)) |
(* 4 (pow y 2)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(/ 1/4 y) |
(* -1 (/ (- (* 1/16 (/ (pow x 2) (pow y 2))) 1/4) y)) |
(* -1 (/ (- (* -1/64 (/ (pow x 4) (pow y 4))) (+ 1/4 (* -1/16 (/ (pow x 2) (pow y 2))))) y)) |
(* -1 (/ (- (* 1/256 (/ (pow x 6) (pow y 6))) (+ 1/4 (+ (* -1/16 (/ (pow x 2) (pow y 2))) (* 1/64 (/ (pow x 4) (pow y 4)))))) y)) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) 1) |
(- (* -1/16 (/ (pow x 4) (pow y 4))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (* 1/64 (/ (pow x 6) (pow y 6))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/16 (/ (pow x 4) (pow y 4)))))) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* 4 (pow y 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(* -4 (pow y 2)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(* 1/4 (/ x (pow y 2))) |
(* x (+ (* -1/16 (/ (pow x 2) (pow y 4))) (* 1/4 (/ 1 (pow y 2))))) |
(* x (+ (* (pow x 2) (- (* 1/64 (/ (pow x 2) (pow y 6))) (* 1/16 (/ 1 (pow y 4))))) (* 1/4 (/ 1 (pow y 2))))) |
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/256 (/ (pow x 2) (pow y 8))) (* 1/64 (/ 1 (pow y 6))))) (* 1/16 (/ 1 (pow y 4))))) (* 1/4 (/ 1 (pow y 2))))) |
(* 4 (pow y 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(/ 1/4 y) |
(+ (* -1/16 (/ (pow x 2) (pow y 3))) (* 1/4 (/ 1 y))) |
(+ (* (pow x 2) (- (* 1/64 (/ (pow x 2) (pow y 5))) (* 1/16 (/ 1 (pow y 3))))) (* 1/4 (/ 1 y))) |
(+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/256 (/ (pow x 2) (pow y 7))) (* 1/64 (/ 1 (pow y 5))))) (* 1/16 (/ 1 (pow y 3))))) (* 1/4 (/ 1 y))) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (+ (* -1/16 (/ (pow x 2) (pow y 4))) (* 1/4 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/64 (/ (pow x 2) (pow y 6))) (* 1/16 (/ 1 (pow y 4))))) (* 1/4 (/ 1 (pow y 2))))) 1) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4))))) (+ (* -16 (/ (pow y 4) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(- (+ 1 (+ (* -64 (/ (pow y 6) (pow x 6))) (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4)))))) (+ (* -16 (/ (pow y 4) (pow x 4))) (+ (* 4 (/ (pow y 2) (pow x 2))) (* 64 (/ (pow y 6) (pow x 6)))))) |
(/ 1 x) |
(/ (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) x) |
(/ (- (+ 1 (* 16 (/ (pow y 4) (pow x 4)))) (* 4 (/ (pow y 2) (pow x 2)))) x) |
(/ (- (+ 1 (* -64 (/ (pow y 6) (pow x 6)))) (+ (* -16 (/ (pow y 4) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) x) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(/ y (pow x 2)) |
(/ (+ y (* -4 (/ (pow y 3) (pow x 2)))) (pow x 2)) |
(/ (- (+ y (* 16 (/ (pow y 5) (pow x 4)))) (* 4 (/ (pow y 3) (pow x 2)))) (pow x 2)) |
(/ (- (+ y (* -64 (/ (pow y 7) (pow x 6)))) (+ (* -16 (/ (pow y 5) (pow x 4))) (* 4 (/ (pow y 3) (pow x 2))))) (pow x 2)) |
(* -4 (/ (pow y 2) (pow x 2))) |
(/ (+ (* -4 (pow y 2)) (* 16 (/ (pow y 4) (pow x 2)))) (pow x 2)) |
(/ (+ (* -64 (/ (pow y 6) (pow x 4))) (+ (* -4 (pow y 2)) (* 16 (/ (pow y 4) (pow x 2))))) (pow x 2)) |
(/ (+ (* -64 (/ (pow y 6) (pow x 4))) (+ (* -4 (pow y 2)) (+ (* 16 (/ (pow y 4) (pow x 2))) (* 256 (/ (pow y 8) (pow x 6)))))) (pow x 2)) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4))))) (+ (* -16 (/ (pow y 4) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(- (+ 1 (+ (* -64 (/ (pow y 6) (pow x 6))) (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4)))))) (+ (* -16 (/ (pow y 4) (pow x 4))) (+ (* 4 (/ (pow y 2) (pow x 2))) (* 64 (/ (pow y 6) (pow x 6)))))) |
(/ 1 x) |
(* -1 (/ (- (* 4 (/ (pow y 2) (pow x 2))) 1) x)) |
(* -1 (/ (- (* -16 (/ (pow y 4) (pow x 4))) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) x)) |
(* -1 (/ (- (* 64 (/ (pow y 6) (pow x 6))) (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4)))))) x)) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(/ y (pow x 2)) |
(/ (+ y (* -4 (/ (pow y 3) (pow x 2)))) (pow x 2)) |
(/ (- (+ y (* 16 (/ (pow y 5) (pow x 4)))) (* 4 (/ (pow y 3) (pow x 2)))) (pow x 2)) |
(/ (- (+ y (* -64 (/ (pow y 7) (pow x 6)))) (+ (* -16 (/ (pow y 5) (pow x 4))) (* 4 (/ (pow y 3) (pow x 2))))) (pow x 2)) |
(* -4 (/ (pow y 2) (pow x 2))) |
(/ (+ (* -4 (pow y 2)) (* 16 (/ (pow y 4) (pow x 2)))) (pow x 2)) |
(/ (+ (* -64 (/ (pow y 6) (pow x 4))) (+ (* -4 (pow y 2)) (* 16 (/ (pow y 4) (pow x 2))))) (pow x 2)) |
(/ (+ (* -64 (/ (pow y 6) (pow x 4))) (+ (* -4 (pow y 2)) (+ (* 16 (/ (pow y 4) (pow x 2))) (* 256 (/ (pow y 8) (pow x 6)))))) (pow x 2)) |
| Outputs |
|---|
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 6 binary64)))) #s(literal -128 binary64) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 6 binary64)))) #s(literal -128 binary64) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
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(fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -8 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -4 binary64) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64)) (*.f64 (*.f64 y y) (/.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -8 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -4 binary64) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)))) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -8 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -4 binary64) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64)) (*.f64 (*.f64 y y) (/.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -8 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -4 binary64) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)))) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -8 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -4 binary64) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64)) (*.f64 (*.f64 y y) (/.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -8 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -4 binary64) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)))) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y)) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x)) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x)) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x)) |
(/ (pow x 2) y) |
(/.f64 (*.f64 x x) y) |
(/ (pow x 2) y) |
(/.f64 (*.f64 x x) y) |
(/ (pow x 2) y) |
(/.f64 (*.f64 x x) y) |
(/ (pow x 2) y) |
(/.f64 (*.f64 x x) y) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (*.f64 (fma.f64 (*.f64 y y) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (*.f64 (fma.f64 (*.f64 y y) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (*.f64 (fma.f64 (*.f64 y y) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)) x) x) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -8 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -4 binary64) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64)) (*.f64 (*.f64 y y) (/.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -8 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -4 binary64) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (fma.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (fma.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (fma.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) (*.f64 x x)) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4))))) (+ (* -16 (/ (pow y 4) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 16 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 16 binary64) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)))) |
(- (+ 1 (+ (* -64 (/ (pow y 6) (pow x 6))) (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4)))))) (+ (* -16 (/ (pow y 4) (pow x 4))) (+ (* 4 (/ (pow y 2) (pow x 2))) (* 64 (/ (pow y 6) (pow x 6)))))) |
(fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -64 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -64 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 16 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 16 binary64) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)))))) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(* -1 (/ (- (* 4 (/ (pow y 2) (pow x 2))) 1) x)) |
(/.f64 (fma.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) x) |
(* -1 (/ (- (* -16 (/ (pow y 4) (pow x 4))) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) x)) |
(/.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 16 binary64) (fma.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) x) |
(* -1 (/ (- (* 64 (/ (pow y 6) (pow x 6))) (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4)))))) x)) |
(/.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -64 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 16 binary64) (fma.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)))) x) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (*.f64 (fma.f64 (*.f64 y y) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (*.f64 (fma.f64 (*.f64 y y) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (*.f64 (fma.f64 (*.f64 y y) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)) x) x) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ (+ y (* -4 (/ (pow y 3) (pow x 2)))) (pow x 2)) |
(/.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) x) (/.f64 #s(literal -4 binary64) x) y) (*.f64 x x)) |
(/ (- (+ y (* 16 (/ (pow y 5) (pow x 4)))) (* 4 (/ (pow y 3) (pow x 2)))) (pow x 2)) |
(/.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 5 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 16 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) x) (/.f64 #s(literal -4 binary64) x) y)) (*.f64 x x)) |
(/ (- (+ y (* -64 (/ (pow y 7) (pow x 6)))) (+ (* -16 (/ (pow y 5) (pow x 4))) (* 4 (/ (pow y 3) (pow x 2))))) (pow x 2)) |
(/.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 7 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -64 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 5 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 16 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) x) (/.f64 #s(literal -4 binary64) x) y))) (*.f64 x x)) |
(* -4 (/ (pow y 2) (pow x 2))) |
(*.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x)) |
(/ (+ (* -4 (pow y 2)) (* 16 (/ (pow y 4) (pow x 2)))) (pow x 2)) |
(/.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) x) (/.f64 #s(literal 16 binary64) x) (*.f64 #s(literal -4 binary64) (*.f64 y y))) (*.f64 x x)) |
(/ (+ (* -64 (/ (pow y 6) (pow x 4))) (+ (* -4 (pow y 2)) (* 16 (/ (pow y 4) (pow x 2))))) (pow x 2)) |
(/.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) x) (/.f64 #s(literal 16 binary64) x) (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -64 binary64) (*.f64 #s(literal -4 binary64) (*.f64 y y)))) (*.f64 x x)) |
(/ (+ (* -64 (/ (pow y 6) (pow x 4))) (+ (* -4 (pow y 2)) (+ (* 16 (/ (pow y 4) (pow x 2))) (* 256 (/ (pow y 8) (pow x 6)))))) (pow x 2)) |
(/.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 256 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) x) (/.f64 #s(literal 16 binary64) x) (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -64 binary64) (*.f64 #s(literal -4 binary64) (*.f64 y y))))) (*.f64 x x)) |
| 7 426× | lower-fma.f32 |
| 7 418× | lower-fma.f64 |
| 4 286× | lower-/.f32 |
| 4 276× | lower-/.f64 |
| 4 006× | lower-*.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 32 | 199 |
| 0 | 54 | 185 |
| 1 | 208 | 182 |
| 2 | 1497 | 182 |
| 0 | 8556 | 182 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
(fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) |
(/.f64 (*.f64 x x) y) |
(*.f64 x x) |
(+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
(fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) |
(*.f64 #s(literal -4 binary64) y) |
(fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) |
(/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(*.f64 #s(literal 4 binary64) y) |
(/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
(*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) |
| Outputs |
|---|
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Compiled 53 302 to 2 571 computations (95.2% saved)
10 alts after pruning (8 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 501 | 8 | 1 509 |
| Fresh | 4 | 0 | 4 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 0 | 0 |
| Total | 1 508 | 10 | 1 518 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 48.9% | (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) |
