
Time bar (total: 9.8s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 0 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 1 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 2 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 3 |
| 25% | 25% | 74.9% | 0.1% | 0% | 0% | 0% | 4 |
| 25% | 25% | 74.9% | 0.1% | 0% | 0% | 0% | 5 |
| 25% | 25% | 74.9% | 0.1% | 0% | 0% | 0% | 6 |
| 25% | 25% | 74.9% | 0.1% | 0% | 0% | 0% | 7 |
| 25% | 25% | 74.9% | 0.1% | 0% | 0% | 0% | 8 |
| 26.2% | 25% | 70.2% | 0.1% | 0% | 4.7% | 0% | 9 |
| 28.9% | 25% | 61.4% | 0.1% | 0% | 13.5% | 0% | 10 |
| 31.2% | 26.3% | 58% | 0.1% | 0% | 15.5% | 0% | 11 |
| 37.2% | 28.9% | 48.7% | 0.1% | 0% | 22.3% | 0% | 12 |
Compiled 16 to 13 computations (18.8% saved)
| 614.0ms | 8 256× | 0 | valid |
| 354.0ms | 4 514× | 0 | invalid |
ival-mult: 324.0ms (56.8% of total)ival-add: 135.0ms (23.7% of total)ival-sqrt: 92.0ms (16.1% of total)ival-true: 9.0ms (1.6% of total)exact: 7.0ms (1.2% of total)ival-assert: 4.0ms (0.7% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 79 | 0 | - | 2 | (-3.0234392759558705e-120 -7.25568164956025e-256 -1.0923778360592986e-201) | (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) |
| 10 | 0 | - | 0 | - | (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) |
| 5 | 0 | - | 0 | - | (+.f64 (*.f64 x y) (*.f64 x z)) |
| 0 | 0 | - | 0 | - | z |
| 0 | 0 | - | 0 | - | (*.f64 x z) |
| 0 | 0 | - | 0 | - | (*.f64 x y) |
| 0 | 0 | - | 0 | - | (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) |
| 0 | 0 | - | 0 | - | #s(literal 2 binary64) |
| 0 | 0 | - | 0 | - | y |
| 0 | 0 | - | 0 | - | (*.f64 y z) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
sqrt.f64 | (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) | oflow-rescue | 71 | 0 |
| ↳ | (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) | overflow | 71 | |
| ↳ | (*.f64 y z) | overflow | 32 | |
| ↳ | (+.f64 (*.f64 x y) (*.f64 x z)) | overflow | 55 | |
| ↳ | (*.f64 x z) | overflow | 33 | |
| ↳ | (*.f64 x y) | overflow | 35 | |
+.f64 | (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) | nan-rescue | 10 | 0 |
| ↳ | (+.f64 (*.f64 x y) (*.f64 x z)) | overflow | 55 | |
| ↳ | (*.f64 x z) | overflow | 33 | |
| ↳ | (*.f64 x y) | overflow | 35 | |
| ↳ | (*.f64 y z) | overflow | 32 | |
sqrt.f64 | (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) | uflow-rescue | 6 | 0 |
| ↳ | (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) | underflow | 6 | |
| ↳ | (*.f64 y z) | underflow | 28 | |
| ↳ | (+.f64 (*.f64 x y) (*.f64 x z)) | underflow | 10 | |
| ↳ | (*.f64 x z) | underflow | 29 | |
| ↳ | (*.f64 x y) | underflow | 33 | |
+.f64 | (+.f64 (*.f64 x y) (*.f64 x z)) | nan-rescue | 5 | 0 |
| ↳ | (*.f64 x y) | overflow | 35 | |
| ↳ | (*.f64 x z) | overflow | 33 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 77 | 2 |
| - | 0 | 177 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 77 | 0 | 2 |
| - | 0 | 0 | 177 |
| number | freq |
|---|---|
| 0 | 179 |
| 1 | 66 |
| 2 | 7 |
| 3 | 4 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 64.0ms | 512× | 0 | valid |
Compiled 132 to 37 computations (72% saved)
ival-add: 32.0ms (66.5% of total)ival-mult: 12.0ms (24.9% of total)ival-sqrt: 3.0ms (6.2% 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 |
| 468× | cancel-sign-sub-inv |
| 354× | sub-neg |
| 204× | associate-+l- |
| 204× | unsub-neg |
| 180× | associate--r+ |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 46 | 118 |
| 1 | 133 | 112 |
| 2 | 237 | 108 |
| 3 | 446 | 108 |
| 4 | 929 | 108 |
| 5 | 1336 | 108 |
| 6 | 1729 | 108 |
| 7 | 1794 | 108 |
| 8 | 1806 | 108 |
| 0 | 11 | 14 |
| 0 | 18 | 12 |
| 1 | 28 | 12 |
| 2 | 40 | 12 |
| 3 | 49 | 12 |
| 4 | 50 | 12 |
| 0 | 50 | 11 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) |
| Outputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) |
(*.f64 (sqrt.f64 (fma.f64 (+.f64 z x) y (*.f64 z x))) #s(literal 2 binary64)) |
(sort x y z)
Compiled 14 to 11 computations (21.4% saved)
Compiled 0 to 3 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 70.9% | (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) |
Compiled 14 to 11 computations (21.4% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) | |
| cost-diff | 0 | (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) | |
| cost-diff | 128 | (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) | |
| cost-diff | 320 | (+.f64 (*.f64 x y) (*.f64 x z)) |
| 48× | lower-fma.f64 |
| 48× | lower-fma.f32 |
| 36× | lower-+.f32 |
| 32× | lower-+.f64 |
| 28× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 11 | 57 |
| 0 | 18 | 49 |
| 1 | 28 | 49 |
| 2 | 40 | 49 |
| 3 | 49 | 49 |
| 4 | 50 | 49 |
| 0 | 50 | 46 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) |
#s(literal 2 binary64) |
(sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) |
(+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) |
(+.f64 (*.f64 x y) (*.f64 x z)) |
(*.f64 x y) |
x |
y |
(*.f64 x z) |
z |
(*.f64 y z) |
| Outputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) |
(*.f64 (sqrt.f64 (fma.f64 (+.f64 z x) y (*.f64 z x))) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) |
(sqrt.f64 (fma.f64 (+.f64 z x) y (*.f64 z x))) |
(+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) |
(fma.f64 (+.f64 z x) y (*.f64 z x)) |
(+.f64 (*.f64 x y) (*.f64 x z)) |
(*.f64 (+.f64 z y) x) |
(*.f64 x y) |
(*.f64 y x) |
x |
y |
(*.f64 x z) |
(*.f64 z x) |
z |
(*.f64 y z) |
(*.f64 z y) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) | |
| accuracy | 0.8242187500000001 | (+.f64 (*.f64 x y) (*.f64 x z)) | |
| accuracy | 2.0039062500000004 | (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) | |
| accuracy | 18.425324583112346 | (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) |
| 40.0ms | 256× | 0 | valid |
Compiled 59 to 13 computations (78% saved)
ival-mult: 6.0ms (60.1% of total)ival-add: 2.0ms (20% of total)ival-sqrt: 2.0ms (20% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (+.f64 (*.f64 x y) (*.f64 x z)) (patch (+.f64 (*.f64 x y) (*.f64 x z)) #<representation binary64>) () ()) |
#s(alt (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) (patch (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) (patch (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) (patch (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* x y) (taylor 0 z) (#s(alt (+.f64 (*.f64 x y) (*.f64 x z)) (patch (+.f64 (*.f64 x y) (*.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x y) (* x z)) (taylor 0 z) (#s(alt (+.f64 (*.f64 x y) (*.f64 x z)) (patch (+.f64 (*.f64 x y) (*.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x y) (* x z)) (taylor 0 z) (#s(alt (+.f64 (*.f64 x y) (*.f64 x z)) (patch (+.f64 (*.f64 x y) (*.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x y) (* x z)) (taylor 0 z) (#s(alt (+.f64 (*.f64 x y) (*.f64 x z)) (patch (+.f64 (*.f64 x y) (*.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor 0 z) (#s(alt (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) (patch (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x y) (* z (+ x y))) (taylor 0 z) (#s(alt (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) (patch (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x y) (* z (+ x y))) (taylor 0 z) (#s(alt (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) (patch (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x y) (* z (+ x y))) (taylor 0 z) (#s(alt (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) (patch (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 (sqrt (* x y))) (taylor 0 z) (#s(alt (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) (patch (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) (taylor 0 z) (#s(alt (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) (patch (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 2 (sqrt (* x y))) (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* (sqrt (/ 1 (* x y))) (+ x y))))) (taylor 0 z) (#s(alt (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) (patch (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 2 (sqrt (* x y))) (* z (+ (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3)))))) (* (sqrt (/ 1 (* x y))) (+ x y))))) (taylor 0 z) (#s(alt (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) (patch (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (* x y)) (taylor 0 z) (#s(alt (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) (patch (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (* x y)) (* 1/2 (* (sqrt (/ 1 (* x y))) (* z (+ x y))))) (taylor 0 z) (#s(alt (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) (patch (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (* x y)) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y)))))) (taylor 0 z) (#s(alt (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) (patch (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (* x y)) (* z (+ (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y))) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3))))))))) (taylor 0 z) (#s(alt (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) (patch (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) #<representation binary64>) () ())) ()) |
#s(alt (* x z) (taylor inf z) (#s(alt (+.f64 (*.f64 x y) (*.f64 x z)) (patch (+.f64 (*.f64 x y) (*.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ x (/ (* x y) z))) (taylor inf z) (#s(alt (+.f64 (*.f64 x y) (*.f64 x z)) (patch (+.f64 (*.f64 x y) (*.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ x (/ (* x y) z))) (taylor inf z) (#s(alt (+.f64 (*.f64 x y) (*.f64 x z)) (patch (+.f64 (*.f64 x y) (*.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ x (/ (* x y) z))) (taylor inf z) (#s(alt (+.f64 (*.f64 x y) (*.f64 x z)) (patch (+.f64 (*.f64 x y) (*.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ x y)) (taylor inf z) (#s(alt (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) (patch (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ x (+ y (/ (* x y) z)))) (taylor inf z) (#s(alt (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) (patch (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ x (+ y (/ (* x y) z)))) (taylor inf z) (#s(alt (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) (patch (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ x (+ y (/ (* x y) z)))) (taylor inf z) (#s(alt (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) (patch (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 (sqrt (* z (+ x y)))) (taylor inf z) (#s(alt (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) (patch (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ (* 2 (sqrt (/ (+ x y) z))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y))))))) (taylor inf z) (#s(alt (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) (patch (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ (* -1/4 (* (* (pow x 2) (pow y 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 2 (sqrt (/ (+ x y) z))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))) (taylor inf z) (#s(alt (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) (patch (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ (* -1/4 (* (* (pow x 2) (pow y 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/8 (* (* (pow x 3) (pow y 3)) (sqrt (/ 1 (* (pow z 7) (pow (+ x y) 5)))))) (+ (* 2 (sqrt (/ (+ x y) z))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y))))))))) (taylor inf z) (#s(alt (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) (patch (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (* z (+ x y))) (taylor inf z) (#s(alt (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) (patch (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ (sqrt (/ (+ x y) z)) (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))) (taylor inf z) (#s(alt (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) (patch (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ (sqrt (/ (+ x y) z)) (+ (* -1/8 (* (* (pow x 2) (pow y 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y))))))))) (taylor inf z) (#s(alt (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) (patch (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ (sqrt (/ (+ x y) z)) (+ (* -1/8 (* (* (pow x 2) (pow y 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/16 (* (* (pow x 3) (pow y 3)) (sqrt (/ 1 (* (pow z 7) (pow (+ x y) 5)))))) (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))))) (taylor inf z) (#s(alt (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) (patch (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) #<representation binary64>) () ())) ()) |
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#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) (pow (+ (* -1 y) (* -1 z)) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) (patch (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) #<representation binary64>) () ())) ()) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | x | @ | -inf | ((+ (* x y) (* x z)) (+ (+ (* x y) (* x z)) (* y z)) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (sqrt (+ (+ (* x y) (* x z)) (* y z)))) |
| 3.0ms | y | @ | -inf | ((+ (* x y) (* x z)) (+ (+ (* x y) (* x z)) (* y z)) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (sqrt (+ (+ (* x y) (* x z)) (* y z)))) |
| 3.0ms | z | @ | -inf | ((+ (* x y) (* x z)) (+ (+ (* x y) (* x z)) (* y z)) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (sqrt (+ (+ (* x y) (* x z)) (* y z)))) |
| 2.0ms | y | @ | inf | ((+ (* x y) (* x z)) (+ (+ (* x y) (* x z)) (* y z)) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (sqrt (+ (+ (* x y) (* x z)) (* y z)))) |
| 2.0ms | z | @ | inf | ((+ (* x y) (* x z)) (+ (+ (* x y) (* x z)) (* y z)) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (sqrt (+ (+ (* x y) (* x z)) (* y z)))) |
| 1× | egg-herbie |
| 11 034× | lower-fma.f64 |
| 11 034× | lower-fma.f32 |
| 7 720× | lower-*.f64 |
| 7 720× | lower-*.f32 |
| 3 024× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 501 | 3429 |
| 1 | 1684 | 3363 |
| 2 | 6236 | 3318 |
| 0 | 8106 | 3177 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* x y) |
(+ (* x y) (* x z)) |
(+ (* x y) (* x z)) |
(+ (* x y) (* x z)) |
(* x y) |
(+ (* x y) (* z (+ x y))) |
(+ (* x y) (* z (+ x y))) |
(+ (* x y) (* z (+ x y))) |
(* 2 (sqrt (* x y))) |
(+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3)))))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(sqrt (* x y)) |
(+ (sqrt (* x y)) (* 1/2 (* (sqrt (/ 1 (* x y))) (* z (+ x y))))) |
(+ (sqrt (* x y)) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y)))))) |
(+ (sqrt (* x y)) (* z (+ (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y))) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3))))))))) |
(* x z) |
(* z (+ x (/ (* x y) z))) |
(* z (+ x (/ (* x y) z))) |
(* z (+ x (/ (* x y) z))) |
(* z (+ x y)) |
(* z (+ x (+ y (/ (* x y) z)))) |
(* z (+ x (+ y (/ (* x y) z)))) |
(* z (+ x (+ y (/ (* x y) z)))) |
(* 2 (sqrt (* z (+ x y)))) |
(* z (+ (* 2 (sqrt (/ (+ x y) z))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y))))))) |
(* z (+ (* -1/4 (* (* (pow x 2) (pow y 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 2 (sqrt (/ (+ x y) z))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))) |
(* z (+ (* -1/4 (* (* (pow x 2) (pow y 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/8 (* (* (pow x 3) (pow y 3)) (sqrt (/ 1 (* (pow z 7) (pow (+ x y) 5)))))) (+ (* 2 (sqrt (/ (+ x y) z))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y))))))))) |
(sqrt (* z (+ x y))) |
(* z (+ (sqrt (/ (+ x y) z)) (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))) |
(* z (+ (sqrt (/ (+ x y) z)) (+ (* -1/8 (* (* (pow x 2) (pow y 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y))))))))) |
(* z (+ (sqrt (/ (+ x y) z)) (+ (* -1/8 (* (* (pow x 2) (pow y 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/16 (* (* (pow x 3) (pow y 3)) (sqrt (/ 1 (* (pow z 7) (pow (+ x y) 5)))))) (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))))) |
(* x z) |
(* -1 (* z (+ (* -1 x) (* -1 (/ (* x y) z))))) |
(* -1 (* z (+ (* -1 x) (* -1 (/ (* x y) z))))) |
(* -1 (* z (+ (* -1 x) (* -1 (/ (* x y) z))))) |
(* -1 (* z (+ (* -1 x) (* -1 y)))) |
(* -1 (* z (+ (* -1 x) (+ (* -1 y) (* -1 (/ (* x y) z)))))) |
(* -1 (* z (+ (* -1 x) (+ (* -1 y) (* -1 (/ (* x y) z)))))) |
(* -1 (* z (+ (* -1 x) (+ (* -1 y) (* -1 (/ (* x y) z)))))) |
(* -2 (* (sqrt (* z (+ (* -1 x) (* -1 y)))) (sqrt -1))) |
(* -1 (* z (+ (* 2 (* (sqrt (/ (+ (* -1 x) (* -1 y)) z)) (sqrt -1))) (* (* x (* y (sqrt -1))) (sqrt (/ 1 (* (pow z 3) (+ (* -1 x) (* -1 y))))))))) |
(* -1 (* z (+ (* -1/4 (* (* (pow x 2) (* (pow y 2) (sqrt -1))) (sqrt (/ 1 (* (pow z 5) (pow (+ (* -1 x) (* -1 y)) 3)))))) (+ (* 2 (* (sqrt (/ (+ (* -1 x) (* -1 y)) z)) (sqrt -1))) (* (* x (* y (sqrt -1))) (sqrt (/ 1 (* (pow z 3) (+ (* -1 x) (* -1 y)))))))))) |
(* -1 (* z (+ (* -1/4 (* (* (pow x 2) (* (pow y 2) (sqrt -1))) (sqrt (/ 1 (* (pow z 5) (pow (+ (* -1 x) (* -1 y)) 3)))))) (+ (* 1/8 (* (* (pow x 3) (* (pow y 3) (sqrt -1))) (sqrt (/ 1 (* (pow z 7) (pow (+ (* -1 x) (* -1 y)) 5)))))) (+ (* 2 (* (sqrt (/ (+ (* -1 x) (* -1 y)) z)) (sqrt -1))) (* (* x (* y (sqrt -1))) (sqrt (/ 1 (* (pow z 3) (+ (* -1 x) (* -1 y))))))))))) |
(* -1 (* (sqrt (* z (+ (* -1 x) (* -1 y)))) (sqrt -1))) |
(* -1 (* z (+ (* 1/2 (* (* x (* y (sqrt -1))) (sqrt (/ 1 (* (pow z 3) (+ (* -1 x) (* -1 y))))))) (* (sqrt (/ (+ (* -1 x) (* -1 y)) z)) (sqrt -1))))) |
(* -1 (* z (+ (* -1/8 (* (* (pow x 2) (* (pow y 2) (sqrt -1))) (sqrt (/ 1 (* (pow z 5) (pow (+ (* -1 x) (* -1 y)) 3)))))) (+ (* 1/2 (* (* x (* y (sqrt -1))) (sqrt (/ 1 (* (pow z 3) (+ (* -1 x) (* -1 y))))))) (* (sqrt (/ (+ (* -1 x) (* -1 y)) z)) (sqrt -1)))))) |
(* -1 (* z (+ (* -1/8 (* (* (pow x 2) (* (pow y 2) (sqrt -1))) (sqrt (/ 1 (* (pow z 5) (pow (+ (* -1 x) (* -1 y)) 3)))))) (+ (* 1/16 (* (* (pow x 3) (* (pow y 3) (sqrt -1))) (sqrt (/ 1 (* (pow z 7) (pow (+ (* -1 x) (* -1 y)) 5)))))) (+ (* 1/2 (* (* x (* y (sqrt -1))) (sqrt (/ 1 (* (pow z 3) (+ (* -1 x) (* -1 y))))))) (* (sqrt (/ (+ (* -1 x) (* -1 y)) z)) (sqrt -1))))))) |
(* x z) |
(+ (* x y) (* x z)) |
(+ (* x y) (* x z)) |
(+ (* x y) (* x z)) |
(* x z) |
(+ (* x z) (* y (+ x z))) |
(+ (* x z) (* y (+ x z))) |
(+ (* x z) (* y (+ x z))) |
(* 2 (sqrt (* x z))) |
(+ (* 2 (sqrt (* x z))) (* (sqrt (/ 1 (* x z))) (* y (+ x z)))) |
(+ (* 2 (sqrt (* x z))) (* y (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (* y (pow (+ x z) 2)))) (* (sqrt (/ 1 (* x z))) (+ x z))))) |
(+ (* 2 (sqrt (* x z))) (* y (+ (* y (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow (+ x z) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow z 5)))) (* y (pow (+ x z) 3)))))) (* (sqrt (/ 1 (* x z))) (+ x z))))) |
(sqrt (* x z)) |
(+ (sqrt (* x z)) (* 1/2 (* (sqrt (/ 1 (* x z))) (* y (+ x z))))) |
(+ (sqrt (* x z)) (* y (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (* y (pow (+ x z) 2)))) (* 1/2 (* (sqrt (/ 1 (* x z))) (+ x z)))))) |
(+ (sqrt (* x z)) (* y (+ (* 1/2 (* (sqrt (/ 1 (* x z))) (+ x z))) (* y (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow (+ x z) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow z 5)))) (* y (pow (+ x z) 3))))))))) |
(* x y) |
(* y (+ x (/ (* x z) y))) |
(* y (+ x (/ (* x z) y))) |
(* y (+ x (/ (* x z) y))) |
(* y (+ x z)) |
(* y (+ x (+ z (/ (* x z) y)))) |
(* y (+ x (+ z (/ (* x z) y)))) |
(* y (+ x (+ z (/ (* x z) y)))) |
(* 2 (sqrt (* y (+ x z)))) |
(* y (+ (* 2 (sqrt (/ (+ x z) y))) (* (* x z) (sqrt (/ 1 (* (pow y 3) (+ x z))))))) |
(* y (+ (* -1/4 (* (* (pow x 2) (pow z 2)) (sqrt (/ 1 (* (pow y 5) (pow (+ x z) 3)))))) (+ (* 2 (sqrt (/ (+ x z) y))) (* (* x z) (sqrt (/ 1 (* (pow y 3) (+ x z)))))))) |
(* y (+ (* -1/4 (* (* (pow x 2) (pow z 2)) (sqrt (/ 1 (* (pow y 5) (pow (+ x z) 3)))))) (+ (* 1/8 (* (* (pow x 3) (pow z 3)) (sqrt (/ 1 (* (pow y 7) (pow (+ x z) 5)))))) (+ (* 2 (sqrt (/ (+ x z) y))) (* (* x z) (sqrt (/ 1 (* (pow y 3) (+ x z))))))))) |
(sqrt (* y (+ x z))) |
(* y (+ (sqrt (/ (+ x z) y)) (* 1/2 (* (* x z) (sqrt (/ 1 (* (pow y 3) (+ x z)))))))) |
(* y (+ (sqrt (/ (+ x z) y)) (+ (* -1/8 (* (* (pow x 2) (pow z 2)) (sqrt (/ 1 (* (pow y 5) (pow (+ x z) 3)))))) (* 1/2 (* (* x z) (sqrt (/ 1 (* (pow y 3) (+ x z))))))))) |
(* y (+ (sqrt (/ (+ x z) y)) (+ (* -1/8 (* (* (pow x 2) (pow z 2)) (sqrt (/ 1 (* (pow y 5) (pow (+ x z) 3)))))) (+ (* 1/16 (* (* (pow x 3) (pow z 3)) (sqrt (/ 1 (* (pow y 7) (pow (+ x z) 5)))))) (* 1/2 (* (* x z) (sqrt (/ 1 (* (pow y 3) (+ x z)))))))))) |
(* x y) |
(* -1 (* y (+ (* -1 x) (* -1 (/ (* x z) y))))) |
(* -1 (* y (+ (* -1 x) (* -1 (/ (* x z) y))))) |
(* -1 (* y (+ (* -1 x) (* -1 (/ (* x z) y))))) |
(* -1 (* y (+ (* -1 x) (* -1 z)))) |
(* -1 (* y (+ (* -1 x) (+ (* -1 z) (* -1 (/ (* x z) y)))))) |
(* -1 (* y (+ (* -1 x) (+ (* -1 z) (* -1 (/ (* x z) y)))))) |
(* -1 (* y (+ (* -1 x) (+ (* -1 z) (* -1 (/ (* x z) y)))))) |
(* -2 (* (sqrt (* y (+ (* -1 x) (* -1 z)))) (sqrt -1))) |
(* -1 (* y (+ (* 2 (* (sqrt (/ (+ (* -1 x) (* -1 z)) y)) (sqrt -1))) (* (* x (* z (sqrt -1))) (sqrt (/ 1 (* (pow y 3) (+ (* -1 x) (* -1 z))))))))) |
(* -1 (* y (+ (* -1/4 (* (* (pow x 2) (* (pow z 2) (sqrt -1))) (sqrt (/ 1 (* (pow y 5) (pow (+ (* -1 x) (* -1 z)) 3)))))) (+ (* 2 (* (sqrt (/ (+ (* -1 x) (* -1 z)) y)) (sqrt -1))) (* (* x (* z (sqrt -1))) (sqrt (/ 1 (* (pow y 3) (+ (* -1 x) (* -1 z)))))))))) |
(* -1 (* y (+ (* -1/4 (* (* (pow x 2) (* (pow z 2) (sqrt -1))) (sqrt (/ 1 (* (pow y 5) (pow (+ (* -1 x) (* -1 z)) 3)))))) (+ (* 1/8 (* (* (pow x 3) (* (pow z 3) (sqrt -1))) (sqrt (/ 1 (* (pow y 7) (pow (+ (* -1 x) (* -1 z)) 5)))))) (+ (* 2 (* (sqrt (/ (+ (* -1 x) (* -1 z)) y)) (sqrt -1))) (* (* x (* z (sqrt -1))) (sqrt (/ 1 (* (pow y 3) (+ (* -1 x) (* -1 z))))))))))) |
(* -1 (* (sqrt (* y (+ (* -1 x) (* -1 z)))) (sqrt -1))) |
(* -1 (* y (+ (* 1/2 (* (* x (* z (sqrt -1))) (sqrt (/ 1 (* (pow y 3) (+ (* -1 x) (* -1 z))))))) (* (sqrt (/ (+ (* -1 x) (* -1 z)) y)) (sqrt -1))))) |
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (* (pow z 2) (sqrt -1))) (sqrt (/ 1 (* (pow y 5) (pow (+ (* -1 x) (* -1 z)) 3)))))) (+ (* 1/2 (* (* x (* z (sqrt -1))) (sqrt (/ 1 (* (pow y 3) (+ (* -1 x) (* -1 z))))))) (* (sqrt (/ (+ (* -1 x) (* -1 z)) y)) (sqrt -1)))))) |
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (* (pow z 2) (sqrt -1))) (sqrt (/ 1 (* (pow y 5) (pow (+ (* -1 x) (* -1 z)) 3)))))) (+ (* 1/16 (* (* (pow x 3) (* (pow z 3) (sqrt -1))) (sqrt (/ 1 (* (pow y 7) (pow (+ (* -1 x) (* -1 z)) 5)))))) (+ (* 1/2 (* (* x (* z (sqrt -1))) (sqrt (/ 1 (* (pow y 3) (+ (* -1 x) (* -1 z))))))) (* (sqrt (/ (+ (* -1 x) (* -1 z)) y)) (sqrt -1))))))) |
(* x (+ y z)) |
(* x (+ y z)) |
(* x (+ y z)) |
(* x (+ y z)) |
(* y z) |
(+ (* x (+ y z)) (* y z)) |
(+ (* x (+ y z)) (* y z)) |
(+ (* x (+ y z)) (* y z)) |
(* 2 (sqrt (* y z))) |
(+ (* 2 (sqrt (* y z))) (* (* x (+ y z)) (sqrt (/ 1 (* y z))))) |
(+ (* 2 (sqrt (* y z))) (* x (+ (* -1/4 (* (* x (pow (+ y z) 2)) (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (* (sqrt (/ 1 (* y z))) (+ y z))))) |
(+ (* 2 (sqrt (* y z))) (* x (+ (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow y 3) (pow z 3)))) (pow (+ y z) 2))) (* 1/8 (* (* x (pow (+ y z) 3)) (sqrt (/ 1 (* (pow y 5) (pow z 5)))))))) (* (sqrt (/ 1 (* y z))) (+ y z))))) |
(sqrt (* y z)) |
(+ (sqrt (* y z)) (* 1/2 (* (* x (+ y z)) (sqrt (/ 1 (* y z)))))) |
(+ (sqrt (* y z)) (* x (+ (* -1/8 (* (* x (pow (+ y z) 2)) (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (* 1/2 (* (sqrt (/ 1 (* y z))) (+ y z)))))) |
(+ (sqrt (* y z)) (* x (+ (* 1/2 (* (sqrt (/ 1 (* y z))) (+ y z))) (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow y 3) (pow z 3)))) (pow (+ y z) 2))) (* 1/16 (* (* x (pow (+ y z) 3)) (sqrt (/ 1 (* (pow y 5) (pow z 5))))))))))) |
(* x (+ y z)) |
(* x (+ y z)) |
(* x (+ y z)) |
(* x (+ y z)) |
(* x (+ y z)) |
(* x (+ y (+ z (/ (* y z) x)))) |
(* x (+ y (+ z (/ (* y z) x)))) |
(* x (+ y (+ z (/ (* y z) x)))) |
(* 2 (sqrt (* x (+ y z)))) |
(* x (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))) |
(* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z))))) |
(* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow x 7) (pow (+ y z) 5)))) (* (pow y 3) (pow z 3)))) (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))))) |
(sqrt (* x (+ y z))) |
(* x (+ (sqrt (/ (+ y z) x)) (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z))))) |
(* x (+ (sqrt (/ (+ y z) x)) (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))))) |
(* x (+ (sqrt (/ (+ y z) x)) (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) (pow (+ y z) 5)))) (* (pow y 3) (pow z 3)))) (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z))))))) |
(* -1 (* x (+ (* -1 y) (* -1 z)))) |
(* -1 (* x (+ (* -1 y) (* -1 z)))) |
(* -1 (* x (+ (* -1 y) (* -1 z)))) |
(* -1 (* x (+ (* -1 y) (* -1 z)))) |
(* -1 (* x (+ (* -1 y) (* -1 z)))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(* -2 (* (sqrt (* x (+ (* -1 y) (* -1 z)))) (sqrt -1))) |
(* -1 (* x (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1)))))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow x 7) (pow (+ (* -1 y) (* -1 z)) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))))))) |
(* -1 (* (sqrt (* x (+ (* -1 y) (* -1 z)))) (sqrt -1))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) (pow (+ (* -1 y) (* -1 z)) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))))))) |
| Outputs |
|---|
(* x y) |
(*.f64 y x) |
(+ (* x y) (* x z)) |
(*.f64 (+.f64 z y) x) |
(+ (* x y) (* x z)) |
(*.f64 (+.f64 z y) x) |
(+ (* x y) (* x z)) |
(*.f64 (+.f64 z y) x) |
(* x y) |
(*.f64 y x) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(* 2 (sqrt (* x y))) |
(*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64)) |
(+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) |
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))) (+.f64 y x)) z (*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) z)) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))) (+.f64 y x))) z (*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3)))))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (+.f64 y x) #s(literal 3 binary64)) z)) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 y #s(literal 5 binary64)))) (*.f64 (*.f64 #s(literal -1/4 binary64) (pow.f64 (+.f64 y x) #s(literal 2 binary64))) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (pow.f64 x #s(literal 3 binary64)))))) z (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))) (+.f64 y x))) z (*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64))) |
(sqrt (* x y)) |
(sqrt.f64 (*.f64 y x)) |
(+ (sqrt (* x y)) (* 1/2 (* (sqrt (/ 1 (* x y))) (* z (+ x y))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 y x) z)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))) (sqrt.f64 (*.f64 y x))) |
(+ (sqrt (* x y)) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) z)) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 y x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))))) z (sqrt.f64 (*.f64 y x))) |
(+ (sqrt (* x y)) (* z (+ (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y))) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 (+.f64 y x) #s(literal 3 binary64)) z)) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 y #s(literal 5 binary64)))) (*.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 (+.f64 y x) #s(literal 2 binary64))) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (pow.f64 x #s(literal 3 binary64)))))) z (*.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 y x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))))) z (sqrt.f64 (*.f64 y x))) |
(* x z) |
(*.f64 z x) |
(* z (+ x (/ (* x y) z))) |
(*.f64 (fma.f64 (/.f64 y z) x x) z) |
(* z (+ x (/ (* x y) z))) |
(*.f64 (fma.f64 (/.f64 y z) x x) z) |
(* z (+ x (/ (* x y) z))) |
(*.f64 (fma.f64 (/.f64 y z) x x) z) |
(* z (+ x y)) |
(*.f64 (+.f64 y x) z) |
(* z (+ x (+ y (/ (* x y) z)))) |
(*.f64 (fma.f64 (+.f64 (/.f64 y z) #s(literal 1 binary64)) x y) z) |
(* z (+ x (+ y (/ (* x y) z)))) |
(*.f64 (fma.f64 (+.f64 (/.f64 y z) #s(literal 1 binary64)) x y) z) |
(* z (+ x (+ y (/ (* x y) z)))) |
(*.f64 (fma.f64 (+.f64 (/.f64 y z) #s(literal 1 binary64)) x y) z) |
(* 2 (sqrt (* z (+ x y)))) |
(*.f64 (sqrt.f64 (*.f64 (+.f64 y x) z)) #s(literal 2 binary64)) |
(* z (+ (* 2 (sqrt (/ (+ x y) z))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y))))))) |