| ▶ | 48.4% | (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) |
| 24.2% | (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #s(approx (+ (* x x) (* (* y 4) y)) (*.f64 x x))) | |
| 48.4% | (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) | |
| ▶ | 48.0% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) |
| ▶ | 55.4% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
| ▶ | 48.7% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64))) |
| 26.8% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)))) | |
| ✓ | 46.3% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) |
| ✓ | 53.5% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
Compiled 254 to 172 computations (32.3% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 #s(literal 4 binary64) y) | |
| cost-diff | 0 | (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) | |
| cost-diff | 0 | (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) | |
| cost-diff | 1728 | (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) | |
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | (*.f64 #s(literal -4 binary64) y) | |
| cost-diff | 0 | (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) | |
| cost-diff | 0 | (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) | |
| cost-diff | 0 | (*.f64 #s(literal -8 binary64) y) | |
| cost-diff | 0 | (/.f64 (*.f64 #s(literal -8 binary64) y) x) | |
| cost-diff | 0 | (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) | |
| cost-diff | 0 | (*.f64 (*.f64 y #s(literal 2 binary64)) y) | |
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64)) | |
| cost-diff | 0 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64))) | |
| cost-diff | 0 | (/.f64 x y) | |
| cost-diff | 0 | (*.f64 (/.f64 x y) x) | |
| cost-diff | 0 | (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) | |
| cost-diff | 0 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
| 2 880× | lower-fma.f32 |
| 2 866× | lower-fma.f64 |
| 2 304× | lower-*.f32 |
| 2 286× | lower-*.f64 |
| 1 090× | times-frac |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 42 | 299 |
| 0 | 73 | 283 |
| 1 | 133 | 278 |
| 2 | 233 | 278 |
| 3 | 457 | 278 |
| 4 | 838 | 278 |
| 5 | 1106 | 278 |
| 6 | 1327 | 278 |
| 7 | 1856 | 278 |
| 8 | 3524 | 278 |
| 9 | 4657 | 278 |
| 10 | 5062 | 278 |
| 11 | 5142 | 278 |
| 12 | 5184 | 278 |
| 13 | 5200 | 278 |
| 14 | 5506 | 278 |
| 15 | 5650 | 278 |
| 16 | 5650 | 278 |
| 17 | 5650 | 278 |
| 18 | 5650 | 278 |
| 19 | 5747 | 278 |
| 20 | 5919 | 278 |
| 21 | 6023 | 278 |
| 22 | 6035 | 278 |
| 23 | 6035 | 278 |
| 0 | 6035 | 278 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
(fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) |
(*.f64 (/.f64 x y) x) |
(/.f64 x y) |
x |
y |
(/.f64 #s(literal 1/2 binary64) y) |
#s(literal 1/2 binary64) |
#s(literal -1 binary64) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64))) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64)) |
(*.f64 x x) |
x |
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) |
#s(literal 1 binary64) |
(*.f64 (*.f64 y #s(literal 2 binary64)) y) |
(*.f64 y #s(literal 2 binary64)) |
y |
#s(literal 2 binary64) |
#s(literal -1 binary64) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) |
(fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) |
(/.f64 (*.f64 #s(literal -8 binary64) y) x) |
(*.f64 #s(literal -8 binary64) y) |
#s(literal -8 binary64) |
y |
x |
(/.f64 y x) |
#s(literal 1 binary64) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) |
(fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) |
(*.f64 #s(literal -4 binary64) y) |
#s(literal -4 binary64) |
y |
(*.f64 x x) |
x |
(fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)) |
(*.f64 y y) |
#s(literal 4 binary64) |
(fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) |
(/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
x |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(*.f64 #s(literal 4 binary64) y) |
#s(literal 4 binary64) |
y |
(*.f64 x x) |
(/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
(*.f64 (*.f64 #s(literal -4 binary64) y) y) |
(*.f64 #s(literal -4 binary64) y) |
#s(literal -4 binary64) |
| Outputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))) |
(fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)) |
(*.f64 (/.f64 x y) x) |
(/.f64 x y) |
x |
y |
(/.f64 #s(literal 1/2 binary64) y) |
#s(literal 1/2 binary64) |
#s(literal -1 binary64) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64)) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)) |
(*.f64 x x) |
x |
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) |
(/.f64 (/.f64 #s(literal 1/2 binary64) y) y) |
#s(literal 1 binary64) |
(*.f64 (*.f64 y #s(literal 2 binary64)) y) |
(*.f64 (*.f64 #s(literal 2 binary64) y) y) |
(*.f64 y #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) y) |
y |
#s(literal 2 binary64) |
#s(literal -1 binary64) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 y x) (/.f64 (*.f64 #s(literal -8 binary64) y) x) #s(literal 1 binary64))) |
(fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) |
(fma.f64 (/.f64 y x) (/.f64 (*.f64 #s(literal -8 binary64) y) x) #s(literal 1 binary64)) |
(/.f64 (*.f64 #s(literal -8 binary64) y) x) |
(*.f64 #s(literal -8 binary64) y) |
#s(literal -8 binary64) |
y |
x |
(/.f64 y x) |
#s(literal 1 binary64) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) |
(fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) |
(*.f64 #s(literal -4 binary64) y) |
#s(literal -4 binary64) |
y |
(*.f64 x x) |
x |
(fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)) |
(*.f64 y y) |
#s(literal 4 binary64) |
(fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) |
(/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
(/.f64 x (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) |
x |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)) |
(*.f64 #s(literal 4 binary64) y) |
#s(literal 4 binary64) |
y |
(*.f64 x x) |
(/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
(*.f64 (/.f64 #s(literal -4 binary64) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) (*.f64 y y)) |
(*.f64 (*.f64 #s(literal -4 binary64) y) y) |
(*.f64 (*.f64 y y) #s(literal -4 binary64)) |
(*.f64 #s(literal -4 binary64) y) |
#s(literal -4 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.00390625 | (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) | |
| accuracy | 0.09212875976844201 | (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) | |
| accuracy | 18.022584524566945 | (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) | |
| accuracy | 24.26107980165786 | (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) | |
| accuracy | 0 | (*.f64 #s(literal -4 binary64) y) | |
| accuracy | 0.00390625 | (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)) | |
| accuracy | 1.2499869262524468 | (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) | |
| accuracy | 32.43239088951576 | (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) | |
| accuracy | 0 | (*.f64 #s(literal -8 binary64) y) | |
| accuracy | 0.1171875 | (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) | |
| accuracy | 0.24217027446879305 | (/.f64 (*.f64 #s(literal -8 binary64) y) x) | |
| accuracy | 33.24719163352617 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) | |
| accuracy | 0 | (*.f64 x x) | |
| accuracy | 0.4560685275399381 | (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) | |
| accuracy | 10.417813223611116 | (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64)) | |
| accuracy | 28.559047546275004 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64))) | |
| accuracy | 0 | (/.f64 #s(literal 1/2 binary64) y) | |
| accuracy | 0.1171875 | (*.f64 (/.f64 x y) x) | |
| accuracy | 1.2393679828089452 | (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) | |
| accuracy | 28.559047546275004 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
| 136.0ms | 256× | 0 | valid |
Compiled 279 to 46 computations (83.5% saved)
ival-add: 38.0ms (33.9% of total)ival-div: 37.0ms (33% of total)ival-mult: 34.0ms (30.3% of total)ival-sub: 1.0ms (0.9% of total)exact: 1.0ms (0.9% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 (/.f64 x y) x) (patch (*.f64 (/.f64 x y) x) #<representation binary64>) () ()) |
#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ()) |
#s(alt (*.f64 (*.f64 y #s(literal 2 binary64)) y) (patch (*.f64 (*.f64 y #s(literal 2 binary64)) y) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 #s(literal -8 binary64) y) x) (patch (/.f64 (*.f64 #s(literal -8 binary64) y) x) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal -8 binary64) y) (patch (*.f64 #s(literal -8 binary64) y) #<representation binary64>) () ()) |
#s(alt (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal -4 binary64) y) (patch (*.f64 #s(literal -4 binary64) y) #<representation binary64>) () ()) |
#s(alt (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) (patch (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) #<representation binary64>) () ()) |
#s(alt (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 4 binary64) y) (patch (*.f64 #s(literal 4 binary64) y) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1/2 binary64) y) (patch (/.f64 #s(literal 1/2 binary64) y) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) (patch (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)) (patch (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (/ (pow x 2) (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (/ (pow x 2) y) (taylor 0 y) (#s(alt (*.f64 (/.f64 x y) x) (patch (*.f64 (/.f64 x y) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (pow x 2) y) (taylor 0 y) (#s(alt (*.f64 (/.f64 x y) x) (patch (*.f64 (/.f64 x y) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (pow x 2) y) (taylor 0 y) (#s(alt (*.f64 (/.f64 x y) x) (patch (*.f64 (/.f64 x y) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (pow x 2) y) (taylor 0 y) (#s(alt (*.f64 (/.f64 x y) x) (patch (*.f64 (/.f64 x y) x) #<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>) () ())) ()) |
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#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -8 (/ y x)) (taylor -inf x) (#s(alt (/.f64 (*.f64 #s(literal -8 binary64) y) x) (patch (/.f64 (*.f64 #s(literal -8 binary64) y) x) #<representation binary64>) () ())) ()) |
#s(alt (* -8 (/ y x)) (taylor -inf x) (#s(alt (/.f64 (*.f64 #s(literal -8 binary64) y) x) (patch (/.f64 (*.f64 #s(literal -8 binary64) y) x) #<representation binary64>) () ())) ()) |
#s(alt (* -8 (/ y x)) (taylor -inf x) (#s(alt (/.f64 (*.f64 #s(literal -8 binary64) y) x) (patch (/.f64 (*.f64 #s(literal -8 binary64) y) x) #<representation binary64>) () ())) ()) |
#s(alt (* -8 (/ y x)) (taylor -inf x) (#s(alt (/.f64 (*.f64 #s(literal -8 binary64) y) x) (patch (/.f64 (*.f64 #s(literal -8 binary64) y) x) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor -inf x) (#s(alt (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) (patch (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) (patch (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4))))) (+ (* -16 (/ (pow y 4) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) (patch (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -64 (/ (pow y 6) (pow x 6))) (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4)))))) (+ (* -16 (/ (pow y 4) (pow x 4))) (+ (* 4 (/ (pow y 2) (pow x 2))) (* 64 (/ (pow y 6) (pow x 6)))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) (patch (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (- (* 4 (/ (pow y 2) (pow x 2))) 1) x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (- (* -16 (/ (pow y 4) (pow x 4))) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (- (* 64 (/ (pow y 6) (pow x 6))) (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4)))))) x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)) (patch (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)) (patch (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)) (patch (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)) (patch (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* -4 (/ (pow y 2) (pow x 2))) (taylor -inf x) (#s(alt (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -4 (pow y 2)) (* 16 (/ (pow y 4) (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -64 (/ (pow y 6) (pow x 4))) (+ (* -4 (pow y 2)) (* 16 (/ (pow y 4) (pow x 2))))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -64 (/ (pow y 6) (pow x 4))) (+ (* -4 (pow y 2)) (+ (* 16 (/ (pow y 4) (pow x 2))) (* 256 (/ (pow y 8) (pow x 6)))))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())) ()) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 6.0ms | y | @ | inf | ((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* (/ x y) x) (/ 1/2 y)) -1) (* (/ x y) x) (/ x y) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* x x) (/ 1 (* (* y 2) y))) -1) (* x x) (* (* y 2) y) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* -8 y) x) (/ y x)) 1) (/ (* -8 y) x) (* -8 y) (/ (+ (* (* -4 y) y) (* x x)) (+ (* (* y y) 4) (* x x))) (+ (* (* -4 y) y) (* x x)) (* -4 y) (+ (* (/ x (+ (* (* 4 y) y) (* x x))) x) (/ (* (* -4 y) y) (+ (* (* 4 y) y) (* x x)))) (/ x (+ (* (* 4 y) y) (* x x))) (+ (* (* 4 y) y) (* x x)) (* 4 y) (/ 1/2 y) (/ 1 (* (* y 2) y)) (+ (* (* y y) 4) (* x x)) (/ (* (* -4 y) y) (+ (* (* 4 y) y) (* x x)))) |