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(* z (+ (* -1/4 (* (* (pow x 2) (pow y 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 2 (sqrt (/ (+ x y) z))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))) |
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(* x y) |
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(* -1 (* (sqrt (* x (+ (* -1 y) (* -1 z)))) (sqrt -1))) |
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (-.f64 (neg.f64 z) y) x))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))))) |
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (neg.f64 z) y)) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (*.f64 z y) (sqrt.f64 (/.f64 (-.f64 (neg.f64 z) y) x)))) (neg.f64 x)) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1)))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (neg.f64 z) y) #s(literal 3 binary64))) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (*.f64 (*.f64 (*.f64 z z) y) y)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (neg.f64 z) y)) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (*.f64 z y) (sqrt.f64 (/.f64 (-.f64 (neg.f64 z) y) x))))) (neg.f64 x)) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) (pow (+ (* -1 y) (* -1 z)) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))))))) |
(*.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (neg.f64 z) y) #s(literal 5 binary64))) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64)) (*.f64 (pow.f64 z #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (*.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (neg.f64 z) y) #s(literal 3 binary64))) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (*.f64 (*.f64 (*.f64 z z) y) y))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (neg.f64 z) y)) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (*.f64 z y) (sqrt.f64 (/.f64 (-.f64 (neg.f64 z) y) x))))) (neg.f64 x)) |
| 8 534× | lower-fma.f64 |
| 8 534× | lower-fma.f32 |
| 4 952× | lower-*.f32 |
| 4 944× | lower-*.f64 |
| 2 750× | lower-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 11 | 44 |
| 0 | 18 | 36 |
| 1 | 55 | 36 |
| 2 | 435 | 36 |
| 3 | 6667 | 36 |
| 0 | 8469 | 33 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(+.f64 (*.f64 x y) (*.f64 x z)) |
(+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) |
(sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) |
| Outputs |
|---|
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Compiled 11 150 to 1 656 computations (85.1% saved)
16 alts after pruning (16 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 356 | 16 | 372 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 357 | 16 | 373 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 71.1% | (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
| 70.7% | (*.f64 #s(literal 2 binary64) (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))) | |
| 37.9% | (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 1/4 binary64))) | |
| 19.2% | (*.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 (-.f64 (pow.f64 (*.f64 z y) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 z y) x) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 (*.f64 z y) (*.f64 (+.f64 z y) x))))) | |
| 70.4% | (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x)))))) | |
| ▶ | 47.5% | (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) (*.f64 y z)))) |
| 53.2% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (fma.f64 (+.f64 (/.f64 z x) #s(literal 1 binary64)) y z) x)))) | |
| 55.9% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (fma.f64 (+.f64 (/.f64 y z) #s(literal 1 binary64)) x y) z)))) | |
| ▶ | 37.8% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) |
| 37.1% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z)))) | |
| 35.7% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z y)))) | |
| 3.7% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z x)))) | |
| ▶ | 36.8% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
| ▶ | 3.6% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) |
| 30.8% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 z x)) (pow.f64 y #s(literal 3 binary64)))) (*.f64 z x) (*.f64 (sqrt.f64 (/.f64 (+.f64 z x) y)) #s(literal 2 binary64))) y)) | |
| 37.2% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) (pow.f64 z #s(literal 3 binary64)))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z)) |
Compiled 512 to 386 computations (24.6% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 128 | (+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) (*.f64 y z)) | |
| cost-diff | 320 | (/.f64 x (*.f64 (-.f64 y z) x)) | |
| cost-diff | 1408 | (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) | |
| cost-diff | 6848 | (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) | |
| cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) | |
| cost-diff | 0 | (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64))) | |
| cost-diff | 0 | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) | |
| cost-diff | 0 | (*.f64 (+.f64 z y) x) | |
| cost-diff | 0 | #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x))) | |
| cost-diff | 0 | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) | |
| cost-diff | 0 | (*.f64 y x) | |
| cost-diff | 0 | #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x))) | |
| cost-diff | 0 | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) | |
| cost-diff | 0 | (+.f64 y x) | |
| cost-diff | 0 | (fma.f64 (+.f64 y x) z (*.f64 y x)) | |
| cost-diff | 0 | (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
| 5 996× | lower-fma.f32 |
| 5 990× | lower-fma.f64 |
| 2 986× | lower-*.f32 |
| 2 960× | lower-*.f64 |
| 1 472× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 48 | 437 |
| 0 | 84 | 423 |
| 1 | 148 | 416 |
| 2 | 279 | 398 |
| 3 | 765 | 359 |
| 4 | 2568 | 359 |
| 5 | 5417 | 359 |
| 6 | 7418 | 359 |
| 0 | 8082 | 356 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
(sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(+.f64 y x) |
y |
x |
z |
(*.f64 y x) |
#s(literal 2 binary64) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
#s(literal 2 binary64) |
(sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x))) |
#s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)) |
(*.f64 y x) |
y |
x |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) |
#s(literal 2 binary64) |
(sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x))) |
#s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)) |
(*.f64 (+.f64 z y) x) |
(+.f64 z y) |
z |
y |
x |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) |
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) |
(/.f64 #s(literal 1 binary64) (*.f64 z x)) |
#s(literal 1 binary64) |
(*.f64 z x) |
z |
x |
(+.f64 z x) |
y |
(*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)) |
(sqrt.f64 (*.f64 z x)) |
#s(literal 2 binary64) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) (*.f64 y z)))) |
#s(literal 2 binary64) |
(sqrt.f64 (+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) (*.f64 y z))) |
(+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) (*.f64 y z)) |
(fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) |
(*.f64 (*.f64 y y) x) |
(*.f64 y y) |
y |
x |
(/.f64 x (*.f64 (-.f64 y z) x)) |
(*.f64 (-.f64 y z) x) |
(-.f64 y z) |
z |
(neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z))) |
(/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)) |
(/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) |
(pow.f64 (*.f64 z x) #s(literal 2 binary64)) |
(*.f64 z x) |
(*.f64 y z) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)))) |
(sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) |
(sqrt.f64 (fma.f64 z (+.f64 x y) (*.f64 x y))) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(fma.f64 z (+.f64 x y) (*.f64 x y)) |
(+.f64 y x) |
(+.f64 x y) |
y |
x |
z |
(*.f64 y x) |
(*.f64 x y) |
#s(literal 2 binary64) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
(*.f64 (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 x y))) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x))) |
(sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 x y))) |
#s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)) |
#s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 x y)) |
(*.f64 y x) |
(*.f64 x y) |
y |
x |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) |
(*.f64 (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x))) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x))) |
#s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)) |
(*.f64 (+.f64 z y) x) |
(+.f64 z y) |
z |
y |
x |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (+.f64 z x) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) |
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64))) |
(fma.f64 (*.f64 (+.f64 z x) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) |
(*.f64 (+.f64 z x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x)))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) |
(/.f64 #s(literal 1 binary64) (*.f64 z x)) |
#s(literal 1 binary64) |
(*.f64 z x) |
z |
x |
(+.f64 z x) |
y |
(*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)) |
(sqrt.f64 (*.f64 z x)) |
#s(literal 2 binary64) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) (*.f64 y z)))) |
(*.f64 (sqrt.f64 (fma.f64 (fma.f64 (neg.f64 z) z (*.f64 y y)) (/.f64 x (-.f64 y z)) (*.f64 z y))) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 (+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) (*.f64 y z))) |
(sqrt.f64 (fma.f64 (fma.f64 (neg.f64 z) z (*.f64 y y)) (/.f64 x (-.f64 y z)) (*.f64 z y))) |
(+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) (*.f64 y z)) |
(fma.f64 (fma.f64 (neg.f64 z) z (*.f64 y y)) (/.f64 x (-.f64 y z)) (*.f64 z y)) |
(fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) |
(*.f64 (fma.f64 (neg.f64 z) z (*.f64 y y)) (/.f64 x (-.f64 y z))) |
(*.f64 (*.f64 y y) x) |
(*.f64 y y) |
y |
x |
(/.f64 x (*.f64 (-.f64 y z) x)) |
(/.f64 #s(literal 1 binary64) (-.f64 y z)) |
(*.f64 (-.f64 y z) x) |
(-.f64 y z) |
z |
(neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z))) |
(*.f64 (/.f64 x (-.f64 z y)) (*.f64 z z)) |
(/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)) |
(*.f64 (*.f64 (/.f64 z (-.f64 y z)) z) x) |
(/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) |
(*.f64 (*.f64 z z) x) |
(pow.f64 (*.f64 z x) #s(literal 2 binary64)) |
(*.f64 z x) |
(*.f64 y z) |
(*.f64 z y) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 4.942635017418573 | (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) | |
| accuracy | 6.240208194231419 | (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)) | |
| accuracy | 7.1096211166809296 | (/.f64 x (*.f64 (-.f64 y z) x)) | |
| accuracy | 8.738413422297528 | (sqrt.f64 (+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) (*.f64 y z))) | |
| accuracy | 0.1328125 | (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) | |
| accuracy | 4.375451700095878 | (sqrt.f64 (*.f64 z x)) | |
| accuracy | 4.557866365022058 | (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) | |
| accuracy | 32.47046105034999 | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) | |
| accuracy | 0 | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) | |
| accuracy | 0.0078125 | (*.f64 (+.f64 z y) x) | |
| accuracy | 8.738413422297528 | (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x))) | |
| accuracy | 13.85579660983951 | #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)) | |
| accuracy | 0 | (*.f64 y x) | |
| accuracy | 0 | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) | |
| accuracy | 8.738413422297528 | (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x))) | |
| accuracy | 14.254777510215726 | #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)) | |
| accuracy | 0 | (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) | |
| accuracy | 0 | (*.f64 y x) | |
| accuracy | 0.00390625 | (fma.f64 (+.f64 y x) z (*.f64 y x)) | |
| accuracy | 8.738413422297528 | (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) |
| 66.0ms | 116× | 0 | invalid |
| 39.0ms | 140× | 0 | valid |
Compiled 398 to 45 computations (88.7% saved)
ival-mult: 35.0ms (41.7% of total)ival-add: 30.0ms (35.7% of total)ival-sqrt: 7.0ms (8.3% of total)ival-div: 6.0ms (7.1% of total)ival-pow2: 2.0ms (2.4% of total)ival-sub: 1.0ms (1.2% of total)ival-neg: 1.0ms (1.2% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) (patch (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) (patch (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (+.f64 y x) z (*.f64 y x)) (patch (fma.f64 (+.f64 y x) z (*.f64 y x)) #<representation binary64>) () ()) |
#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) (patch (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x))) (patch (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)) (patch #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)) #<representation binary64>) () ()) |
#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) (patch (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x))) (patch (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)) (patch #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)) #<representation binary64>) () ()) |
#s(alt (*.f64 (+.f64 z y) x) (patch (*.f64 (+.f64 z y) x) #<representation binary64>) () ()) |
#s(alt #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) (patch #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64))) (patch (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64))) #<representation binary64>) () ()) |
#s(alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) #<representation binary64>) () ()) |
#s(alt (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (patch (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) (patch (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) #<representation binary64>) () ()) |
#s(alt (/.f64 x (*.f64 (-.f64 y z) x)) (patch (/.f64 x (*.f64 (-.f64 y z) x)) #<representation binary64>) () ()) |
#s(alt (+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) (*.f64 y z)) (patch (+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) (*.f64 y z)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (*.f64 z x)) (patch (sqrt.f64 (*.f64 z x)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) (*.f64 y z))) (patch (sqrt.f64 (+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) (*.f64 y z))) #<representation binary64>) () ()) |
#s(alt (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)) (patch (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* 2 (sqrt (* x y))) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) (patch (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) (patch (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 2 (sqrt (* x y))) (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* (sqrt (/ 1 (* x y))) (+ x y))))) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) (patch (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 2 (sqrt (* x y))) (* z (+ (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3)))))) (* (sqrt (/ 1 (* x y))) (+ x y))))) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) (patch (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (* x y)) (taylor 0 z) (#s(alt (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) (patch (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (* x y)) (* 1/2 (* (sqrt (/ 1 (* x y))) (* z (+ x y))))) (taylor 0 z) (#s(alt (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) (patch (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (* x y)) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y)))))) (taylor 0 z) (#s(alt (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) (patch (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (* x y)) (* z (+ (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y))) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3))))))))) (taylor 0 z) (#s(alt (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) (patch (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor 0 z) (#s(alt (fma.f64 (+.f64 y x) z (*.f64 y x)) (patch (fma.f64 (+.f64 y x) z (*.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x y) (* z (+ x y))) (taylor 0 z) (#s(alt (fma.f64 (+.f64 y x) z (*.f64 y x)) (patch (fma.f64 (+.f64 y x) z (*.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x y) (* z (+ x y))) (taylor 0 z) (#s(alt (fma.f64 (+.f64 y x) z (*.f64 y x)) (patch (fma.f64 (+.f64 y x) z (*.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x y) (* z (+ x y))) (taylor 0 z) (#s(alt (fma.f64 (+.f64 y x) z (*.f64 y x)) (patch (fma.f64 (+.f64 y x) z (*.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 (sqrt (* x y))) (taylor 0 z) (#s(alt (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) (patch (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) (taylor 0 z) (#s(alt (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) (patch (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 2 (sqrt (* x y))) (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* (sqrt (/ 1 (* x y))) (+ x y))))) (taylor 0 z) (#s(alt (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) (patch (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 2 (sqrt (* x y))) (* z (+ (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3)))))) (* (sqrt (/ 1 (* x y))) (+ x y))))) (taylor 0 z) (#s(alt (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) (patch (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (* x y)) (taylor 0 z) (#s(alt (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x))) (patch (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (* x y)) (* 1/2 (* (sqrt (/ 1 (* x y))) (* z (+ x y))))) (taylor 0 z) (#s(alt (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x))) (patch (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (* x y)) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y)))))) (taylor 0 z) (#s(alt (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x))) (patch (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (* x y)) (* z (+ (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y))) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3))))))))) (taylor 0 z) (#s(alt (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x))) (patch (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor 0 z) (#s(alt #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)) (patch #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x y) (* z (+ x y))) (taylor 0 z) (#s(alt #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)) (patch #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x y) (* z (+ x y))) (taylor 0 z) (#s(alt #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)) (patch #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x y) (* z (+ x y))) (taylor 0 z) (#s(alt #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)) (patch #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)) #<representation binary64>) () ())) ()) |
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9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 25.0ms | y | @ | 0 | ((* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (+ y x) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (sqrt (+ (+ (* x y) (* x z)) (* y z))) (+ (+ (* x y) (* x z)) (* y z)) (* y x) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (sqrt (+ (+ (* x y) (* x z)) (* y z))) (+ (+ (* x y) (* x z)) (* y z)) (* (+ z y) x) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (* (sqrt (/ 1 (* z x))) (+ z x)) (sqrt (/ 1 (* z x))) (/ (pow (* z x) 2) x) (+ (* (* (* y y) x) (/ x (* (- y z) x))) (neg (/ (/ (pow (* z x) 2) x) (- y z)))) (/ x (* (- y z) x)) (+ (+ (* (* (* y y) x) (/ x (* (- y z) x))) (neg (/ (/ (pow (* z x) 2) x) (- y z)))) (* y z)) (sqrt (* z x)) (sqrt (+ (+ (* (* (* y y) x) (/ x (* (- y z) x))) (neg (/ (/ (pow (* z x) 2) x) (- y z)))) (* y z))) (/ (/ (pow (* z x) 2) x) (- y z))) |
| 9.0ms | y | @ | -inf | ((* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (+ y x) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (sqrt (+ (+ (* x y) (* x z)) (* y z))) (+ (+ (* x y) (* x z)) (* y z)) (* y x) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (sqrt (+ (+ (* x y) (* x z)) (* y z))) (+ (+ (* x y) (* x z)) (* y z)) (* (+ z y) x) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (* (sqrt (/ 1 (* z x))) (+ z x)) (sqrt (/ 1 (* z x))) (/ (pow (* z x) 2) x) (+ (* (* (* y y) x) (/ x (* (- y z) x))) (neg (/ (/ (pow (* z x) 2) x) (- y z)))) (/ x (* (- y z) x)) (+ (+ (* (* (* y y) x) (/ x (* (- y z) x))) (neg (/ (/ (pow (* z x) 2) x) (- y z)))) (* y z)) (sqrt (* z x)) (sqrt (+ (+ (* (* (* y y) x) (/ x (* (- y z) x))) (neg (/ (/ (pow (* z x) 2) x) (- y z)))) (* y z))) (/ (/ (pow (* z x) 2) x) (- y z))) |
| 7.0ms | z | @ | -inf | ((* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (+ y x) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (sqrt (+ (+ (* x y) (* x z)) (* y z))) (+ (+ (* x y) (* x z)) (* y z)) (* y x) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (sqrt (+ (+ (* x y) (* x z)) (* y z))) (+ (+ (* x y) (* x z)) (* y z)) (* (+ z y) x) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (* (sqrt (/ 1 (* z x))) (+ z x)) (sqrt (/ 1 (* z x))) (/ (pow (* z x) 2) x) (+ (* (* (* y y) x) (/ x (* (- y z) x))) (neg (/ (/ (pow (* z x) 2) x) (- y z)))) (/ x (* (- y z) x)) (+ (+ (* (* (* y y) x) (/ x (* (- y z) x))) (neg (/ (/ (pow (* z x) 2) x) (- y z)))) (* y z)) (sqrt (* z x)) (sqrt (+ (+ (* (* (* y y) x) (/ x (* (- y z) x))) (neg (/ (/ (pow (* z x) 2) x) (- y z)))) (* y z))) (/ (/ (pow (* z x) 2) x) (- y z))) |
| 7.0ms | x | @ | -inf | ((* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (+ y x) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (sqrt (+ (+ (* x y) (* x z)) (* y z))) (+ (+ (* x y) (* x z)) (* y z)) (* y x) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (sqrt (+ (+ (* x y) (* x z)) (* y z))) (+ (+ (* x y) (* x z)) (* y z)) (* (+ z y) x) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (* (sqrt (/ 1 (* z x))) (+ z x)) (sqrt (/ 1 (* z x))) (/ (pow (* z x) 2) x) (+ (* (* (* y y) x) (/ x (* (- y z) x))) (neg (/ (/ (pow (* z x) 2) x) (- y z)))) (/ x (* (- y z) x)) (+ (+ (* (* (* y y) x) (/ x (* (- y z) x))) (neg (/ (/ (pow (* z x) 2) x) (- y z)))) (* y z)) (sqrt (* z x)) (sqrt (+ (+ (* (* (* y y) x) (/ x (* (- y z) x))) (neg (/ (/ (pow (* z x) 2) x) (- y z)))) (* y z))) (/ (/ (pow (* z x) 2) x) (- y z))) |
| 7.0ms | z | @ | 0 | ((* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (+ y x) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (sqrt (+ (+ (* x y) (* x z)) (* y z))) (+ (+ (* x y) (* x z)) (* y z)) (* y x) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (sqrt (+ (+ (* x y) (* x z)) (* y z))) (+ (+ (* x y) (* x z)) (* y z)) (* (+ z y) x) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (* (sqrt (/ 1 (* z x))) (+ z x)) (sqrt (/ 1 (* z x))) (/ (pow (* z x) 2) x) (+ (* (* (* y y) x) (/ x (* (- y z) x))) (neg (/ (/ (pow (* z x) 2) x) (- y z)))) (/ x (* (- y z) x)) (+ (+ (* (* (* y y) x) (/ x (* (- y z) x))) (neg (/ (/ (pow (* z x) 2) x) (- y z)))) (* y z)) (sqrt (* z x)) (sqrt (+ (+ (* (* (* y y) x) (/ x (* (- y z) x))) (neg (/ (/ (pow (* z x) 2) x) (- y z)))) (* y z))) (/ (/ (pow (* z x) 2) x) (- y z))) |
| 1× | egg-herbie |
| 7 908× | lower-fma.f64 |
| 7 908× | lower-fma.f32 |
| 7 062× | lower-*.f64 |
| 7 062× | lower-*.f32 |
| 5 192× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1158 | 17035 |
| 1 | 3844 | 16312 |
| 0 | 8186 | 15684 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 2 (sqrt (* x y))) |
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y |
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(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (* (pow z 2) (sqrt -1))) (sqrt (/ 1 (* (pow y 5) (pow (+ (* -1 x) (* -1 z)) 3)))))) (+ (* 1/2 (* (* x (* z (sqrt -1))) (sqrt (/ 1 (* (pow y 3) (+ (* -1 x) (* -1 z))))))) (* (sqrt (/ (+ (* -1 x) (* -1 z)) y)) (sqrt -1)))))) |
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (* (pow z 2) (sqrt -1))) (sqrt (/ 1 (* (pow y 5) (pow (+ (* -1 x) (* -1 z)) 3)))))) (+ (* 1/16 (* (* (pow x 3) (* (pow z 3) (sqrt -1))) (sqrt (/ 1 (* (pow y 7) (pow (+ (* -1 x) (* -1 z)) 5)))))) (+ (* 1/2 (* (* x (* z (sqrt -1))) (sqrt (/ 1 (* (pow y 3) (+ (* -1 x) (* -1 z))))))) (* (sqrt (/ (+ (* -1 x) (* -1 z)) y)) (sqrt -1))))))) |
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(* -1 (* y (+ (* -1/4 (* (* (pow x 2) (* (pow z 2) (sqrt -1))) (sqrt (/ 1 (* (pow y 5) (pow (+ (* -1 x) (* -1 z)) 3)))))) (+ (* 2 (* (sqrt (/ (+ (* -1 x) (* -1 z)) y)) (sqrt -1))) (* (* x (* z (sqrt -1))) (sqrt (/ 1 (* (pow y 3) (+ (* -1 x) (* -1 z)))))))))) |
(* -1 (* y (+ (* -1/4 (* (* (pow x 2) (* (pow z 2) (sqrt -1))) (sqrt (/ 1 (* (pow y 5) (pow (+ (* -1 x) (* -1 z)) 3)))))) (+ (* 1/8 (* (* (pow x 3) (* (pow z 3) (sqrt -1))) (sqrt (/ 1 (* (pow y 7) (pow (+ (* -1 x) (* -1 z)) 5)))))) (+ (* 2 (* (sqrt (/ (+ (* -1 x) (* -1 z)) y)) (sqrt -1))) (* (* x (* z (sqrt -1))) (sqrt (/ 1 (* (pow y 3) (+ (* -1 x) (* -1 z))))))))))) |
(* (sqrt (/ 1 (* x z))) (* y (+ x z))) |
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(* -1 (* y (+ (* -2 (* (sqrt (* x z)) (/ 1 y))) (* -1 (* (sqrt (/ 1 (* x z))) (+ x z)))))) |
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(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow z 3) y)) (pow z 2)) y)) (* -1 z)) y)) 1) y)) |
(* -1 (* y (+ (* -1 x) (* -1 z)))) |
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(* -1 (* y (+ (* 1/2 (* (* x (* z (sqrt -1))) (sqrt (/ 1 (* (pow y 3) (+ (* -1 x) (* -1 z))))))) (* (sqrt (/ (+ (* -1 x) (* -1 z)) y)) (sqrt -1))))) |
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (* (pow z 2) (sqrt -1))) (sqrt (/ 1 (* (pow y 5) (pow (+ (* -1 x) (* -1 z)) 3)))))) (+ (* 1/2 (* (* x (* z (sqrt -1))) (sqrt (/ 1 (* (pow y 3) (+ (* -1 x) (* -1 z))))))) (* (sqrt (/ (+ (* -1 x) (* -1 z)) y)) (sqrt -1)))))) |
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (* (pow z 2) (sqrt -1))) (sqrt (/ 1 (* (pow y 5) (pow (+ (* -1 x) (* -1 z)) 3)))))) (+ (* 1/16 (* (* (pow x 3) (* (pow z 3) (sqrt -1))) (sqrt (/ 1 (* (pow y 7) (pow (+ (* -1 x) (* -1 z)) 5)))))) (+ (* 1/2 (* (* x (* z (sqrt -1))) (sqrt (/ 1 (* (pow y 3) (+ (* -1 x) (* -1 z))))))) (* (sqrt (/ (+ (* -1 x) (* -1 z)) y)) (sqrt -1))))))) |
(/ (* x (pow z 2)) y) |
(* -1 (/ (+ (* -1 (* x (pow z 2))) (* -1 (/ (* x (pow z 3)) y))) y)) |
(* -1 (/ (+ (* -1 (* x (pow z 2))) (* -1 (/ (+ (* x (pow z 3)) (/ (* x (pow z 4)) y)) y))) y)) |
(* -1 (/ (+ (* -1 (* x (pow z 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* x (pow z 4))) (* -1 (/ (* x (pow z 5)) y))) y)) (* x (pow z 3))) y))) y)) |
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(+ (* 2 (sqrt (* y z))) (* x (+ (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow y 3) (pow z 3)))) (pow (+ y z) 2))) (* 1/8 (* (* x (pow (+ y z) 3)) (sqrt (/ 1 (* (pow y 5) (pow z 5)))))))) (* (sqrt (/ 1 (* y z))) (+ y z))))) |
(sqrt (* y z)) |
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(+ (sqrt (* y z)) (* x (+ (* -1/8 (* (* x (pow (+ y z) 2)) (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (* 1/2 (* (sqrt (/ 1 (* y z))) (+ y z)))))) |
(+ (sqrt (* y z)) (* x (+ (* 1/2 (* (sqrt (/ 1 (* y z))) (+ y z))) (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow y 3) (pow z 3)))) (pow (+ y z) 2))) (* 1/16 (* (* x (pow (+ y z) 3)) (sqrt (/ 1 (* (pow y 5) (pow z 5))))))))))) |
(* y z) |
(+ (* x (+ y z)) (* y z)) |
(+ (* x (+ y z)) (* y z)) |
(+ (* x (+ y z)) (* y z)) |
y |
(+ x y) |
(+ x y) |
(+ x y) |
(* 2 (sqrt (* y z))) |
(+ (* 2 (sqrt (* y z))) (* (* x (+ y z)) (sqrt (/ 1 (* y z))))) |
(+ (* 2 (sqrt (* y z))) (* x (+ (* -1/4 (* (* x (pow (+ y z) 2)) (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (* (sqrt (/ 1 (* y z))) (+ y z))))) |
(+ (* 2 (sqrt (* y z))) (* x (+ (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow y 3) (pow z 3)))) (pow (+ y z) 2))) (* 1/8 (* (* x (pow (+ y z) 3)) (sqrt (/ 1 (* (pow y 5) (pow z 5)))))))) (* (sqrt (/ 1 (* y z))) (+ y z))))) |
(sqrt (* y z)) |
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(+ (sqrt (* y z)) (* x (+ (* -1/8 (* (* x (pow (+ y z) 2)) (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (* 1/2 (* (sqrt (/ 1 (* y z))) (+ y z)))))) |