| 5.0ms | y | @ | 0 | ((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* (/ x y) x) (/ 1/2 y)) -1) (* (/ x y) x) (/ x y) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* x x) (/ 1 (* (* y 2) y))) -1) (* x x) (* (* y 2) y) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* -8 y) x) (/ y x)) 1) (/ (* -8 y) x) (* -8 y) (/ (+ (* (* -4 y) y) (* x x)) (+ (* (* y y) 4) (* x x))) (+ (* (* -4 y) y) (* x x)) (* -4 y) (+ (* (/ x (+ (* (* 4 y) y) (* x x))) x) (/ (* (* -4 y) y) (+ (* (* 4 y) y) (* x x)))) (/ x (+ (* (* 4 y) y) (* x x))) (+ (* (* 4 y) y) (* x x)) (* 4 y) (/ 1/2 y) (/ 1 (* (* y 2) y)) (+ (* (* y y) 4) (* x x)) (/ (* (* -4 y) y) (+ (* (* 4 y) y) (* x x)))) |
| 3.0ms | y | @ | -inf | ((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* (/ x y) x) (/ 1/2 y)) -1) (* (/ x y) x) (/ x y) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* x x) (/ 1 (* (* y 2) y))) -1) (* x x) (* (* y 2) y) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* -8 y) x) (/ y x)) 1) (/ (* -8 y) x) (* -8 y) (/ (+ (* (* -4 y) y) (* x x)) (+ (* (* y y) 4) (* x x))) (+ (* (* -4 y) y) (* x x)) (* -4 y) (+ (* (/ x (+ (* (* 4 y) y) (* x x))) x) (/ (* (* -4 y) y) (+ (* (* 4 y) y) (* x x)))) (/ x (+ (* (* 4 y) y) (* x x))) (+ (* (* 4 y) y) (* x x)) (* 4 y) (/ 1/2 y) (/ 1 (* (* y 2) y)) (+ (* (* y y) 4) (* x x)) (/ (* (* -4 y) y) (+ (* (* 4 y) y) (* x x)))) |
| 2.0ms | x | @ | -inf | ((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* (/ x y) x) (/ 1/2 y)) -1) (* (/ x y) x) (/ x y) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* x x) (/ 1 (* (* y 2) y))) -1) (* x x) (* (* y 2) y) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* -8 y) x) (/ y x)) 1) (/ (* -8 y) x) (* -8 y) (/ (+ (* (* -4 y) y) (* x x)) (+ (* (* y y) 4) (* x x))) (+ (* (* -4 y) y) (* x x)) (* -4 y) (+ (* (/ x (+ (* (* 4 y) y) (* x x))) x) (/ (* (* -4 y) y) (+ (* (* 4 y) y) (* x x)))) (/ x (+ (* (* 4 y) y) (* x x))) (+ (* (* 4 y) y) (* x x)) (* 4 y) (/ 1/2 y) (/ 1 (* (* y 2) y)) (+ (* (* y y) 4) (* x x)) (/ (* (* -4 y) y) (+ (* (* 4 y) y) (* x x)))) |
| 2.0ms | x | @ | inf | ((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* (/ x y) x) (/ 1/2 y)) -1) (* (/ x y) x) (/ x y) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* x x) (/ 1 (* (* y 2) y))) -1) (* x x) (* (* y 2) y) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* -8 y) x) (/ y x)) 1) (/ (* -8 y) x) (* -8 y) (/ (+ (* (* -4 y) y) (* x x)) (+ (* (* y y) 4) (* x x))) (+ (* (* -4 y) y) (* x x)) (* -4 y) (+ (* (/ x (+ (* (* 4 y) y) (* x x))) x) (/ (* (* -4 y) y) (+ (* (* 4 y) y) (* x x)))) (/ x (+ (* (* 4 y) y) (* x x))) (+ (* (* 4 y) y) (* x x)) (* 4 y) (/ 1/2 y) (/ 1 (* (* y 2) y)) (+ (* (* y y) 4) (* x x)) (/ (* (* -4 y) y) (+ (* (* 4 y) y) (* x x)))) |
| 1× | egg-herbie |
| 16 180× | lower-fma.f64 |
| 16 180× | lower-fma.f32 |
| 3 870× | lower-*.f64 |
| 3 870× | lower-*.f32 |
| 3 594× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 299 | 6082 |
| 1 | 848 | 5432 |
| 2 | 2447 | 5200 |
| 3 | 7073 | 5144 |
| 0 | 8238 | 4808 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ x y) |
(/ x y) |
(/ x y) |
(/ x y) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(* 2 (pow y 2)) |
(* 2 (pow y 2)) |
(* 2 (pow y 2)) |
(* 2 (pow y 2)) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
(* -8 y) |
(* -8 y) |
(* -8 y) |
(* -8 y) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(pow x 2) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(* -4 y) |
(* -4 y) |
(* -4 y) |
(* -4 y) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(/ 1 x) |
(+ (* -4 (/ (pow y 2) (pow x 3))) (/ 1 x)) |
(+ (* (pow y 2) (- (* 16 (/ (pow y 2) (pow x 5))) (* 4 (/ 1 (pow x 3))))) (/ 1 x)) |
(+ (* (pow y 2) (- (* (pow y 2) (+ (* -64 (/ (pow y 2) (pow x 7))) (* 16 (/ 1 (pow x 5))))) (* 4 (/ 1 (pow x 3))))) (/ 1 x)) |
(pow x 2) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(/ 1/2 y) |
(/ 1/2 y) |
(/ 1/2 y) |
(/ 1/2 y) |
(/ 1/2 (pow y 2)) |
(/ 1/2 (pow y 2)) |
(/ 1/2 (pow y 2)) |
(/ 1/2 (pow y 2)) |
(pow x 2) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(* -4 (/ (pow y 2) (pow x 2))) |
(* (pow y 2) (- (* 16 (/ (pow y 2) (pow x 4))) (* 4 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (* (pow y 2) (+ (* -64 (/ (pow y 2) (pow x 6))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (* (pow y 2) (+ (* (pow y 2) (- (* 256 (/ (pow y 2) (pow x 8))) (* 64 (/ 1 (pow x 6))))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2))))) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ x y) |
(/ x y) |
(/ x y) |
(/ x y) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(* 2 (pow y 2)) |
(* 2 (pow y 2)) |
(* 2 (pow y 2)) |
(* 2 (pow y 2)) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
(* -8 (/ (pow y 2) (pow x 2))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
(* -8 y) |
(* -8 y) |
(* -8 y) |
(* -8 y) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
(* -4 (pow y 2)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* -4 y) |
(* -4 y) |
(* -4 y) |
(* -4 y) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/32 (/ (pow x 6) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/8 (/ (pow x 4) (pow y 4)))))) |
(* 1/4 (/ x (pow y 2))) |
(/ (+ (* -1/16 (/ (pow x 3) (pow y 2))) (* 1/4 x)) (pow y 2)) |
(/ (- (+ (* 1/64 (/ (pow x 5) (pow y 4))) (* 1/4 x)) (* 1/16 (/ (pow x 3) (pow y 2)))) (pow y 2)) |
(/ (- (+ (* -1/256 (/ (pow x 7) (pow y 6))) (* 1/4 x)) (+ (* -1/64 (/ (pow x 5) (pow y 4))) (* 1/16 (/ (pow x 3) (pow y 2))))) (pow y 2)) |
(* 4 (pow y 2)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(/ 1/2 y) |
(/ 1/2 y) |
(/ 1/2 y) |
(/ 1/2 y) |
(/ 1/2 (pow y 2)) |
(/ 1/2 (pow y 2)) |
(/ 1/2 (pow y 2)) |
(/ 1/2 (pow y 2)) |
(* 4 (pow y 2)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) 1) |
(- (* -1/16 (/ (pow x 4) (pow y 4))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (* 1/64 (/ (pow x 6) (pow y 6))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/16 (/ (pow x 4) (pow y 4)))))) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ x y) |
(/ x y) |
(/ x y) |
(/ x y) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(* 2 (pow y 2)) |
(* 2 (pow y 2)) |
(* 2 (pow y 2)) |
(* 2 (pow y 2)) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
(* -8 (/ (pow y 2) (pow x 2))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
(* -8 y) |
(* -8 y) |
(* -8 y) |
(* -8 y) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
(* -4 (pow y 2)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* -4 y) |
(* -4 y) |
(* -4 y) |
(* -4 y) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/32 (/ (pow x 6) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/8 (/ (pow x 4) (pow y 4)))))) |
(* 1/4 (/ x (pow y 2))) |
(/ (+ (* -1/16 (/ (pow x 3) (pow y 2))) (* 1/4 x)) (pow y 2)) |
(/ (- (+ (* 1/64 (/ (pow x 5) (pow y 4))) (* 1/4 x)) (* 1/16 (/ (pow x 3) (pow y 2)))) (pow y 2)) |
(/ (- (+ (* -1/256 (/ (pow x 7) (pow y 6))) (* 1/4 x)) (+ (* -1/64 (/ (pow x 5) (pow y 4))) (* 1/16 (/ (pow x 3) (pow y 2))))) (pow y 2)) |
(* 4 (pow y 2)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(/ 1/2 y) |
(/ 1/2 y) |
(/ 1/2 y) |
(/ 1/2 y) |
(/ 1/2 (pow y 2)) |
(/ 1/2 (pow y 2)) |
(/ 1/2 (pow y 2)) |
(/ 1/2 (pow y 2)) |
(* 4 (pow y 2)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) 1) |
(- (* -1/16 (/ (pow x 4) (pow y 4))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (* 1/64 (/ (pow x 6) (pow y 6))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/16 (/ (pow x 4) (pow y 4)))))) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ x y) |
(/ x y) |
(/ x y) |
(/ x y) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(* -8 (/ (pow y 2) (pow x 2))) |
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2)) |
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2)) |
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2)) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(* -4 (pow y 2)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(* 1/4 (/ x (pow y 2))) |
(* x (+ (* -1/16 (/ (pow x 2) (pow y 4))) (* 1/4 (/ 1 (pow y 2))))) |
(* x (+ (* (pow x 2) (- (* 1/64 (/ (pow x 2) (pow y 6))) (* 1/16 (/ 1 (pow y 4))))) (* 1/4 (/ 1 (pow y 2))))) |
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/256 (/ (pow x 2) (pow y 8))) (* 1/64 (/ 1 (pow y 6))))) (* 1/16 (/ 1 (pow y 4))))) (* 1/4 (/ 1 (pow y 2))))) |
(* 4 (pow y 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(* 4 (pow y 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (+ (* -1/16 (/ (pow x 2) (pow y 4))) (* 1/4 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/64 (/ (pow x 2) (pow y 6))) (* 1/16 (/ 1 (pow y 4))))) (* 1/4 (/ 1 (pow y 2))))) 1) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ x y) |
(/ x y) |
(/ x y) |
(/ x y) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4))))) (+ (* -16 (/ (pow y 4) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(- (+ 1 (+ (* -64 (/ (pow y 6) (pow x 6))) (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4)))))) (+ (* -16 (/ (pow y 4) (pow x 4))) (+ (* 4 (/ (pow y 2) (pow x 2))) (* 64 (/ (pow y 6) (pow x 6)))))) |
(/ 1 x) |
(/ (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) x) |
(/ (- (+ 1 (* 16 (/ (pow y 4) (pow x 4)))) (* 4 (/ (pow y 2) (pow x 2)))) x) |
(/ (- (+ 1 (* -64 (/ (pow y 6) (pow x 6)))) (+ (* -16 (/ (pow y 4) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) x) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* -4 (/ (pow y 2) (pow x 2))) |
(/ (+ (* -4 (pow y 2)) (* 16 (/ (pow y 4) (pow x 2)))) (pow x 2)) |
(/ (+ (* -64 (/ (pow y 6) (pow x 4))) (+ (* -4 (pow y 2)) (* 16 (/ (pow y 4) (pow x 2))))) (pow x 2)) |
(/ (+ (* -64 (/ (pow y 6) (pow x 4))) (+ (* -4 (pow y 2)) (+ (* 16 (/ (pow y 4) (pow x 2))) (* 256 (/ (pow y 8) (pow x 6)))))) (pow x 2)) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ (pow x 2) y) |
(/ x y) |
(/ x y) |
(/ x y) |
(/ x y) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
(* -8 (/ y x)) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4))))) (+ (* -16 (/ (pow y 4) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(- (+ 1 (+ (* -64 (/ (pow y 6) (pow x 6))) (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4)))))) (+ (* -16 (/ (pow y 4) (pow x 4))) (+ (* 4 (/ (pow y 2) (pow x 2))) (* 64 (/ (pow y 6) (pow x 6)))))) |
(/ 1 x) |
(* -1 (/ (- (* 4 (/ (pow y 2) (pow x 2))) 1) x)) |
(* -1 (/ (- (* -16 (/ (pow y 4) (pow x 4))) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) x)) |
(* -1 (/ (- (* 64 (/ (pow y 6) (pow x 6))) (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4)))))) x)) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* -4 (/ (pow y 2) (pow x 2))) |
(/ (+ (* -4 (pow y 2)) (* 16 (/ (pow y 4) (pow x 2)))) (pow x 2)) |
(/ (+ (* -64 (/ (pow y 6) (pow x 4))) (+ (* -4 (pow y 2)) (* 16 (/ (pow y 4) (pow x 2))))) (pow x 2)) |
(/ (+ (* -64 (/ (pow y 6) (pow x 4))) (+ (* -4 (pow y 2)) (+ (* 16 (/ (pow y 4) (pow x 2))) (* 256 (/ (pow y 8) (pow x 6)))))) (pow x 2)) |
| Outputs |
|---|
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 32 binary64) y) (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64)) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) |
(/ (pow x 2) y) |
(/.f64 (*.f64 x x) y) |
(/ (pow x 2) y) |
(/.f64 (*.f64 x x) y) |