(+ (sqrt (* y z)) (* x (+ (* 1/2 (* (sqrt (/ 1 (* y z))) (+ y z))) (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow y 3) (pow z 3)))) (pow (+ y z) 2))) (* 1/16 (* (* x (pow (+ y z) 3)) (sqrt (/ 1 (* (pow y 5) (pow z 5))))))))))) |
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(+ (* x (+ y z)) (* y z)) |
(+ (* x (+ y z)) (* y z)) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* 2 (sqrt (* y z))) |
(+ (* 2 (sqrt (* y z))) (* (* x (+ y z)) (sqrt (/ 1 (* y z))))) |
(+ (* 2 (sqrt (* y z))) (* x (+ (* -1/4 (* (* x (pow (+ y z) 2)) (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (* (sqrt (/ 1 (* y z))) (+ y z))))) |
(+ (* 2 (sqrt (* y z))) (* x (+ (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow y 3) (pow z 3)))) (pow (+ y z) 2))) (* 1/8 (* (* x (pow (+ y z) 3)) (sqrt (/ 1 (* (pow y 5) (pow z 5)))))))) (* (sqrt (/ 1 (* y z))) (+ y z))))) |
(sqrt (* y z)) |
(+ (sqrt (* y z)) (* 1/2 (* (* x (+ y z)) (sqrt (/ 1 (* y z)))))) |
(+ (sqrt (* y z)) (* x (+ (* -1/8 (* (* x (pow (+ y z) 2)) (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (* 1/2 (* (sqrt (/ 1 (* y z))) (+ y z)))))) |
(+ (sqrt (* y z)) (* x (+ (* 1/2 (* (sqrt (/ 1 (* y z))) (+ y z))) (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow y 3) (pow z 3)))) (pow (+ y z) 2))) (* 1/16 (* (* x (pow (+ y z) 3)) (sqrt (/ 1 (* (pow y 5) (pow z 5))))))))))) |
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(+ (* x (+ y z)) (* y z)) |
(+ (* x (+ y z)) (* y z)) |
(* x (+ y z)) |
(* x (+ y z)) |
(* x (+ y z)) |
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(+ (* 2 (sqrt (* y z))) (* x (+ (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow y 3) (pow z 3)))) (pow (+ y z) 2))) (* 1/8 (* (* x (pow (+ y z) 3)) (sqrt (/ 1 (* (pow y 5) (pow z 5)))))))) (* (sqrt (/ 1 (* y z))) (+ y z))))) |
(* (sqrt (/ z x)) y) |
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(/ (+ (* x (+ (* 2 (sqrt (* x z))) (* (sqrt (/ x z)) y))) (* (sqrt (* x z)) y)) x) |
(/ (+ (* x (+ (* 2 (sqrt (* x z))) (* (sqrt (/ x z)) y))) (* (sqrt (* x z)) y)) x) |
(sqrt (/ z x)) |
(/ (+ (sqrt (* x z)) (sqrt (/ (pow x 3) z))) x) |
(/ (+ (sqrt (* x z)) (sqrt (/ (pow x 3) z))) x) |
(/ (+ (sqrt (* x z)) (sqrt (/ (pow x 3) z))) x) |
(sqrt (/ 1 (* x z))) |
(sqrt (/ 1 (* x z))) |
(sqrt (/ 1 (* x z))) |
(sqrt (/ 1 (* x z))) |
(* x (pow z 2)) |
(* x (pow z 2)) |
(* x (pow z 2)) |
(* x (pow z 2)) |
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(/ 1 (- y z)) |
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(/ 1 (- y z)) |
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(sqrt (* x z)) |
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(sqrt (* y z)) |
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(+ (sqrt (* y z)) (* x (+ (* -1/8 (* (* x (pow (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z))) 2)) (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (* 1/2 (* (sqrt (/ 1 (* y z))) (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z)))))))) |
(+ (sqrt (* y z)) (* x (+ (* 1/2 (* (sqrt (/ 1 (* y z))) (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z))))) (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow y 3) (pow z 3)))) (pow (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z))) 2))) (* 1/16 (* (* x (pow (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z))) 3)) (sqrt (/ 1 (* (pow y 5) (pow z 5))))))))))) |
(/ (* x (pow z 2)) (- y z)) |
(/ (* x (pow z 2)) (- y z)) |
(/ (* x (pow z 2)) (- y z)) |
(/ (* x (pow z 2)) (- y z)) |
(* 2 (sqrt (* x (+ y z)))) |
(* x (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))) |
(* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z))))) |
(* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow x 7) (pow (+ y z) 5)))) (* (pow y 3) (pow z 3)))) (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))))) |
(sqrt (* x (+ y z))) |
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(* x (+ (sqrt (/ (+ y z) x)) (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))))) |
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(* x (+ y z)) |
(* x (+ y (+ z (/ (* y z) x)))) |
(* x (+ y (+ z (/ (* y z) x)))) |
(* x (+ y (+ z (/ (* y z) x)))) |
x |
(* x (+ 1 (/ y x))) |
(* x (+ 1 (/ y x))) |
(* x (+ 1 (/ y x))) |
(* 2 (sqrt (* x (+ y z)))) |
(* x (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))) |
(* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z))))) |
(* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow x 7) (pow (+ y z) 5)))) (* (pow y 3) (pow z 3)))) (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))))) |
(sqrt (* x (+ y z))) |
(* x (+ (sqrt (/ (+ y z) x)) (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z))))) |
(* x (+ (sqrt (/ (+ y z) x)) (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))))) |
(* x (+ (sqrt (/ (+ y z) x)) (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) (pow (+ y z) 5)))) (* (pow y 3) (pow z 3)))) (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z))))))) |
(* x (+ y z)) |
(* x (+ y (+ z (/ (* y z) x)))) |
(* x (+ y (+ z (/ (* y z) x)))) |
(* x (+ y (+ z (/ (* y z) x)))) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* 2 (sqrt (* x (+ y z)))) |
(* x (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))) |
(* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z))))) |
(* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow x 7) (pow (+ y z) 5)))) (* (pow y 3) (pow z 3)))) (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))))) |
(sqrt (* x (+ y z))) |
(* x (+ (sqrt (/ (+ y z) x)) (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z))))) |
(* x (+ (sqrt (/ (+ y z) x)) (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))))) |
(* x (+ (sqrt (/ (+ y z) x)) (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) (pow (+ y z) 5)))) (* (pow y 3) (pow z 3)))) (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z))))))) |
(* x (+ y z)) |
(* x (+ y (+ z (/ (* y z) x)))) |
(* x (+ y (+ z (/ (* y z) x)))) |
(* x (+ y (+ z (/ (* y z) x)))) |
(* x (+ y z)) |
(* x (+ y z)) |
(* x (+ y z)) |
(* x (+ y z)) |
(* 2 (sqrt (* x (+ y z)))) |
(* x (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))) |
(* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z))))) |
(* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow x 7) (pow (+ y z) 5)))) (* (pow y 3) (pow z 3)))) (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))))) |
(* x (+ (* 2 (sqrt (/ z x))) (* (sqrt (/ 1 (* x z))) y))) |
(* x (+ (* 2 (sqrt (/ z x))) (+ (* (sqrt (/ 1 (* x z))) y) (* (sqrt (/ z (pow x 3))) y)))) |
(* x (+ (* 2 (sqrt (/ z x))) (+ (* (sqrt (/ 1 (* x z))) y) (* (sqrt (/ z (pow x 3))) y)))) |
(* x (+ (* 2 (sqrt (/ z x))) (+ (* (sqrt (/ 1 (* x z))) y) (* (sqrt (/ z (pow x 3))) y)))) |
(sqrt (/ x z)) |
(* x (+ (sqrt (/ 1 (* x z))) (sqrt (/ z (pow x 3))))) |
(* x (+ (sqrt (/ 1 (* x z))) (sqrt (/ z (pow x 3))))) |
(* x (+ (sqrt (/ 1 (* x z))) (sqrt (/ z (pow x 3))))) |
(sqrt (/ 1 (* x z))) |
(sqrt (/ 1 (* x z))) |
(sqrt (/ 1 (* x z))) |
(sqrt (/ 1 (* x z))) |
(* x (pow z 2)) |
(* x (pow z 2)) |
(* x (pow z 2)) |
(* x (pow z 2)) |
(* x (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z)))) |
(* x (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z)))) |
(* x (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z)))) |
(* x (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z)))) |
(/ 1 (- y z)) |
(/ 1 (- y z)) |
(/ 1 (- y z)) |
(/ 1 (- y z)) |
(* x (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z)))) |
(* x (- (+ (/ (* y z) x) (/ (pow y 2) (- y z))) (/ (pow z 2) (- y z)))) |
(* x (- (+ (/ (* y z) x) (/ (pow y 2) (- y z))) (/ (pow z 2) (- y z)))) |
(* x (- (+ (/ (* y z) x) (/ (pow y 2) (- y z))) (/ (pow z 2) (- y z)))) |
(sqrt (* x z)) |
(sqrt (* x z)) |
(sqrt (* x z)) |
(sqrt (* x z)) |
(sqrt (* x (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z))))) |
(* x (+ (sqrt (/ (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z))) x)) (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z)))))) (* y z))))) |
(* x (+ (sqrt (/ (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z))) x)) (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z))) 3)))) (* (pow y 2) (pow z 2)))) (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z)))))) (* y z)))))) |
(* x (+ (sqrt (/ (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z))) x)) (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z))) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) (pow (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z))) 5)))) (* (pow y 3) (pow z 3)))) (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (- (/ (pow y 2) (- y z)) (/ (pow z 2) (- y z)))))) (* y z))))))) |
(/ (* x (pow z 2)) (- y z)) |
(/ (* x (pow z 2)) (- y z)) |
(/ (* x (pow z 2)) (- y z)) |
(/ (* x (pow z 2)) (- y z)) |
(* -2 (* (sqrt (* x (+ (* -1 y) (* -1 z)))) (sqrt -1))) |
(* -1 (* x (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1)))))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow x 7) (pow (+ (* -1 y) (* -1 z)) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))))))) |
(* -1 (* (sqrt (* x (+ (* -1 y) (* -1 z)))) (sqrt -1))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) (pow (+ (* -1 y) (* -1 z)) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))))))) |
(* -1 (* x (+ (* -1 y) (* -1 z)))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
x |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(* -2 (* (sqrt (* x (+ (* -1 y) (* -1 z)))) (sqrt -1))) |
(* -1 (* x (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1)))))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow x 7) (pow (+ (* -1 y) (* -1 z)) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))))))) |
(* -1 (* (sqrt (* x (+ (* -1 y) (* -1 z)))) (sqrt -1))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) (pow (+ (* -1 y) (* -1 z)) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))))))) |
(* -1 (* x (+ (* -1 y) (* -1 z)))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* -2 (* (sqrt (* x (+ (* -1 y) (* -1 z)))) (sqrt -1))) |
(* -1 (* x (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1)))))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow x 7) (pow (+ (* -1 y) (* -1 z)) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))))))) |
(* -1 (* (sqrt (* x (+ (* -1 y) (* -1 z)))) (sqrt -1))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) (pow (+ (* -1 y) (* -1 z)) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))))))) |
(* -1 (* x (+ (* -1 y) (* -1 z)))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(* x (+ y z)) |
(* x (+ y z)) |
(* x (+ y z)) |
(* x (+ y z)) |
(* -2 (* (sqrt (* x (+ (* -1 y) (* -1 z)))) (sqrt -1))) |
(* -1 (* x (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1)))))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow x 7) (pow (+ (* -1 y) (* -1 z)) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))))))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))) (+ (* -1 (* (sqrt (/ z (pow x 3))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))) (+ (* -1 (* (sqrt (/ z (pow x 3))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))) (+ (* -1 (* (sqrt (/ z (pow x 3))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2))))))) |
(* (sqrt (/ x z)) (pow (sqrt -1) 2)) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ z (pow x 3))) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ z (pow x 3))) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ z (pow x 3))) (pow (sqrt -1) 2)))))) |
(* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2)) |
(* x (pow z 2)) |
(* x (pow z 2)) |
(* x (pow z 2)) |
(* x (pow z 2)) |
(* -1 (* x (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))))) |
(* -1 (* x (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))))) |
(* -1 (* x (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))))) |
(* -1 (* x (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))))) |
(/ 1 (- y z)) |
(/ 1 (- y z)) |
(/ 1 (- y z)) |
(/ 1 (- y z)) |
(* -1 (* x (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))))) |
(* -1 (* x (- (+ (* -1 (/ (* y z) x)) (* -1 (/ (pow y 2) (- y z)))) (* -1 (/ (pow z 2) (- y z)))))) |
(* -1 (* x (- (+ (* -1 (/ (* y z) x)) (* -1 (/ (pow y 2) (- y z)))) (* -1 (/ (pow z 2) (- y z)))))) |
(* -1 (* x (- (+ (* -1 (/ (* y z) x)) (* -1 (/ (pow y 2) (- y z)))) (* -1 (/ (pow z 2) (- y z)))))) |
(* -1 (* (sqrt (* x z)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (* x z)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (* x z)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (* x z)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (* x (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))))) (sqrt -1))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z))))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))) x)) (sqrt -1))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z))))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))) x)) (sqrt -1)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) (pow (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z))))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))) x)) (sqrt -1))))))) |
(/ (* x (pow z 2)) (- y z)) |
(/ (* x (pow z 2)) (- y z)) |
(/ (* x (pow z 2)) (- y z)) |
(/ (* x (pow z 2)) (- y z)) |
| Outputs |
|---|
(* 2 (sqrt (* x y))) |
(*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64)) |
(+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) |
(fma.f64 (*.f64 (+.f64 y x) z) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))) (*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (*.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) z) (*.f64 (+.f64 y x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))))) z (*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3)))))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 y #s(literal 5 binary64))))) (*.f64 (pow.f64 (+.f64 y x) #s(literal 3 binary64)) z) (*.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (pow.f64 (+.f64 y x) #s(literal 2 binary64)))) z (*.f64 (+.f64 y x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))))) z (*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64))) |
(sqrt (* x y)) |
(sqrt.f64 (*.f64 y x)) |
(+ (sqrt (* x y)) (* 1/2 (* (sqrt (/ 1 (* x y))) (* z (+ x y))))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (+.f64 y x) z) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x)))) (sqrt.f64 (*.f64 y x))) |