(/ (pow x 2) y) |
(/.f64 (*.f64 x x) y) |
(/ (pow x 2) y) |
(/.f64 (*.f64 x x) y) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 32 binary64) y) (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64)) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) |
(* 2 (pow y 2)) |
(*.f64 (*.f64 y y) #s(literal 2 binary64)) |
(* 2 (pow y 2)) |
(*.f64 (*.f64 y y) #s(literal 2 binary64)) |
(* 2 (pow y 2)) |
(*.f64 (*.f64 y y) #s(literal 2 binary64)) |
(* 2 (pow y 2)) |
(*.f64 (*.f64 y y) #s(literal 2 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 32 binary64) y) (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)) |
(* -8 (/ y x)) |
(*.f64 (/.f64 y x) #s(literal -8 binary64)) |
(* -8 (/ y x)) |
(*.f64 (/.f64 y x) #s(literal -8 binary64)) |
(* -8 (/ y x)) |
(*.f64 (/.f64 y x) #s(literal -8 binary64)) |
(* -8 (/ y x)) |
(*.f64 (/.f64 y x) #s(literal -8 binary64)) |
(* -8 y) |
(*.f64 y #s(literal -8 binary64)) |
(* -8 y) |
(*.f64 y #s(literal -8 binary64)) |
(* -8 y) |
(*.f64 y #s(literal -8 binary64)) |
(* -8 y) |
(*.f64 y #s(literal -8 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 32 binary64) y) (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64)) |
(pow x 2) |
(*.f64 x x) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) |
(* -4 y) |
(*.f64 #s(literal -4 binary64) y) |
(* -4 y) |
(*.f64 #s(literal -4 binary64) y) |
(* -4 y) |
(*.f64 #s(literal -4 binary64) y) |
(* -4 y) |
(*.f64 #s(literal -4 binary64) y) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 32 binary64) y) (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(+ (* -4 (/ (pow y 2) (pow x 3))) (/ 1 x)) |
(/.f64 (fma.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) x) |
(+ (* (pow y 2) (- (* 16 (/ (pow y 2) (pow x 5))) (* 4 (/ 1 (pow x 3))))) (/ 1 x)) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 5 binary64))) y) y (/.f64 #s(literal -4 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 y y) (/.f64 #s(literal 1 binary64) x)) |
(+ (* (pow y 2) (- (* (pow y 2) (+ (* -64 (/ (pow y 2) (pow x 7))) (* 16 (/ 1 (pow x 5))))) (* 4 (/ 1 (pow x 3))))) (/ 1 x)) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -64 binary64) y) (/.f64 y (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 y y) (/.f64 #s(literal -4 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 y y) (/.f64 #s(literal 1 binary64) x)) |
(pow x 2) |
(*.f64 x x) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(* 4 y) |
(*.f64 #s(literal 4 binary64) y) |
(* 4 y) |
(*.f64 #s(literal 4 binary64) y) |
(* 4 y) |
(*.f64 #s(literal 4 binary64) y) |
(* 4 y) |
(*.f64 #s(literal 4 binary64) y) |
(/ 1/2 y) |
(/.f64 #s(literal 1/2 binary64) y) |
(/ 1/2 y) |
(/.f64 #s(literal 1/2 binary64) y) |
(/ 1/2 y) |
(/.f64 #s(literal 1/2 binary64) y) |
(/ 1/2 y) |
(/.f64 #s(literal 1/2 binary64) y) |
(/ 1/2 (pow y 2)) |
(/.f64 (/.f64 #s(literal 1/2 binary64) y) y) |
(/ 1/2 (pow y 2)) |
(/.f64 (/.f64 #s(literal 1/2 binary64) y) y) |
(/ 1/2 (pow y 2)) |
(/.f64 (/.f64 #s(literal 1/2 binary64) y) y) |
(/ 1/2 (pow y 2)) |
(/.f64 (/.f64 #s(literal 1/2 binary64) y) y) |
(pow x 2) |
(*.f64 x x) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x)) |
(* -4 (/ (pow y 2) (pow x 2))) |
(*.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x)) |
(* (pow y 2) (- (* 16 (/ (pow y 2) (pow x 4))) (* 4 (/ 1 (pow x 2))))) |
(*.f64 (fma.f64 (*.f64 (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 #s(literal -4 binary64) (*.f64 x x))) (*.f64 y y)) |
(* (pow y 2) (- (* (pow y 2) (+ (* -64 (/ (pow y 2) (pow x 6))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -64 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 #s(literal -4 binary64) (*.f64 x x))) (*.f64 y y)) |
(* (pow y 2) (- (* (pow y 2) (+ (* (pow y 2) (- (* 256 (/ (pow y 2) (pow x 8))) (* 64 (/ 1 (pow x 6))))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2))))) |
(*.f64 (fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 256 binary64) y) (/.f64 y (pow.f64 x #s(literal 8 binary64))) (/.f64 #s(literal -64 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (*.f64 (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 #s(literal -4 binary64) (*.f64 x x)))) (*.f64 y y)) |
-1 |
#s(literal -1 binary64) |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
(fma.f64 (*.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)))) |
-1 |
#s(literal -1 binary64) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)) |
(/ (pow x 2) y) |
(/.f64 (*.f64 x x) y) |
(/ (pow x 2) y) |
(/.f64 (*.f64 x x) y) |
(/ (pow x 2) y) |
(/.f64 (*.f64 x x) y) |
(/ (pow x 2) y) |
(/.f64 (*.f64 x x) y) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
(/ x y) |
(/.f64 x y) |
-1 |
#s(literal -1 binary64) |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
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(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)) |
(* -8 (/ y x)) |
(*.f64 (/.f64 y x) #s(literal -8 binary64)) |
(* -8 (/ y x)) |
(*.f64 (/.f64 y x) #s(literal -8 binary64)) |
(* -8 (/ y x)) |
(*.f64 (/.f64 y x) #s(literal -8 binary64)) |
(* -8 (/ y x)) |
(*.f64 (/.f64 y x) #s(literal -8 binary64)) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal -4 binary64) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 (pow.f64 (*.f64 y y) #s(literal 3 binary64)) #s(literal -8 binary64)) (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal -4 binary64) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (fma.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (fma.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (fma.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) (*.f64 x x)) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4))))) (+ (* -16 (/ (pow y 4) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 32 binary64) (fma.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)))) |
(- (+ 1 (+ (* -64 (/ (pow y 6) (pow x 6))) (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4)))))) (+ (* -16 (/ (pow y 4) (pow x 4))) (+ (* 4 (/ (pow y 2) (pow x 2))) (* 64 (/ (pow y 6) (pow x 6)))))) |
(fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -64 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -64 binary64) (fma.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 32 binary64) (fma.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)))))) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(* -1 (/ (- (* 4 (/ (pow y 2) (pow x 2))) 1) x)) |
(/.f64 (fma.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) x) |
(* -1 (/ (- (* -16 (/ (pow y 4) (pow x 4))) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) x)) |
(fma.f64 (/.f64 #s(literal -4 binary64) (pow.f64 x #s(literal 3 binary64))) (*.f64 y y) (/.f64 (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) x)) |
(* -1 (/ (- (* 64 (/ (pow y 6) (pow x 6))) (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (pow y 4) (pow x 4)))))) x)) |
(/.f64 (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal -64 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))) x) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (*.f64 (fma.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 y y) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (*.f64 (fma.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 y y) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (*.f64 (fma.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 y y) #s(literal 1 binary64)) x) x) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (*.f64 (fma.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 y y) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (*.f64 (fma.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 y y) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(*.f64 (*.f64 (fma.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 y y) #s(literal 1 binary64)) x) x) |
(* -4 (/ (pow y 2) (pow x 2))) |
(*.f64 (/.f64 (*.f64 #s(literal -4 binary64) y) x) (/.f64 y x)) |
(/ (+ (* -4 (pow y 2)) (* 16 (/ (pow y 4) (pow x 2)))) (pow x 2)) |
(/.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) x) (/.f64 #s(literal 16 binary64) x) (*.f64 #s(literal -4 binary64) (*.f64 y y))) (*.f64 x x)) |
(/ (+ (* -64 (/ (pow y 6) (pow x 4))) (+ (* -4 (pow y 2)) (* 16 (/ (pow y 4) (pow x 2))))) (pow x 2)) |
(/.f64 (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal -64 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) x) (/.f64 #s(literal 16 binary64) x) (*.f64 #s(literal -4 binary64) (*.f64 y y)))) (*.f64 x x)) |
(/ (+ (* -64 (/ (pow y 6) (pow x 4))) (+ (* -4 (pow y 2)) (+ (* 16 (/ (pow y 4) (pow x 2))) (* 256 (/ (pow y 8) (pow x 6)))))) (pow x 2)) |
(/.f64 (fma.f64 (pow.f64 y #s(literal 8 binary64)) (/.f64 #s(literal 256 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal -64 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) x) (/.f64 #s(literal 16 binary64) x) (*.f64 #s(literal -4 binary64) (*.f64 y y))))) (*.f64 x x)) |
| 4 798× | lower-*.f32 |
| 4 780× | lower-*.f64 |
| 4 274× | lower-/.f32 |
| 4 258× | lower-/.f64 |
| 3 830× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 42 | 255 |
| 0 | 73 | 239 |
| 1 | 302 | 234 |
| 2 | 2191 | 232 |
| 0 | 8365 | 230 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
(fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) |
(*.f64 (/.f64 x y) x) |
(/.f64 x y) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64))) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64)) |
(*.f64 x x) |
(*.f64 (*.f64 y #s(literal 2 binary64)) y) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) |
(fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) |
(/.f64 (*.f64 #s(literal -8 binary64) y) x) |
(*.f64 #s(literal -8 binary64) y) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) |
(fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) |
(*.f64 #s(literal -4 binary64) y) |
(fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) |
(/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(*.f64 #s(literal 4 binary64) y) |
(/.f64 #s(literal 1/2 binary64) y) |
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) |
(fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)) |
(/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
| Outputs |
|---|
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Compiled 52 226 to 2 532 computations (95.2% saved)
10 alts after pruning (4 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 654 | 2 | 1 656 |
| Fresh | 1 | 2 | 3 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 2 | 2 |
| Total | 1 656 | 10 | 1 666 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 48.9% | (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) |
| ✓ | 48.4% | (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) |
| ▶ | 48.4% | (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) |
| ✓ | 55.4% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
| ✓ | 48.7% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64))) |
| ▶ | 44.3% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) |
| ▶ | 26.8% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)))) |
| ▶ | 25.4% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) |
| ✓ | 46.3% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) |
| ✓ | 53.5% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
Compiled 130 to 92 computations (29.2% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 #s(literal 4 binary64) y) | |
| cost-diff | 0 | (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) | |
| cost-diff | 0 | (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))) | |
| cost-diff | 704 | (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) | |
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | (*.f64 #s(literal -8 binary64) y) | |
| cost-diff | 0 | (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) | |
| cost-diff | 0 | (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) | |
| cost-diff | 0 | #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y))) | |
| cost-diff | 0 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)))) | |
| cost-diff | 64 | (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) | |
| cost-diff | 0 | (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) | |
| cost-diff | 0 | #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x)) | |
| cost-diff | 0 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) | |
| cost-diff | 320 | (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x) |
| 3 784× | lower-fma.f32 |
| 3 774× | lower-fma.f64 |
| 3 164× | lower-*.f32 |
| 3 150× | lower-*.f64 |
| 2 542× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 47 | 335 |
| 0 | 73 | 334 |
| 1 | 135 | 329 |
| 2 | 224 | 327 |
| 3 | 385 | 321 |
| 4 | 764 | 321 |
| 5 | 1165 | 321 |
| 6 | 2025 | 321 |
| 7 | 4204 | 321 |
| 8 | 6395 | 313 |
| 0 | 8125 | 308 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) |
#s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x)) |
(/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x) |
(/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) |
(fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) |
(*.f64 y #s(literal -8 binary64)) |
y |
#s(literal -8 binary64) |
(*.f64 x x) |
x |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)))) |
#s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
(*.f64 (neg.f64 y) y) |
(neg.f64 y) |
y |
(*.f64 y y) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64)) |
(*.f64 #s(literal -8 binary64) y) |
#s(literal -8 binary64) |
y |
(/.f64 y (*.f64 x x)) |
(*.f64 x x) |
x |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) |
#s(literal 1 binary64) |
(/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))) |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(*.f64 #s(literal 4 binary64) y) |
#s(literal 4 binary64) |
y |
(*.f64 x x) |
x |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(*.f64 y y) |
#s(literal -4 binary64) |
| Outputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (fma.f64 (/.f64 (/.f64 #s(literal -8 binary64) x) x) (*.f64 y y) #s(literal 1 binary64)))) |
#s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x)) |
#s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (fma.f64 (/.f64 (/.f64 #s(literal -8 binary64) x) x) (*.f64 y y) #s(literal 1 binary64))) |
(/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x) |
(fma.f64 (/.f64 (/.f64 #s(literal -8 binary64) x) x) (*.f64 y y) #s(literal 1 binary64)) |
(/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) |
(/.f64 (fma.f64 (*.f64 #s(literal -8 binary64) y) y (*.f64 x x)) x) |
(fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) |
(fma.f64 (*.f64 #s(literal -8 binary64) y) y (*.f64 x x)) |
(*.f64 y #s(literal -8 binary64)) |
(*.f64 #s(literal -8 binary64) y) |
y |
#s(literal -8 binary64) |
(*.f64 x x) |
x |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)))) |
#s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y))) |
#s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
(*.f64 (neg.f64 y) y) |
(neg.f64 y) |
y |
(*.f64 y y) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (/.f64 #s(literal -8 binary64) x) x) (*.f64 y y) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64)) |
(fma.f64 (/.f64 (/.f64 #s(literal -8 binary64) x) x) (*.f64 y y) #s(literal 1 binary64)) |
(*.f64 #s(literal -8 binary64) y) |
#s(literal -8 binary64) |
y |
(/.f64 y (*.f64 x x)) |
(/.f64 (/.f64 y x) x) |
(*.f64 x x) |
x |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) |
(/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 x x (*.f64 (*.f64 #s(literal 4 binary64) y) y))) |
#s(literal 1 binary64) |
(/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))) |
(/.f64 (fma.f64 x x (*.f64 (*.f64 #s(literal 4 binary64) y) y)) (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))) |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(fma.f64 x x (*.f64 (*.f64 #s(literal 4 binary64) y) y)) |
(*.f64 #s(literal 4 binary64) y) |
#s(literal 4 binary64) |
y |
(*.f64 x x) |
x |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) |
(*.f64 y y) |
#s(literal -4 binary64) |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.00390625 | (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) | |
| accuracy | 0.02734375 | (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) | |
| accuracy | 2.2578021791510294 | (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) | |
| accuracy | 32.42458050344741 | (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))) | |
| accuracy | 0 | (*.f64 #s(literal -8 binary64) y) | |
| accuracy | 3.316031790580409 | (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64)) | |
| accuracy | 6.392437058799943 | (/.f64 y (*.f64 x x)) | |
| accuracy | 33.24719163352617 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) | |
| accuracy | 0 | #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y))) | |
| accuracy | 1.249986238027801 | (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) | |
| accuracy | 24.16641026512216 | (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) | |
| accuracy | 28.559047546275004 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)))) | |
| accuracy | 1.2577994262524468 | (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) | |
| accuracy | 2.1728765808487642 | (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x) | |
| accuracy | 17.333552824974678 | (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) | |
| accuracy | 33.24719163352617 | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) |
| 123.0ms | 256× | 0 | valid |
Compiled 260 to 47 computations (81.9% saved)
ival-neg: 36.0ms (39.1% of total)ival-mult: 27.0ms (29.4% of total)ival-div: 18.0ms (19.6% of total)ival-add: 8.0ms (8.7% of total)ival-sub: 1.0ms (1.1% of total)exact: 1.0ms (1.1% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x) (patch (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x)) (patch #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) (patch (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) #<representation binary64>) () ()) |
#s(alt (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) (patch (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y))) (patch #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal -8 binary64) y) (patch (*.f64 #s(literal -8 binary64) y) #<representation binary64>) () ()) |
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) #<representation binary64>) () ()) |
#s(alt (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 4 binary64) y) (patch (*.f64 #s(literal 4 binary64) y) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) (patch (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (/.f64 y (*.f64 x x)) (patch (/.f64 y (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) (patch (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x) (patch (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x) (patch (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x) (patch (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x) (patch (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x)) (patch #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x)) (patch #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x)) (patch #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x)) (patch #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) (patch (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* -8 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) (patch (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* -8 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) (patch (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* -8 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) (patch (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (/ (pow x 2) (pow y 2))) (taylor 0 y) (#s(alt (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) (patch (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) (patch (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) (patch (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) (patch (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) #<representation binary64>) () ())) ()) |
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#s(alt (- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor -inf x) (#s(alt (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* 4 (/ (pow y 2) (pow x 2)))) (* -4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* 4 (/ (* (pow y 2) (- (* 4 (pow y 2)) (* -4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (* -4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (+ (* 4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* 4 (pow y 2)) (* -4 (pow y 2)))) (pow x 6))))) (+ (* -4 (/ (* (pow y 2) (- (* 4 (pow y 2)) (* -4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) (patch (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) (patch (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) (patch (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) (patch (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (/ y (pow x 2)) (taylor -inf x) (#s(alt (/.f64 y (*.f64 x x)) (patch (/.f64 y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (/ y (pow x 2)) (taylor -inf x) (#s(alt (/.f64 y (*.f64 x x)) (patch (/.f64 y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (/ y (pow x 2)) (taylor -inf x) (#s(alt (/.f64 y (*.f64 x x)) (patch (/.f64 y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (/ y (pow x 2)) (taylor -inf x) (#s(alt (/.f64 y (*.f64 x x)) (patch (/.f64 y (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) (patch (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) (patch (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) (patch (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) (patch (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 10.0ms | y | @ | -inf | ((/ (/ (+ (* (* y -8) y) (* x x)) x) x) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* -8 y) x) (/ y x)) 1) (/ (+ (* (* y -8) y) (* x x)) x) (/ (+ (* (* 1/2 x) x) (* (neg y) y)) (* y y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (+ (* (* 1/2 x) x) (* (neg y) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* -8 y) (/ y (* x x))) 1) (* -8 y) (* x x) (/ 1 (/ (+ (* (* 4 y) y) (* x x)) (+ (* (* y y) -4) (* x x)))) (/ (+ (* (* 4 y) y) (* x x)) (+ (* (* y y) -4) (* x x))) (+ (* (* 4 y) y) (* x x)) (* 4 y) (+ (* (* y -8) y) (* x x)) (/ y (* x x)) (+ (* (* y y) -4) (* x x))) |
| 4.0ms | y | @ | 0 | ((/ (/ (+ (* (* y -8) y) (* x x)) x) x) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* -8 y) x) (/ y x)) 1) (/ (+ (* (* y -8) y) (* x x)) x) (/ (+ (* (* 1/2 x) x) (* (neg y) y)) (* y y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (+ (* (* 1/2 x) x) (* (neg y) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* -8 y) (/ y (* x x))) 1) (* -8 y) (* x x) (/ 1 (/ (+ (* (* 4 y) y) (* x x)) (+ (* (* y y) -4) (* x x)))) (/ (+ (* (* 4 y) y) (* x x)) (+ (* (* y y) -4) (* x x))) (+ (* (* 4 y) y) (* x x)) (* 4 y) (+ (* (* y -8) y) (* x x)) (/ y (* x x)) (+ (* (* y y) -4) (* x x))) |
| 3.0ms | y | @ | inf | ((/ (/ (+ (* (* y -8) y) (* x x)) x) x) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* -8 y) x) (/ y x)) 1) (/ (+ (* (* y -8) y) (* x x)) x) (/ (+ (* (* 1/2 x) x) (* (neg y) y)) (* y y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (+ (* (* 1/2 x) x) (* (neg y) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* -8 y) (/ y (* x x))) 1) (* -8 y) (* x x) (/ 1 (/ (+ (* (* 4 y) y) (* x x)) (+ (* (* y y) -4) (* x x)))) (/ (+ (* (* 4 y) y) (* x x)) (+ (* (* y y) -4) (* x x))) (+ (* (* 4 y) y) (* x x)) (* 4 y) (+ (* (* y -8) y) (* x x)) (/ y (* x x)) (+ (* (* y y) -4) (* x x))) |
| 3.0ms | x | @ | inf | ((/ (/ (+ (* (* y -8) y) (* x x)) x) x) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* -8 y) x) (/ y x)) 1) (/ (+ (* (* y -8) y) (* x x)) x) (/ (+ (* (* 1/2 x) x) (* (neg y) y)) (* y y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (+ (* (* 1/2 x) x) (* (neg y) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* -8 y) (/ y (* x x))) 1) (* -8 y) (* x x) (/ 1 (/ (+ (* (* 4 y) y) (* x x)) (+ (* (* y y) -4) (* x x)))) (/ (+ (* (* 4 y) y) (* x x)) (+ (* (* y y) -4) (* x x))) (+ (* (* 4 y) y) (* x x)) (* 4 y) (+ (* (* y -8) y) (* x x)) (/ y (* x x)) (+ (* (* y y) -4) (* x x))) |
| 2.0ms | x | @ | 0 | ((/ (/ (+ (* (* y -8) y) (* x x)) x) x) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* -8 y) x) (/ y x)) 1) (/ (+ (* (* y -8) y) (* x x)) x) (/ (+ (* (* 1/2 x) x) (* (neg y) y)) (* y y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (+ (* (* 1/2 x) x) (* (neg y) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* -8 y) (/ y (* x x))) 1) (* -8 y) (* x x) (/ 1 (/ (+ (* (* 4 y) y) (* x x)) (+ (* (* y y) -4) (* x x)))) (/ (+ (* (* 4 y) y) (* x x)) (+ (* (* y y) -4) (* x x))) (+ (* (* 4 y) y) (* x x)) (* 4 y) (+ (* (* y -8) y) (* x x)) (/ y (* x x)) (+ (* (* y y) -4) (* x x))) |