(+ (sqrt (* x y)) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y)))))) |
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(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 (-.f64 (neg.f64 z) y) #s(literal 3 binary64))))) (*.f64 (*.f64 (*.f64 z y) (*.f64 z y)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))) (pow.f64 (-.f64 (neg.f64 z) y) #s(literal 5 binary64))))) (*.f64 (*.f64 (pow.f64 z #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (-.f64 (neg.f64 z) y)))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) z) y) (*.f64 (sqrt.f64 (/.f64 (-.f64 (neg.f64 z) y) x)) (sqrt.f64 #s(literal -1 binary64)))))) (neg.f64 x)) |
(* -1 (* x (+ (* -1 y) (* -1 z)))) |
(*.f64 (-.f64 (neg.f64 z) y) (neg.f64 x)) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(*.f64 (-.f64 (neg.f64 (fma.f64 y (/.f64 z x) z)) y) (neg.f64 x)) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(*.f64 (-.f64 (neg.f64 (fma.f64 y (/.f64 z x) z)) y) (neg.f64 x)) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(*.f64 (-.f64 (neg.f64 (fma.f64 y (/.f64 z x) z)) y) (neg.f64 x)) |
(* x (+ y z)) |
(*.f64 (+.f64 z y) x) |
(* x (+ y z)) |
(*.f64 (+.f64 z y) x) |
(* x (+ y z)) |
(*.f64 (+.f64 z y) x) |
(* x (+ y z)) |
(*.f64 (+.f64 z y) x) |
(* -2 (* (sqrt (* x (+ (* -1 y) (* -1 z)))) (sqrt -1))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 (-.f64 (neg.f64 z) y) x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -2 binary64)) |
(* -1 (* x (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (-.f64 (neg.f64 z) y) x))) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) z) y) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (-.f64 (neg.f64 z) y))))) (neg.f64 x)) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1)))))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 z y) (*.f64 z y)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 (-.f64 (neg.f64 z) y) #s(literal 3 binary64))))) #s(literal -1/4 binary64) (fma.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (-.f64 (neg.f64 z) y) x))) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) z) y) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (-.f64 (neg.f64 z) y)))))) (neg.f64 x)) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow x 7) (pow (+ (* -1 y) (* -1 z)) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 z y) (*.f64 z y)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 (-.f64 (neg.f64 z) y) #s(literal 3 binary64))))) #s(literal -1/4 binary64) (fma.f64 (*.f64 (*.f64 (*.f64 (pow.f64 z #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))) (pow.f64 (-.f64 (neg.f64 z) y) #s(literal 5 binary64))))) #s(literal 1/8 binary64) (fma.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (-.f64 (neg.f64 z) y) x))) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) z) y) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (-.f64 (neg.f64 z) y))))))) (neg.f64 x)) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x)))) (neg.f64 y) (*.f64 (*.f64 (sqrt.f64 (/.f64 z x)) #s(literal 2 binary64)) #s(literal -1 binary64))) (neg.f64 x)) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))) (+ (* -1 (* (sqrt (/ z (pow x 3))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2))))))) |
(*.f64 (fma.f64 (neg.f64 y) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (neg.f64 (sqrt.f64 (/.f64 z (pow.f64 x #s(literal 3 binary64)))))) (*.f64 (*.f64 (sqrt.f64 (/.f64 z x)) #s(literal 2 binary64)) #s(literal -1 binary64))) (neg.f64 x)) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))) (+ (* -1 (* (sqrt (/ z (pow x 3))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2))))))) |
(*.f64 (fma.f64 (neg.f64 y) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (neg.f64 (sqrt.f64 (/.f64 z (pow.f64 x #s(literal 3 binary64)))))) (*.f64 (*.f64 (sqrt.f64 (/.f64 z x)) #s(literal 2 binary64)) #s(literal -1 binary64))) (neg.f64 x)) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))) (+ (* -1 (* (sqrt (/ z (pow x 3))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2))))))) |
(*.f64 (fma.f64 (neg.f64 y) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (neg.f64 (sqrt.f64 (/.f64 z (pow.f64 x #s(literal 3 binary64)))))) (*.f64 (*.f64 (sqrt.f64 (/.f64 z x)) #s(literal 2 binary64)) #s(literal -1 binary64))) (neg.f64 x)) |
(* (sqrt (/ x z)) (pow (sqrt -1) 2)) |
(*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 x z))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ z (pow x 3))) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 z (pow.f64 x #s(literal 3 binary64)))) #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) #s(literal 1 binary64))) (neg.f64 x)) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ z (pow x 3))) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 z (pow.f64 x #s(literal 3 binary64)))) #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) #s(literal 1 binary64))) (neg.f64 x)) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ z (pow x 3))) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 z (pow.f64 x #s(literal 3 binary64)))) #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) #s(literal 1 binary64))) (neg.f64 x)) |
(* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x)))) |
(* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x)))) |
(* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x)))) |
(* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x)))) |
(* x (pow z 2)) |
(*.f64 (*.f64 z z) x) |
(* x (pow z 2)) |
(*.f64 (*.f64 z z) x) |
(* x (pow z 2)) |
(*.f64 (*.f64 z z) x) |
(* x (pow z 2)) |
(*.f64 (*.f64 z z) x) |
(* -1 (* x (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))))) |
(*.f64 (fma.f64 (/.f64 (*.f64 y y) (-.f64 y z)) #s(literal -1 binary64) (/.f64 (*.f64 z z) (-.f64 y z))) (neg.f64 x)) |
(* -1 (* x (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))))) |
(*.f64 (fma.f64 (/.f64 (*.f64 y y) (-.f64 y z)) #s(literal -1 binary64) (/.f64 (*.f64 z z) (-.f64 y z))) (neg.f64 x)) |
(* -1 (* x (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))))) |
(*.f64 (fma.f64 (/.f64 (*.f64 y y) (-.f64 y z)) #s(literal -1 binary64) (/.f64 (*.f64 z z) (-.f64 y z))) (neg.f64 x)) |
(* -1 (* x (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))))) |
(*.f64 (fma.f64 (/.f64 (*.f64 y y) (-.f64 y z)) #s(literal -1 binary64) (/.f64 (*.f64 z z) (-.f64 y z))) (neg.f64 x)) |
(/ 1 (- y z)) |
(/.f64 #s(literal 1 binary64) (-.f64 y z)) |
(/ 1 (- y z)) |
(/.f64 #s(literal 1 binary64) (-.f64 y z)) |
(/ 1 (- y z)) |
(/.f64 #s(literal 1 binary64) (-.f64 y z)) |
(/ 1 (- y z)) |
(/.f64 #s(literal 1 binary64) (-.f64 y z)) |
(* -1 (* x (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))))) |
(*.f64 (fma.f64 (/.f64 (*.f64 y y) (-.f64 y z)) #s(literal -1 binary64) (/.f64 (*.f64 z z) (-.f64 y z))) (neg.f64 x)) |
(* -1 (* x (- (+ (* -1 (/ (* y z) x)) (* -1 (/ (pow y 2) (- y z)))) (* -1 (/ (pow z 2) (- y z)))))) |
(*.f64 (fma.f64 #s(literal -1 binary64) (fma.f64 y (/.f64 z x) (/.f64 (*.f64 y y) (-.f64 y z))) (/.f64 (*.f64 z z) (-.f64 y z))) (neg.f64 x)) |
(* -1 (* x (- (+ (* -1 (/ (* y z) x)) (* -1 (/ (pow y 2) (- y z)))) (* -1 (/ (pow z 2) (- y z)))))) |
(*.f64 (fma.f64 #s(literal -1 binary64) (fma.f64 y (/.f64 z x) (/.f64 (*.f64 y y) (-.f64 y z))) (/.f64 (*.f64 z z) (-.f64 y z))) (neg.f64 x)) |
(* -1 (* x (- (+ (* -1 (/ (* y z) x)) (* -1 (/ (pow y 2) (- y z)))) (* -1 (/ (pow z 2) (- y z)))))) |
(*.f64 (fma.f64 #s(literal -1 binary64) (fma.f64 y (/.f64 z x) (/.f64 (*.f64 y y) (-.f64 y z))) (/.f64 (*.f64 z z) (-.f64 y z))) (neg.f64 x)) |
(* -1 (* (sqrt (* x z)) (pow (sqrt -1) 2))) |
(sqrt.f64 (*.f64 z x)) |
(* -1 (* (sqrt (* x z)) (pow (sqrt -1) 2))) |
(sqrt.f64 (*.f64 z x)) |
(* -1 (* (sqrt (* x z)) (pow (sqrt -1) 2))) |
(sqrt.f64 (*.f64 z x)) |
(* -1 (* (sqrt (* x z)) (pow (sqrt -1) 2))) |
(sqrt.f64 (*.f64 z x)) |
(* -1 (* (sqrt (* x (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))))) (sqrt -1))) |
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (fma.f64 (/.f64 (*.f64 y y) (-.f64 y z)) #s(literal -1 binary64) (/.f64 (*.f64 z z) (-.f64 y z))) x))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z))))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))) x)) (sqrt -1))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 y y) (-.f64 y z)) #s(literal -1 binary64) (/.f64 (*.f64 z z) (-.f64 y z)))))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) z) y) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (*.f64 y y) (-.f64 y z)) #s(literal -1 binary64) (/.f64 (*.f64 z z) (-.f64 y z))) x)) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 x)) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z))))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))) x)) (sqrt -1)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 (fma.f64 (/.f64 (*.f64 y y) (-.f64 y z)) #s(literal -1 binary64) (/.f64 (*.f64 z z) (-.f64 y z))) #s(literal 3 binary64))))) (*.f64 (*.f64 (*.f64 z y) (*.f64 z y)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 y y) (-.f64 y z)) #s(literal -1 binary64) (/.f64 (*.f64 z z) (-.f64 y z)))))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) z) y) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (*.f64 y y) (-.f64 y z)) #s(literal -1 binary64) (/.f64 (*.f64 z z) (-.f64 y z))) x)) (sqrt.f64 #s(literal -1 binary64))))) (neg.f64 x)) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) (pow (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z))))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (- (* -1 (/ (pow y 2) (- y z))) (* -1 (/ (pow z 2) (- y z)))) x)) (sqrt -1))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 (fma.f64 (/.f64 (*.f64 y y) (-.f64 y z)) #s(literal -1 binary64) (/.f64 (*.f64 z z) (-.f64 y z))) #s(literal 3 binary64))))) (*.f64 (*.f64 (*.f64 z y) (*.f64 z y)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))) (pow.f64 (fma.f64 (/.f64 (*.f64 y y) (-.f64 y z)) #s(literal -1 binary64) (/.f64 (*.f64 z z) (-.f64 y z))) #s(literal 5 binary64))))) (*.f64 (*.f64 (pow.f64 z #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 y y) (-.f64 y z)) #s(literal -1 binary64) (/.f64 (*.f64 z z) (-.f64 y z)))))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) z) y) (*.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (*.f64 y y) (-.f64 y z)) #s(literal -1 binary64) (/.f64 (*.f64 z z) (-.f64 y z))) x)) (sqrt.f64 #s(literal -1 binary64)))))) (neg.f64 x)) |
(/ (* x (pow z 2)) (- y z)) |
(/.f64 (*.f64 (*.f64 z z) x) (-.f64 y z)) |
(/ (* x (pow z 2)) (- y z)) |
(/.f64 (*.f64 (*.f64 z z) x) (-.f64 y z)) |
(/ (* x (pow z 2)) (- y z)) |
(/.f64 (*.f64 (*.f64 z z) x) (-.f64 y z)) |
(/ (* x (pow z 2)) (- y z)) |
(/.f64 (*.f64 (*.f64 z z) x) (-.f64 y z)) |
| 5 522× | lower-*.f32 |
| 5 498× | lower-*.f64 |
| 5 002× | lower-/.f32 |
| 4 994× | lower-/.f64 |
| 4 232× | lower-fma.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 47 | 323 |
| 0 | 82 | 247 |
| 1 | 306 | 233 |
| 2 | 2320 | 229 |
| 0 | 9928 | 229 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
(sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(+.f64 y x) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
(sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x))) |
#s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)) |
(*.f64 y x) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) |
(sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x))) |
#s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)) |
(*.f64 (+.f64 z y) x) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) |
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) |
(/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) |
(fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) |
(/.f64 x (*.f64 (-.f64 y z) x)) |
(+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) (*.f64 y z)) |
(sqrt.f64 (*.f64 z x)) |
(sqrt.f64 (+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) (*.f64 y z))) |
(/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)) |
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Compiled 99 269 to 9 339 computations (90.6% saved)
31 alts after pruning (29 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 2 561 | 28 | 2 589 |
| Fresh | 10 | 1 | 11 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 0 | 0 |
| Total | 2 574 | 31 | 2 605 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 70.7% | (*.f64 (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) |
| 37.9% | (*.f64 (pow.f64 (*.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) (fma.f64 z (+.f64 x y) (*.f64 x y))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) | |
| 19.3% | (*.f64 (/.f64 (sqrt.f64 (-.f64 (pow.f64 (*.f64 z (+.f64 x y)) #s(literal 2 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 z (+.f64 x y) (*.f64 (neg.f64 x) y)))) #s(literal 2 binary64)) | |
| 53.2% | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x))) #s(literal 2 binary64)) | |
| 37.1% | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 y x) z))) #s(literal 2 binary64)) | |
| 35.7% | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) | |
| ▶ | 3.7% | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) |
| 36.6% | (*.f64 #s(literal 2 binary64) (pow.f64 (pow.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64))) | |
| 20.5% | (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)) #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x))) #s(literal 1/4 binary64))) | |
| 19.1% | (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 x y)) #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 x y))) #s(literal 1/4 binary64))) | |
| ▶ | 70.4% | (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x)))))) |
| 56.2% | (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 #s(approx (/ (/ (pow (* z x) 2) x) (- y z)) (*.f64 (neg.f64 x) z)))) (*.f64 y z)))) | |
| 35.4% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z)))))) | |
| 37.8% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 z x (*.f64 x y))))) | |
| ✓ | 37.8% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) |
| ✓ | 36.8% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