| 1× | egg-herbie |
| 22 278× | lower-fma.f64 |
| 22 278× | lower-fma.f32 |
| 5 262× | lower-*.f64 |
| 5 262× | lower-*.f32 |
| 2 254× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 205 | 5217 |
| 1 | 607 | 4917 |
| 2 | 1886 | 4607 |
| 3 | 5888 | 4459 |
| 0 | 8139 | 4117 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
x |
(+ x (* -8 (/ (pow y 2) x))) |
(+ x (* -8 (/ (pow y 2) x))) |
(+ x (* -8 (/ (pow y 2) x))) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(* 1/2 (pow x 2)) |
(+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) |
(+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) |
(+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(* -8 y) |
(* -8 y) |
(* -8 y) |
(* -8 y) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
1 |
(+ 1 (* 8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* (pow y 2) (+ (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(+ 1 (* (pow y 2) (+ (* (pow y 2) (+ (* 128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(pow x 2) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(pow x 2) |
(+ (* -8 (pow y 2)) (pow x 2)) |
(+ (* -8 (pow y 2)) (pow x 2)) |
(+ (* -8 (pow y 2)) (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(pow x 2) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(* -8 (/ (pow y 2) (pow x 2))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
(* -8 (/ (pow y 2) (pow x 2))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* -8 (/ (pow y 2) x)) |
(* (pow y 2) (- (/ x (pow y 2)) (* 8 (/ 1 x)))) |
(* (pow y 2) (- (/ x (pow y 2)) (* 8 (/ 1 x)))) |
(* (pow y 2) (- (/ x (pow y 2)) (* 8 (/ 1 x)))) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(* -1 (pow y 2)) |
(* (pow y 2) (- (* 1/2 (/ (pow x 2) (pow y 2))) 1)) |
(* (pow y 2) (- (* 1/2 (/ (pow x 2) (pow y 2))) 1)) |
(* (pow y 2) (- (* 1/2 (/ (pow x 2) (pow y 2))) 1)) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
(* -8 (/ (pow y 2) (pow x 2))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* -8 y) |
(* -8 y) |
(* -8 y) |
(* -8 y) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
-1 |
(- (* -1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* 1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* -1/4 (pow x 2)) (* 1/4 (pow x 2)))) (pow y 4)))) (+ 1 (* 1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/16 (/ (* (pow x 4) (- (* -1/4 (pow x 2)) (* 1/4 (pow x 2)))) (pow y 6)))) (+ 1 (+ (* -1/4 (/ (* (pow x 2) (- (* -1/4 (pow x 2)) (* 1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))))) |
(* 4 (pow y 2)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(* -8 (pow y 2)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 8)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 8)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 8)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(* -4 (pow y 2)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* -8 (/ (pow y 2) (pow x 2))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
(* -8 (/ (pow y 2) (pow x 2))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* -8 (/ (pow y 2) x)) |
(* (pow y 2) (- (/ x (pow y 2)) (* 8 (/ 1 x)))) |
(* (pow y 2) (- (/ x (pow y 2)) (* 8 (/ 1 x)))) |
(* (pow y 2) (- (/ x (pow y 2)) (* 8 (/ 1 x)))) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(* -1 (pow y 2)) |
(* (pow y 2) (- (* 1/2 (/ (pow x 2) (pow y 2))) 1)) |
(* (pow y 2) (- (* 1/2 (/ (pow x 2) (pow y 2))) 1)) |
(* (pow y 2) (- (* 1/2 (/ (pow x 2) (pow y 2))) 1)) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
(* -8 (/ (pow y 2) (pow x 2))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(* -8 y) |
(* -8 y) |
(* -8 y) |
(* -8 y) |
-1 |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
-1 |
(- (* -1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* 1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* -1/4 (pow x 2)) (* 1/4 (pow x 2)))) (pow y 4)))) (+ 1 (* 1/4 (/ (pow x 2) (pow y 2))))) |
(- (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/16 (/ (* (pow x 4) (- (* -1/4 (pow x 2)) (* 1/4 (pow x 2)))) (pow y 6)))) (+ 1 (+ (* -1/4 (/ (* (pow x 2) (- (* -1/4 (pow x 2)) (* 1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))))) |
(* 4 (pow y 2)) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(* 4 y) |
(* -8 (pow y 2)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 8)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 8)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 8)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(* -4 (pow y 2)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) |
(* -8 (/ (pow y 2) (pow x 2))) |
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2)) |
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2)) |
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2)) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(* -8 (/ (pow y 2) (pow x 2))) |
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2)) |
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2)) |
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2)) |
(* -8 (/ (pow y 2) x)) |
(/ (+ (* -8 (pow y 2)) (pow x 2)) x) |
(/ (+ (* -8 (pow y 2)) (pow x 2)) x) |
(/ (+ (* -8 (pow y 2)) (pow x 2)) x) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(* -1 (pow y 2)) |
(+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) |
(+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) |
(+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(* -8 (/ (pow y 2) (pow x 2))) |
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2)) |
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2)) |
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2)) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
-1 |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1) |
-1 |
(- (* -1/2 (/ (pow x 2) (pow y 2))) 1) |
(- (* (pow x 2) (- (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1) |
(* 4 (pow y 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(* -8 (pow y 2)) |
(+ (* -8 (pow y 2)) (pow x 2)) |
(+ (* -8 (pow y 2)) (pow x 2)) |
(+ (* -8 (pow y 2)) (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(* -4 (pow y 2)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
x |
(* x (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) |
(* x (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) |
(* x (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* 1/2 (pow x 2)) |
(* (pow x 2) (+ 1/2 (* -1 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1/2 (* -1 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1/2 (* -1 (/ (pow y 2) (pow x 2))))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
1 |
(- (+ 1 (* 4 (/ (pow y 2) (pow x 2)))) (* -4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* 4 (/ (* (pow y 2) (- (* 4 (pow y 2)) (* -4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (* -4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* 4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* 4 (pow y 2)) (* -4 (pow y 2)))) (pow x 6))))) (+ (* -4 (/ (* (pow y 2) (- (* 4 (pow y 2)) (* -4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
x |
(* -1 (* x (- (* 8 (/ (pow y 2) (pow x 2))) 1))) |
(* -1 (* x (- (* 8 (/ (pow y 2) (pow x 2))) 1))) |
(* -1 (* x (- (* 8 (/ (pow y 2) (pow x 2))) 1))) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(* 1/2 (pow x 2)) |
(* (pow x 2) (+ 1/2 (* -1 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1/2 (* -1 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1/2 (* -1 (/ (pow y 2) (pow x 2))))) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
1 |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
1 |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
1 |
(- (+ 1 (* 4 (/ (pow y 2) (pow x 2)))) (* -4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* 4 (/ (* (pow y 2) (- (* 4 (pow y 2)) (* -4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (* -4 (/ (pow y 2) (pow x 2)))) |
(- (+ 1 (+ (* 4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* 4 (pow y 2)) (* -4 (pow y 2)))) (pow x 6))))) (+ (* -4 (/ (* (pow y 2) (- (* 4 (pow y 2)) (* -4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(/ y (pow x 2)) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
| Outputs |
|---|
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 (/.f64 #s(literal -8 binary64) x) x)) (*.f64 y y) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 (/.f64 #s(literal -8 binary64) x) x)) (*.f64 y y) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
x |
(+ x (* -8 (/ (pow y 2) x))) |
(fma.f64 (/.f64 (*.f64 y y) x) #s(literal -8 binary64) x) |
(+ x (* -8 (/ (pow y 2) x))) |
(fma.f64 (/.f64 (*.f64 y y) x) #s(literal -8 binary64) x) |
(+ x (* -8 (/ (pow y 2) x))) |
(fma.f64 (/.f64 (*.f64 y y) x) #s(literal -8 binary64) x) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 (/.f64 #s(literal -8 binary64) x) x)) (*.f64 y y) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 (/.f64 #s(literal -8 binary64) x) x)) (*.f64 y y) #s(literal 1 binary64)) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
(* 1/2 (pow x 2)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x x)) |
(+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) |
(neg.f64 (fma.f64 y y (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))) |
(+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) |
(neg.f64 (fma.f64 y y (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))) |
(+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) |
(neg.f64 (fma.f64 y y (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 (/.f64 #s(literal -8 binary64) x) x)) (*.f64 y y) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 (/.f64 #s(literal -8 binary64) x) x)) (*.f64 y y) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(* -8 y) |
(*.f64 y #s(literal -8 binary64)) |
(* -8 y) |
(*.f64 y #s(literal -8 binary64)) |
(* -8 y) |
(*.f64 y #s(literal -8 binary64)) |
(* -8 y) |
(*.f64 y #s(literal -8 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 (/.f64 #s(literal -8 binary64) x) x)) (*.f64 y y) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 (/.f64 #s(literal -8 binary64) x) x)) (*.f64 y y) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 #s(literal 8 binary64) x) (/.f64 (*.f64 y y) x) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (+ (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 #s(literal 8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64)) |
(+ 1 (* (pow y 2) (+ (* (pow y 2) (+ (* 128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) |
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (/.f64 #s(literal 8 binary64) x) (/.f64 (*.f64 y y) x) #s(literal 1 binary64))) |
(pow x 2) |
(*.f64 x x) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(+ (* 4 (pow y 2)) (pow x 2)) |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(* 4 y) |
(*.f64 #s(literal 4 binary64) y) |
(* 4 y) |
(*.f64 #s(literal 4 binary64) y) |
(* 4 y) |
(*.f64 #s(literal 4 binary64) y) |
(* 4 y) |
(*.f64 #s(literal 4 binary64) y) |
(pow x 2) |
(*.f64 x x) |
(+ (* -8 (pow y 2)) (pow x 2)) |
(fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) |
(+ (* -8 (pow y 2)) (pow x 2)) |
(fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) |
(+ (* -8 (pow y 2)) (pow x 2)) |
(fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(pow x 2) |
(*.f64 x x) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) |
(+ (* -4 (pow y 2)) (pow x 2)) |
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) |
(* -8 (/ (pow y 2) (pow x 2))) |
(*.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x)) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
-1 |
#s(literal -1 binary64) |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
(fma.f64 (*.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)))) |
(* -8 (/ (pow y 2) (pow x 2))) |
(*.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x)) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(* -8 (/ (pow y 2) x)) |
(*.f64 (/.f64 (*.f64 y y) x) #s(literal -8 binary64)) |
(* (pow y 2) (- (/ x (pow y 2)) (* 8 (/ 1 x)))) |
(*.f64 (*.f64 (-.f64 (/.f64 x (*.f64 y y)) (/.f64 #s(literal 8 binary64) x)) y) y) |
(* (pow y 2) (- (/ x (pow y 2)) (* 8 (/ 1 x)))) |
(*.f64 (*.f64 (-.f64 (/.f64 x (*.f64 y y)) (/.f64 #s(literal 8 binary64) x)) y) y) |
(* (pow y 2) (- (/ x (pow y 2)) (* 8 (/ 1 x)))) |
(*.f64 (*.f64 (-.f64 (/.f64 x (*.f64 y y)) (/.f64 #s(literal 8 binary64) x)) y) y) |
-1 |
#s(literal -1 binary64) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
-1 |
#s(literal -1 binary64) |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64))) |
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) |
(fma.f64 (*.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)))) |
-1 |
#s(literal -1 binary64) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
(* -1 (pow y 2)) |
(*.f64 (neg.f64 y) y) |
(* (pow y 2) (- (* 1/2 (/ (pow x 2) (pow y 2))) 1)) |
(*.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) (*.f64 y y)) |
(* (pow y 2) (- (* 1/2 (/ (pow x 2) (pow y 2))) 1)) |
(*.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) (*.f64 y y)) |
(* (pow y 2) (- (* 1/2 (/ (pow x 2) (pow y 2))) 1)) |
(*.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) (*.f64 y y)) |
-1 |
#s(literal -1 binary64) |
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
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(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 (pow.f64 (*.f64 y y) #s(literal 3 binary64)) #s(literal -8 binary64)) (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)))) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* 4 (/ (pow y 2) (pow x 2)))) (* -4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 #s(literal 8 binary64) x) (/.f64 (*.f64 y y) x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* 4 (/ (* (pow y 2) (- (* 4 (pow y 2)) (* -4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (* -4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 4 binary64) (fma.f64 (/.f64 #s(literal 8 binary64) x) (/.f64 (*.f64 y y) x) #s(literal 1 binary64))) |
(- (+ 1 (+ (* 4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* 4 (pow y 2)) (* -4 (pow y 2)))) (pow x 6))))) (+ (* -4 (/ (* (pow y 2) (- (* 4 (pow y 2)) (* -4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 (pow.f64 (*.f64 y y) #s(literal 3 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 4 binary64) (fma.f64 (/.f64 #s(literal 8 binary64) x) (/.f64 (*.f64 y y) x) #s(literal 1 binary64)))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) |
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) |
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 (pow.f64 (*.f64 y y) #s(literal 3 binary64)) #s(literal -8 binary64)) (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
x |
(* -1 (* x (- (* 8 (/ (pow y 2) (pow x 2))) 1))) |
(fma.f64 (*.f64 (/.f64 (*.f64 y y) x) #s(literal -8 binary64)) #s(literal 1 binary64) x) |
(* -1 (* x (- (* 8 (/ (pow y 2) (pow x 2))) 1))) |
(fma.f64 (*.f64 (/.f64 (*.f64 y y) x) #s(literal -8 binary64)) #s(literal 1 binary64) x) |
(* -1 (* x (- (* 8 (/ (pow y 2) (pow x 2))) 1))) |
(fma.f64 (*.f64 (/.f64 (*.f64 y y) x) #s(literal -8 binary64)) #s(literal 1 binary64) x) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y)) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 (pow.f64 (*.f64 y y) #s(literal 3 binary64)) #s(literal -8 binary64)) (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)))) |
(* 1/2 (/ (pow x 2) (pow y 2))) |
(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y)) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)) |
(* 1/2 (pow x 2)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/2 (* -1 (/ (pow y 2) (pow x 2))))) |
(neg.f64 (fma.f64 y y (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))) |
(* (pow x 2) (+ 1/2 (* -1 (/ (pow y 2) (pow x 2))))) |
(neg.f64 (fma.f64 y y (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))) |
(* (pow x 2) (+ 1/2 (* -1 (/ (pow y 2) (pow x 2))))) |
(neg.f64 (fma.f64 y y (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 (pow.f64 (*.f64 y y) #s(literal 3 binary64)) #s(literal -8 binary64)) (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* -8 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64))) |
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 (pow.f64 (*.f64 y y) #s(literal 3 binary64)) #s(literal -8 binary64)) (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (*.f64 y #s(literal -8 binary64)) x) (/.f64 y x) #s(literal 1 binary64)))) |
1 |
#s(literal 1 binary64) |
(- (+ 1 (* 4 (/ (pow y 2) (pow x 2)))) (* -4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (/.f64 #s(literal 8 binary64) x) (/.f64 (*.f64 y y) x) #s(literal 1 binary64)) |
(- (+ 1 (+ (* 4 (/ (* (pow y 2) (- (* 4 (pow y 2)) (* -4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (* -4 (/ (pow y 2) (pow x 2)))) |
(fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 4 binary64) (fma.f64 (/.f64 #s(literal 8 binary64) x) (/.f64 (*.f64 y y) x) #s(literal 1 binary64))) |
(- (+ 1 (+ (* 4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* 4 (pow y 2)) (* -4 (pow y 2)))) (pow x 6))))) (+ (* -4 (/ (* (pow y 2) (- (* 4 (pow y 2)) (* -4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 (pow.f64 (*.f64 y y) #s(literal 3 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 4 binary64) (fma.f64 (/.f64 #s(literal 8 binary64) x) (/.f64 (*.f64 y y) x) #s(literal 1 binary64)))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) |
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) |
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2))))) |
(fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(/ y (pow x 2)) |
(/.f64 y (*.f64 x x)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) |
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) |
| 4 884× | lower-/.f32 |
| 4 872× | lower-/.f64 |
| 4 728× | lower-fma.f32 |
| 4 718× | lower-fma.f64 |
| 4 344× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 47 | 296 |
| 0 | 73 | 291 |
| 1 | 307 | 286 |
| 2 | 2241 | 282 |
| 0 | 8966 | 276 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) |
#s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x)) |
(/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)))) |
#s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64)) |
(*.f64 #s(literal -8 binary64) y) |
(*.f64 x x) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) |
(/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))) |
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) |
(*.f64 #s(literal 4 binary64) y) |
(fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) |
(/.f64 y (*.f64 x x)) |
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) |
| Outputs |
|---|
#<batchref> |
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#<batchref> |
#<batchref> |
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Compiled 23 491 to 2 493 computations (89.4% saved)
12 alts after pruning (3 fresh and 9 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 055 | 3 | 1 058 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 3 | 4 |
| Done | 0 | 6 | 6 |
| Total | 1 056 | 12 | 1 068 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 48.9% | (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) |
| ✓ | 48.4% | (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) |
| ✓ | 48.4% | (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) |
| 54.7% | (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 4 y) y) (* x x)) (+ (* (* y y) -4) (* x x))) (fma.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)))) | |
| ✓ | 55.4% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
| ✓ | 48.7% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64))) |
| ✓ | 44.3% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) |
| ✓ | 26.8% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)))) |
| 24.5% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (fma.f64 (*.f64 #s(literal -8 binary64) y) y (*.f64 x x)) (*.f64 x x)))) | |
| 25.3% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y y) #s(literal -8 binary64) (*.f64 x x)) x) x))) | |
| ✓ | 46.3% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) |
| ✓ | 53.5% | #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
Compiled 522 to 212 computations (59.4% saved)
| Inputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (fma.f64 (*.f64 #s(literal -8 binary64) y) y (*.f64 x x)) (*.f64 x x)))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64))) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #s(approx (+ (* x x) (* (* y 4) y)) (*.f64 x x))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y y) #s(literal -8 binary64) (*.f64 x x)) x) x))) |
(/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 4 y) y) (* x x)) (+ (* (* y y) -4) (* x x))) (fma.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)))) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) |
(fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) |
(fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (/.f64 (*.f64 (*.f64 #s(literal -4 binary64) y) y) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) |
(/.f64 (-.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (/.f64 (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) x) x) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (*.f64 (/.f64 (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) x) x) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) |
| Outputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
(fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) |
5 calls:
| 10.0ms | (*.f64 x x) |
| 9.0ms | x |
| 7.0ms | y |
| 7.0ms | (*.f64 (*.f64 y #s(literal 4 binary64)) y) |
| 6.0ms | (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 80.9% | 3 | x |
| 80.5% | 3 | y |
| 77.5% | 2 | (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
| 80.9% | 3 | (*.f64 x x) |
| 80.5% | 3 | (*.f64 (*.f64 y #s(literal 4 binary64)) y) |
Compiled 29 to 21 computations (27.6% saved)
| Inputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (fma.f64 (*.f64 #s(literal -8 binary64) y) y (*.f64 x x)) (*.f64 x x)))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64))) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #s(approx (+ (* x x) (* (* y 4) y)) (*.f64 x x))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y y) #s(literal -8 binary64) (*.f64 x x)) x) x))) |
(/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 4 y) y) (* x x)) (+ (* (* y y) -4) (* x x))) (fma.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) x) y) (/.f64 x y) #s(literal -1 binary64)))) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)))) |
| Outputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) |
2 calls:
| 6.0ms | x |
| 6.0ms | (*.f64 x x) |
| Accuracy | Segments | Branch |
|---|---|---|
| 80.6% | 3 | x |
| 80.6% | 3 | (*.f64 x x) |
Compiled 4 to 5 computations (-25% saved)
| Inputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (fma.f64 (*.f64 #s(literal -8 binary64) y) y (*.f64 x x)) (*.f64 x x)))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64))) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #s(approx (+ (* x x) (* (* y 4) y)) (*.f64 x x))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y y) #s(literal -8 binary64) (*.f64 x x)) x) x))) |
(/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
| Outputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
(/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) |
2 calls:
| 6.0ms | (*.f64 x x) |
| 5.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 80.6% | 3 | x |
| 80.6% | 3 | (*.f64 x x) |
Compiled 4 to 5 computations (-25% saved)
| Inputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (fma.f64 (*.f64 #s(literal -8 binary64) y) y (*.f64 x x)) (*.f64 x x)))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64))) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #s(approx (+ (* x x) (* (* y 4) y)) (*.f64 x x))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 y y)))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y #s(literal -8 binary64)) y (*.f64 x x)) x) x))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (/.f64 (fma.f64 (*.f64 y y) #s(literal -8 binary64) (*.f64 x x)) x) x))) |
| Outputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) |
5 calls:
| 6.0ms | (*.f64 (*.f64 y #s(literal 4 binary64)) y) |
| 4.0ms | x |
| 4.0ms | y |
| 4.0ms | (*.f64 x x) |