| 22.5% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) #s(approx (* (+ z y) x) (*.f64 (fma.f64 x (/.f64 y z) x) z))))) | |
| ▶ | 37.2% | #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z)) |
| 30.4% | #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 z x) (*.f64 (sqrt.f64 (/.f64 (+.f64 z x) y)) #s(literal 2 binary64))) y)) | |
| 3.0% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (/.f64 (fma.f64 z (sqrt.f64 (*.f64 z x)) (*.f64 (sqrt.f64 (*.f64 z x)) x)) (*.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) | |
| 3.6% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (/.f64 (+.f64 z x) (sqrt.f64 (*.f64 z x))) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) | |
| 3.6% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 z x) #s(literal -1/4 binary64)) #s(literal 2 binary64)) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) | |
| 1.8% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 z)) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) | |
| 3.6% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 z x)) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 (*.f64 z x)) #s(literal -1/2 binary64))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) | |
| 3.6% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 z x)) #s(literal -1/2 binary64))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) | |
| 3.4% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 #s(approx (* (sqrt (/ 1 (* z x))) (+ z x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 x z)))) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) | |
| 3.4% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64))) z (*.f64 (sqrt.f64 (*.f64 z x)) y)) z))) | |
| ▶ | 1.9% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x))) |
| 2.2% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 (fma.f64 (sqrt.f64 (/.f64 x z)) #s(literal 2 binary64) (*.f64 y (+.f64 (sqrt.f64 (/.f64 x (pow.f64 z #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x)))))) z))) | |
| 3.2% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) y (*.f64 (sqrt.f64 (/.f64 z x)) #s(literal 2 binary64))) x))) | |
| 2.5% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 (sqrt.f64 (/.f64 z x)) y))) |
Compiled 1 062 to 773 computations (27.2% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) | |
| cost-diff | 0 | (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) | |
| cost-diff | 0 | (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z) | |
| cost-diff | 0 | #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z)) | |
| cost-diff | 0 | (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x) | |
| cost-diff | 0 | #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x)) | |
| cost-diff | 0 | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x))) | |
| cost-diff | 960 | (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x))) | |
| cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x)))) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x))))) | |
| cost-diff | 320 | (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x)))))) | |
| cost-diff | 0 | (*.f64 z x) | |
| cost-diff | 0 | #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x)) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) | |
| cost-diff | 0 | (fma.f64 z (+.f64 x y) (*.f64 x y)) | |
| cost-diff | 0 | (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) | |
| cost-diff | 0 | (*.f64 (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) | |
| cost-diff | 12288 | (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
| 360× | lower-fma.f32 |
| 350× | lower-fma.f64 |
| 340× | lower-*.f32 |
| 320× | lower-*.f64 |
| 126× | *-commutative |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 66 | 492 |
| 0 | 106 | 487 |
| 1 | 167 | 483 |
| 2 | 243 | 481 |
| 3 | 367 | 477 |
| 4 | 469 | 477 |
| 5 | 492 | 477 |
| 0 | 492 | 467 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) |
(fma.f64 z (+.f64 x y) (*.f64 x y)) |
z |
(+.f64 x y) |
x |
y |
(*.f64 x y) |
#s(literal 1/4 binary64) |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) |
(sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) |
#s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x)) |
(*.f64 z x) |
z |
x |
#s(literal 2 binary64) |
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x)))))) |
#s(literal 2 binary64) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x))))) |
#s(literal 1 binary64) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x)))) |
(/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x))) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(+.f64 y x) |
y |
x |
z |
(*.f64 y x) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x))) |
#s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x)) |
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x) |
(fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) |
(fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) |
(sqrt.f64 (*.f64 z x)) |
(*.f64 z x) |
z |
x |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 (/.f64 x z)) y) |
(sqrt.f64 (/.f64 x z)) |
(/.f64 x z) |
y |
(*.f64 (sqrt.f64 (*.f64 z x)) y) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z)) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z) |
(fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) |
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x)) |
(/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) |
#s(literal 1 binary64) |
(pow.f64 z #s(literal 3 binary64)) |
z |
#s(literal 3 binary64) |
(+.f64 y x) |
y |
x |
(*.f64 y x) |
(*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64)) |
(sqrt.f64 (/.f64 (+.f64 y x) z)) |
(/.f64 (+.f64 y x) z) |
#s(literal 2 binary64) |
| Outputs |
|---|
(*.f64 (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) |
(pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) |
(pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/4 binary64)) |
(fma.f64 z (+.f64 x y) (*.f64 x y)) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
z |
(+.f64 x y) |
(+.f64 y x) |
x |
y |
(*.f64 x y) |
(*.f64 y x) |
#s(literal 1/4 binary64) |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 x z))) #s(literal 2 binary64)) |
(sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) |
(sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 x z))) |
#s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x)) |
#s(approx (+ (* (+ y x) z) (* y x)) (*.f64 x z)) |
(*.f64 z x) |
(*.f64 x z) |
z |
x |
#s(literal 2 binary64) |
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x)))))) |
(/.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x))))) |
#s(literal 2 binary64) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x))))) |
#s(literal 1 binary64) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x)))) |
(/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x))) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(+.f64 y x) |
y |
x |
z |
(*.f64 y x) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x))) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) x y) (sqrt.f64 (*.f64 x z)) (*.f64 (sqrt.f64 (/.f64 x z)) (*.f64 y x))) x))) |
#s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x)) |
#s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) x y) (sqrt.f64 (*.f64 x z)) (*.f64 (sqrt.f64 (/.f64 x z)) (*.f64 y x))) x)) |
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x) |
(/.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) x y) (sqrt.f64 (*.f64 x z)) (*.f64 (sqrt.f64 (/.f64 x z)) (*.f64 y x))) x) |
(fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) |
(fma.f64 (fma.f64 #s(literal 2 binary64) x y) (sqrt.f64 (*.f64 x z)) (*.f64 (sqrt.f64 (/.f64 x z)) (*.f64 y x))) |
(fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) |
(fma.f64 (sqrt.f64 (*.f64 x z)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) |
(sqrt.f64 (*.f64 z x)) |
(sqrt.f64 (*.f64 x z)) |
(*.f64 z x) |
(*.f64 x z) |
z |
x |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 (/.f64 x z)) y) |
(sqrt.f64 (/.f64 x z)) |
(/.f64 x z) |
y |
(*.f64 (sqrt.f64 (*.f64 z x)) y) |
(*.f64 (sqrt.f64 (*.f64 x z)) y) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z)) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) (pow.f64 z #s(literal 3 binary64)))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z)) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) (pow.f64 z #s(literal 3 binary64)))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z) |
(fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) |
(fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) (pow.f64 z #s(literal 3 binary64)))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) |
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) |
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) (pow.f64 z #s(literal 3 binary64)))) |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x)) |
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) (pow.f64 z #s(literal 3 binary64))) |
(/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) |
#s(literal 1 binary64) |
(pow.f64 z #s(literal 3 binary64)) |
z |
#s(literal 3 binary64) |
(+.f64 y x) |
y |
x |
(*.f64 y x) |
(*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64)) |
(sqrt.f64 (/.f64 (+.f64 y x) z)) |
(/.f64 (+.f64 y x) z) |
#s(literal 2 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 6.41032767274895 | (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z) | |
| accuracy | 12.202663961355563 | (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) | |
| accuracy | 12.554764678883357 | (sqrt.f64 (/.f64 (+.f64 y x) z)) | |
| accuracy | 18.320317191545595 | #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z)) | |
| accuracy | 10.54040493051722 | (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x) | |
| accuracy | 18.237163243126066 | (sqrt.f64 (/.f64 x z)) | |
| accuracy | 18.351527135643654 | #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x)) | |
| accuracy | 32.47046105034999 | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x))) | |
| accuracy | 0.00390625 | (fma.f64 (+.f64 y x) z (*.f64 y x)) | |
| accuracy | 0.1640625 | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x))))) | |
| accuracy | 0.20976670669265643 | (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x))) | |
| accuracy | 8.728258417604977 | (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x)))) | |
| accuracy | 0 | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) | |
| accuracy | 0 | (*.f64 z x) | |
| accuracy | 8.738413422297528 | (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) | |
| accuracy | 30.145504167573936 | #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x)) | |
| accuracy | 0 | (*.f64 x y) | |
| accuracy | 0.00390625 | (fma.f64 z (+.f64 x y) (*.f64 x y)) | |
| accuracy | 0.317070019536884 | (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) | |
| accuracy | 8.900929596609215 | (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) |
| 110.0ms | 116× | 0 | invalid |
| 59.0ms | 140× | 0 | valid |
Compiled 411 to 59 computations (85.6% saved)
ival-mult: 43.0ms (37.7% of total)ival-sqrt: 33.0ms (28.9% of total)ival-add: 13.0ms (11.4% of total)ival-div: 12.0ms (10.5% of total)ival-pow: 9.0ms (7.9% of total)ival-pow2: 2.0ms (1.8% of total)exact: 1.0ms (0.9% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (patch (*.f64 (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 z (+.f64 x y) (*.f64 x y)) (patch (fma.f64 z (+.f64 x y) (*.f64 x y)) #<representation binary64>) () ()) |
#s(alt (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) (patch (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) (patch (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x)) (patch #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x)) #<representation binary64>) () ()) |
#s(alt (*.f64 z x) (patch (*.f64 z x) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x)))))) (patch (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x)))))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x))))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x))))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x)))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) (patch (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) #<representation binary64>) () ()) |
#s(alt #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x))) (patch #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x)) (patch #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x) (patch (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x) #<representation binary64>) () ()) |
#s(alt #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z)) (patch #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z)) #<representation binary64>) () ()) |
#s(alt (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z) (patch (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z) #<representation binary64>) () ()) |
#s(alt (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) (patch (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) #<representation binary64>) () ()) |
#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ()) |