| 4.0ms | (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 77.0% | 3 | (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
| 76.4% | 2 | y |
| 76.4% | 2 | (*.f64 (*.f64 y #s(literal 4 binary64)) y) |
| 77.3% | 2 | x |
| 77.3% | 2 | (*.f64 x x) |
Compiled 29 to 21 computations (27.6% saved)
| Inputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (fma.f64 (*.f64 #s(literal -8 binary64) y) y (*.f64 x x)) (*.f64 x x)))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64))) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #s(approx (+ (* x x) (* (* y 4) y)) (*.f64 x x))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) |
| Outputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) |
4 calls:
| 24.0ms | (*.f64 (*.f64 y #s(literal 4 binary64)) y) |
| 3.0ms | y |
| 3.0ms | x |
| 3.0ms | (*.f64 x x) |
| Accuracy | Segments | Branch |
|---|---|---|
| 76.0% | 2 | y |
| 76.0% | 2 | (*.f64 (*.f64 y #s(literal 4 binary64)) y) |
| 76.3% | 2 | x |
| 76.3% | 2 | (*.f64 x x) |
Compiled 10 to 12 computations (-20% saved)
| Inputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* -8 y) x) (/ y x)) 1) (/.f64 (fma.f64 (*.f64 #s(literal -8 binary64) y) y (*.f64 x x)) (*.f64 x x)))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y #s(literal 2 binary64)) y)) #s(literal -1 binary64))) |
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #s(approx (+ (* x x) (* (* y 4) y)) (*.f64 x x))) |
| Outputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64))) |
2 calls:
| 3.0ms | x |
| 2.0ms | (*.f64 x x) |
| Accuracy | Segments | Branch |
|---|---|---|
| 76.1% | 2 | x |
| 76.1% | 2 | (*.f64 x x) |
Compiled 4 to 5 computations (-25% saved)
| Inputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) |
| Outputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) |
4 calls:
| 5.0ms | y |
| 2.0ms | (*.f64 (*.f64 y #s(literal 4 binary64)) y) |
| 2.0ms | x |
| 1.0ms | (*.f64 x x) |
| Accuracy | Segments | Branch |
|---|---|---|
| 75.4% | 2 | y |
| 75.4% | 2 | (*.f64 (*.f64 y #s(literal 4 binary64)) y) |
| 75.6% | 2 | x |
| 75.6% | 2 | (*.f64 x x) |
Compiled 10 to 12 computations (-20% saved)
Total 0.0b remaining (0%)
Threshold costs 0b (0%)
| Inputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
| Outputs |
|---|
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
5 calls:
| 1.0ms | y |
| 1.0ms | x |
| 1.0ms | (*.f64 (*.f64 y #s(literal 4 binary64)) y) |
| 1.0ms | (*.f64 x x) |
| 1.0ms | (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 53.5% | 1 | y |
| 53.5% | 1 | (*.f64 (*.f64 y #s(literal 4 binary64)) y) |
| 53.5% | 1 | (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) |
| 53.5% | 1 | x |
| 53.5% | 1 | (*.f64 x x) |
Compiled 29 to 21 computations (27.6% saved)
| 2× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.6897985263497567e+216 | 8.743538847359145e+220 |
| 0.0ms | 1.9666389577669955e-173 | 4.199327882494031e-173 |
Compiled 20 to 14 computations (30% saved)
| 2× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.6897985263497567e+216 | 8.743538847359145e+220 |
| 0.0ms | 1.9666389577669955e-173 | 4.199327882494031e-173 |
Compiled 20 to 14 computations (30% saved)
| 2× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.6897985263497567e+216 | 8.743538847359145e+220 |
| 0.0ms | 1.9666389577669955e-173 | 4.199327882494031e-173 |
Compiled 20 to 14 computations (30% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 4215443818209025000.0 | 2.3348507351617864e+39 |
Compiled 20 to 14 computations (30% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 4215443818209025000.0 | 2.3348507351617864e+39 |
Compiled 20 to 14 computations (30% saved)
| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 17.0ms | 4215443818209025000.0 | 2.3348507351617864e+39 |
| 9.0ms | 176× | 0 | valid |
Compiled 141 to 168 computations (-19.1% saved)
ival-mult: 2.0ms (39.5% of total)ival-sub: 1.0ms (19.7% of total)ival-div: 1.0ms (19.7% of total)ival-add: 1.0ms (19.7% 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× | predicate-same |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 4215443818209025000.0 | 2.3348507351617864e+39 |
Compiled 24 to 24 computations (0% saved)
| 1× | egg-herbie |
| 12× | *-commutative-binary64-*.f64 |
| 2× | 1-exp-binary32-exp.f32 |
| 2× | 1-exp-binary64-exp.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 61 | 525 |
| 1 | 70 | 525 |
| 1× | saturated |
| Inputs |
|---|
(if (<=.f64 (*.f64 x x) #s(literal 696173189944793/34808659497239648579720852704622583960672214563358764118798771041101647699040812580153753748454066465596331097210650690541753423472407821641942301328447068696990926165468330002463334596608 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (if (<=.f64 (*.f64 x x) #s(literal 2000000000000000042843093916083914884986269493489898588353418190684583481166660738809762058694254899725914558636661864181657900957739886843189208296670960146935684485884880403647747761611295732625305407912459924144128 binary64)) (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))))) |
(if (<=.f64 (*.f64 x x) #s(literal 696173189944793/34808659497239648579720852704622583960672214563358764118798771041101647699040812580153753748454066465596331097210650690541753423472407821641942301328447068696990926165468330002463334596608 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (if (<=.f64 (*.f64 x x) #s(literal 2000000000000000042843093916083914884986269493489898588353418190684583481166660738809762058694254899725914558636661864181657900957739886843189208296670960146935684485884880403647747761611295732625305407912459924144128 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))))) |
(if (<=.f64 (*.f64 x x) #s(literal 696173189944793/34808659497239648579720852704622583960672214563358764118798771041101647699040812580153753748454066465596331097210650690541753423472407821641942301328447068696990926165468330002463334596608 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (if (<=.f64 (*.f64 x x) #s(literal 2000000000000000042843093916083914884986269493489898588353418190684583481166660738809762058694254899725914558636661864181657900957739886843189208296670960146935684485884880403647747761611295732625305407912459924144128 binary64)) (/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))))) |
(if (<=.f64 (*.f64 x x) #s(literal 5000000000000000000 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))) |
(if (<=.f64 (*.f64 x x) #s(literal 5000000000000000000 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))) |
(if (<=.f64 (*.f64 x x) #s(literal 12000000000000000000000 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64)))) |
(if (<=.f64 (*.f64 x x) #s(literal 5000000000000000000 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
| Outputs |
|---|
(if (<=.f64 (*.f64 x x) #s(literal 696173189944793/34808659497239648579720852704622583960672214563358764118798771041101647699040812580153753748454066465596331097210650690541753423472407821641942301328447068696990926165468330002463334596608 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (if (<=.f64 (*.f64 x x) #s(literal 2000000000000000042843093916083914884986269493489898588353418190684583481166660738809762058694254899725914558636661864181657900957739886843189208296670960146935684485884880403647747761611295732625305407912459924144128 binary64)) (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (*.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))))) |
(if (<=.f64 (*.f64 x x) #s(literal 696173189944793/34808659497239648579720852704622583960672214563358764118798771041101647699040812580153753748454066465596331097210650690541753423472407821641942301328447068696990926165468330002463334596608 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (if (<=.f64 (*.f64 x x) #s(literal 2000000000000000042843093916083914884986269493489898588353418190684583481166660738809762058694254899725914558636661864181657900957739886843189208296670960146935684485884880403647747761611295732625305407912459924144128 binary64)) (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x (*.f64 (/.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (*.f64 #s(literal -4 binary64) y))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))))) |
(if (<=.f64 (*.f64 x x) #s(literal 696173189944793/34808659497239648579720852704622583960672214563358764118798771041101647699040812580153753748454066465596331097210650690541753423472407821641942301328447068696990926165468330002463334596608 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (if (<=.f64 (*.f64 x x) #s(literal 2000000000000000042843093916083914884986269493489898588353418190684583481166660738809762058694254899725914558636661864181657900957739886843189208296670960146935684485884880403647747761611295732625305407912459924144128 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))))) |
(if (<=.f64 (*.f64 x x) #s(literal 696173189944793/34808659497239648579720852704622583960672214563358764118798771041101647699040812580153753748454066465596331097210650690541753423472407821641942301328447068696990926165468330002463334596608 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (if (<=.f64 (*.f64 x x) #s(literal 2000000000000000042843093916083914884986269493489898588353418190684583481166660738809762058694254899725914558636661864181657900957739886843189208296670960146935684485884880403647747761611295732625305407912459924144128 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))))) |
(if (<=.f64 (*.f64 x x) #s(literal 696173189944793/34808659497239648579720852704622583960672214563358764118798771041101647699040812580153753748454066465596331097210650690541753423472407821641942301328447068696990926165468330002463334596608 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (if (<=.f64 (*.f64 x x) #s(literal 2000000000000000042843093916083914884986269493489898588353418190684583481166660738809762058694254899725914558636661864181657900957739886843189208296670960146935684485884880403647747761611295732625305407912459924144128 binary64)) (/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))))) |
(if (<=.f64 (*.f64 x x) #s(literal 696173189944793/34808659497239648579720852704622583960672214563358764118798771041101647699040812580153753748454066465596331097210650690541753423472407821641942301328447068696990926165468330002463334596608 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (if (<=.f64 (*.f64 x x) #s(literal 2000000000000000042843093916083914884986269493489898588353418190684583481166660738809762058694254899725914558636661864181657900957739886843189208296670960146935684485884880403647747761611295732625305407912459924144128 binary64)) (/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))))) |
(if (<=.f64 (*.f64 x x) #s(literal 5000000000000000000 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))) |
(if (<=.f64 (*.f64 x x) #s(literal 5000000000000000000 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 x y) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))) |
(if (<=.f64 (*.f64 x x) #s(literal 5000000000000000000 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))) |
(if (<=.f64 (*.f64 x x) #s(literal 5000000000000000000 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))) |
(if (<=.f64 (*.f64 x x) #s(literal 12000000000000000000000 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) y) (/.f64 y (*.f64 x x)) #s(literal 1 binary64)))) |
(if (<=.f64 (*.f64 x x) #s(literal 5000000000000000000 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))) |
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) |
| 18 822× | lower-fma.f64 |
| 18 822× | lower-fma.f32 |
| 16 292× | lower-fma.f64 |
| 16 292× | lower-fma.f32 |
| 7 426× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 115 | 954 |
| 1 | 319 | 954 |
| 2 | 956 | 808 |
| 3 | 4078 | 800 |
| 0 | 8264 | 730 |
| 0 | 42 | 255 |
| 0 | 73 | 239 |
| 1 | 302 | 234 |
| 2 | 2191 | 232 |
| 0 | 8365 | 230 |
| 0 | 9 | 40 |
| 0 | 15 | 40 |
| 1 | 54 | 40 |
| 2 | 397 | 40 |
| 3 | 6323 | 40 |
| 0 | 8488 | 36 |
| 0 | 32 | 199 |
| 0 | 54 | 185 |
| 1 | 208 | 182 |
| 2 | 1497 | 182 |
| 0 | 8556 | 182 |
| 0 | 374 | 5576 |
| 1 | 1098 | 5019 |
| 2 | 3135 | 4781 |
| 0 | 8320 | 4424 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 563 to 247 computations (56.1% saved)
(abs x)
(abs y)
Compiled 920 to 298 computations (67.6% saved)
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