#s(alt (fma.f64 (+.f64 y x) z (*.f64 y x)) (patch (fma.f64 (+.f64 y x) z (*.f64 y x)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (/.f64 x z)) (patch (sqrt.f64 (/.f64 x z)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (/.f64 (+.f64 y x) z)) (patch (sqrt.f64 (/.f64 (+.f64 y x) z)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (sqrt (* x y)) (taylor 0 z) (#s(alt (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (* x y)) (* 1/2 (* (sqrt (/ 1 (* x y))) (* z (+ x y))))) (taylor 0 z) (#s(alt (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (* x y)) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y)))))) (taylor 0 z) (#s(alt (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (* x y)) (* z (+ (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y))) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3))))))))) (taylor 0 z) (#s(alt (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 (sqrt (* x y))) (taylor 0 z) (#s(alt (*.f64 (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (patch (*.f64 (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) (taylor 0 z) (#s(alt (*.f64 (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (patch (*.f64 (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 2 (sqrt (* x y))) (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* (sqrt (/ 1 (* x y))) (+ x y))))) (taylor 0 z) (#s(alt (*.f64 (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (patch (*.f64 (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 2 (sqrt (* x y))) (* z (+ (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3)))))) (* (sqrt (/ 1 (* x y))) (+ x y))))) (taylor 0 z) (#s(alt (*.f64 (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (patch (*.f64 (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (pow (* 1 (* x y)) 1/4) (taylor 0 z) (#s(alt (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 1/4 (* (pow (* 1 (* x y)) 1/4) (* z (+ (/ 1 x) (/ 1 y))))) (pow (* 1 (* x y)) 1/4)) (taylor 0 z) (#s(alt (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* z (+ (* 1/4 (* (pow (* 1 (* x y)) 1/4) (+ (/ 1 x) (/ 1 y)))) (* (pow (* 1 (* x y)) 1/4) (* z (+ (* -1/8 (/ (pow (+ x y) 2) (* (pow x 2) (pow y 2)))) (* 1/32 (pow (+ (/ 1 x) (/ 1 y)) 2))))))) (pow (* 1 (* x y)) 1/4)) (taylor 0 z) (#s(alt (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* z (+ (* 1/4 (* (pow (* 1 (* x y)) 1/4) (+ (/ 1 x) (/ 1 y)))) (* z (+ (* (pow (* 1 (* x y)) 1/4) (* z (+ (* -1/32 (/ (* (pow (+ x y) 2) (+ (/ 1 x) (/ 1 y))) (* (pow x 2) (pow y 2)))) (+ (* 1/384 (pow (+ (/ 1 x) (/ 1 y)) 3)) (* 1/12 (/ (pow (+ x y) 3) (* (pow x 3) (pow y 3)))))))) (* (pow (* 1 (* x y)) 1/4) (+ (* -1/8 (/ (pow (+ x y) 2) (* (pow x 2) (pow y 2)))) (* 1/32 (pow (+ (/ 1 x) (/ 1 y)) 2)))))))) (pow (* 1 (* x y)) 1/4)) (taylor 0 z) (#s(alt (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor 0 z) (#s(alt (fma.f64 z (+.f64 x y) (*.f64 x y)) (patch (fma.f64 z (+.f64 x y) (*.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x y) (* z (+ x y))) (taylor 0 z) (#s(alt (fma.f64 z (+.f64 x y) (*.f64 x y)) (patch (fma.f64 z (+.f64 x y) (*.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x y) (* z (+ x y))) (taylor 0 z) (#s(alt (fma.f64 z (+.f64 x y) (*.f64 x y)) (patch (fma.f64 z (+.f64 x y) (*.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x y) (* z (+ x y))) (taylor 0 z) (#s(alt (fma.f64 z (+.f64 x y) (*.f64 x y)) (patch (fma.f64 z (+.f64 x y) (*.f64 x y)) #<representation binary64>) () ())) ()) |
#s(alt (* 2 (sqrt (* x y))) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) (patch (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) (patch (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 2 (sqrt (* x y))) (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* (sqrt (/ 1 (* x y))) (+ x y))))) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) (patch (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 2 (sqrt (* x y))) (* z (+ (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3)))))) (* (sqrt (/ 1 (* x y))) (+ x y))))) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) (patch (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt (* x y)) (taylor 0 z) (#s(alt (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) (patch (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (* x y)) (* 1/2 (* (sqrt (/ 1 (* x y))) (* z (+ x y))))) (taylor 0 z) (#s(alt (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) (patch (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (* x y)) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y)))))) (taylor 0 z) (#s(alt (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) (patch (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt (* x y)) (* z (+ (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y))) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3))))))))) (taylor 0 z) (#s(alt (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) (patch (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #<representation binary64>) () ())) ()) |
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#s(alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (* (pow x 5) z))) (pow y 3))) (+ (* z (+ (* -1 (* (sqrt (/ 1 (* x (pow z 3)))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))))) (/ (* z (+ (* 1/2 (* (sqrt (/ x (pow z 3))) (pow y 2))) (* (sqrt (/ x z)) y))) (pow x 2)))))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z) (patch (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (* z (+ (* -1/4 (* (sqrt (/ (pow x 3) z)) (/ (pow y 2) (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt (* x (pow z 3))) (* y (+ (* -1/4 (/ (* x (pow y 2)) (* (pow z 3) (pow (sqrt -1) 2)))) (/ (pow y 3) (pow z 3)))))))) x)) (* 1/2 (* (sqrt (/ x z)) (pow y 3)))) (pow x 3))) (+ (* z (+ (* -1 (* (sqrt (/ 1 (* x (pow z 3)))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))))) (/ (* z (+ (* 1/2 (* (sqrt (/ x (pow z 3))) (pow y 2))) (* (sqrt (/ x z)) y))) (pow x 2)))))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z) (patch (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x (pow z 3)))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) (patch (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x (pow z 3)))) (* y (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow y 2))) (+ (* 2 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (* (pow x 3) z))) y)))))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) (patch (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x (pow z 3)))) (* y (pow (sqrt -1) 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow x 5) (pow z 3)))) (pow y 3))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow y 2))) (+ (* 2 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (* (pow x 3) z))) y))))))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) (patch (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x (pow z 3)))) (* y (pow (sqrt -1) 2)))) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ (pow x 3) z)) (/ (pow y 2) (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt (* x (pow z 3))) (* y (+ (* -1/4 (/ (* x (pow y 2)) (* (pow z 3) (pow (sqrt -1) 2)))) (/ (pow y 3) (pow z 3))))))) x)) (* 1/2 (* (sqrt (/ x (pow z 3))) (pow y 3)))) (pow x 3))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow y 2))) (+ (* 2 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (* (pow x 3) z))) y))))))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) (patch (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* (sqrt (/ 1 (* x (pow z 3)))) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1/2 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) y)) (* (sqrt (/ 1 (* x (pow z 3)))) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1/2 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) y)) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 5) (pow z 3)))) (pow y 2))) (* (sqrt (/ 1 (* x (pow z 3)))) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ x (pow z 3))) (pow y 2))) (* 1/2 (* (sqrt (/ (pow z 3) x)) (+ (* -1/4 (/ (* x (pow y 2)) (* (pow z 3) (pow (sqrt -1) 2)))) (/ (pow y 3) (pow z 3)))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) y)) (* (sqrt (/ 1 (* x (pow z 3)))) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 y) (* -1 z)))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 y x) z (*.f64 y x)) (patch (fma.f64 (+.f64 y x) z (*.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 y x) z (*.f64 y x)) (patch (fma.f64 (+.f64 y x) z (*.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 y x) z (*.f64 y x)) (patch (fma.f64 (+.f64 y x) z (*.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 y x) z (*.f64 y x)) (patch (fma.f64 (+.f64 y x) z (*.f64 y x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 x z)) (patch (sqrt.f64 (/.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 x z)) (patch (sqrt.f64 (/.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 x z)) (patch (sqrt.f64 (/.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 x z)) (patch (sqrt.f64 (/.f64 x z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 y x) z)) (patch (sqrt.f64 (/.f64 (+.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) z))) y)) (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 y x) z)) (patch (sqrt.f64 (/.f64 (+.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) z))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) z))) y)) (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 y x) z)) (patch (sqrt.f64 (/.f64 (+.f64 y x) z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) z))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) z))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) z))) y)) (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 y x) z)) (patch (sqrt.f64 (/.f64 (+.f64 y x) z)) #<representation binary64>) () ())) ()) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 21.0ms | y | @ | -inf | ((pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (pow (+ (* z (+ x y)) (* x y)) 1/4) (+ (* z (+ x y)) (* x y)) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (* z x) (* 2 (/ 1 (sqrt (/ 1 (+ (* (+ y x) z) (* y x)))))) (/ 1 (sqrt (/ 1 (+ (* (+ y x) z) (* y x))))) (sqrt (/ 1 (+ (* (+ y x) z) (* y x)))) (/ 1 (+ (* (+ y x) z) (* y x))) (+ (* (+ (* (sqrt (* z x)) 2) (* (sqrt (/ x z)) y)) x) (* (sqrt (* z x)) y)) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/ (+ (* (+ (* (sqrt (* z x)) 2) (* (sqrt (/ x z)) y)) x) (* (sqrt (* z x)) y)) x) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (* (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) z) (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* x y) (+ (* (+ y x) z) (* y x)) (sqrt (/ x z)) (sqrt (/ (+ y x) z))) |
| 15.0ms | y | @ | 0 | ((pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (pow (+ (* z (+ x y)) (* x y)) 1/4) (+ (* z (+ x y)) (* x y)) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (* z x) (* 2 (/ 1 (sqrt (/ 1 (+ (* (+ y x) z) (* y x)))))) (/ 1 (sqrt (/ 1 (+ (* (+ y x) z) (* y x))))) (sqrt (/ 1 (+ (* (+ y x) z) (* y x)))) (/ 1 (+ (* (+ y x) z) (* y x))) (+ (* (+ (* (sqrt (* z x)) 2) (* (sqrt (/ x z)) y)) x) (* (sqrt (* z x)) y)) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/ (+ (* (+ (* (sqrt (* z x)) 2) (* (sqrt (/ x z)) y)) x) (* (sqrt (* z x)) y)) x) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (* (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) z) (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* x y) (+ (* (+ y x) z) (* y x)) (sqrt (/ x z)) (sqrt (/ (+ y x) z))) |
| 13.0ms | x | @ | -inf | ((pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (pow (+ (* z (+ x y)) (* x y)) 1/4) (+ (* z (+ x y)) (* x y)) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (* z x) (* 2 (/ 1 (sqrt (/ 1 (+ (* (+ y x) z) (* y x)))))) (/ 1 (sqrt (/ 1 (+ (* (+ y x) z) (* y x))))) (sqrt (/ 1 (+ (* (+ y x) z) (* y x)))) (/ 1 (+ (* (+ y x) z) (* y x))) (+ (* (+ (* (sqrt (* z x)) 2) (* (sqrt (/ x z)) y)) x) (* (sqrt (* z x)) y)) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/ (+ (* (+ (* (sqrt (* z x)) 2) (* (sqrt (/ x z)) y)) x) (* (sqrt (* z x)) y)) x) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (* (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) z) (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* x y) (+ (* (+ y x) z) (* y x)) (sqrt (/ x z)) (sqrt (/ (+ y x) z))) |
| 12.0ms | y | @ | inf | ((pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (pow (+ (* z (+ x y)) (* x y)) 1/4) (+ (* z (+ x y)) (* x y)) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (* z x) (* 2 (/ 1 (sqrt (/ 1 (+ (* (+ y x) z) (* y x)))))) (/ 1 (sqrt (/ 1 (+ (* (+ y x) z) (* y x))))) (sqrt (/ 1 (+ (* (+ y x) z) (* y x)))) (/ 1 (+ (* (+ y x) z) (* y x))) (+ (* (+ (* (sqrt (* z x)) 2) (* (sqrt (/ x z)) y)) x) (* (sqrt (* z x)) y)) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/ (+ (* (+ (* (sqrt (* z x)) 2) (* (sqrt (/ x z)) y)) x) (* (sqrt (* z x)) y)) x) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (* (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) z) (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* x y) (+ (* (+ y x) z) (* y x)) (sqrt (/ x z)) (sqrt (/ (+ y x) z))) |
| 9.0ms | z | @ | inf | ((pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (pow (+ (* z (+ x y)) (* x y)) 1/4) (+ (* z (+ x y)) (* x y)) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (* z x) (* 2 (/ 1 (sqrt (/ 1 (+ (* (+ y x) z) (* y x)))))) (/ 1 (sqrt (/ 1 (+ (* (+ y x) z) (* y x))))) (sqrt (/ 1 (+ (* (+ y x) z) (* y x)))) (/ 1 (+ (* (+ y x) z) (* y x))) (+ (* (+ (* (sqrt (* z x)) 2) (* (sqrt (/ x z)) y)) x) (* (sqrt (* z x)) y)) (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/ (+ (* (+ (* (sqrt (* z x)) 2) (* (sqrt (/ x z)) y)) x) (* (sqrt (* z x)) y)) x) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (* (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) z) (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* x y) (+ (* (+ y x) z) (* y x)) (sqrt (/ x z)) (sqrt (/ (+ y x) z))) |
| 1× | egg-herbie |
| 7 082× | lower-*.f64 |
| 7 082× | lower-*.f32 |
| 4 770× | lower-fma.f64 |
| 4 770× | lower-fma.f32 |
| 4 178× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 2012 | 26214 |
| 1 | 5980 | 25054 |
| 0 | 8232 | 24109 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt (* x y)) |
(+ (sqrt (* x y)) (* 1/2 (* (sqrt (/ 1 (* x y))) (* z (+ x y))))) |
(+ (sqrt (* x y)) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y)))))) |
(+ (sqrt (* x y)) (* z (+ (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y))) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3))))))))) |
(* 2 (sqrt (* x y))) |
(+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3)))))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(pow (* 1 (* x y)) 1/4) |
(+ (* 1/4 (* (pow (* 1 (* x y)) 1/4) (* z (+ (/ 1 x) (/ 1 y))))) (pow (* 1 (* x y)) 1/4)) |
(+ (* z (+ (* 1/4 (* (pow (* 1 (* x y)) 1/4) (+ (/ 1 x) (/ 1 y)))) (* (pow (* 1 (* x y)) 1/4) (* z (+ (* -1/8 (/ (pow (+ x y) 2) (* (pow x 2) (pow y 2)))) (* 1/32 (pow (+ (/ 1 x) (/ 1 y)) 2))))))) (pow (* 1 (* x y)) 1/4)) |
(+ (* z (+ (* 1/4 (* (pow (* 1 (* x y)) 1/4) (+ (/ 1 x) (/ 1 y)))) (* z (+ (* (pow (* 1 (* x y)) 1/4) (* z (+ (* -1/32 (/ (* (pow (+ x y) 2) (+ (/ 1 x) (/ 1 y))) (* (pow x 2) (pow y 2)))) (+ (* 1/384 (pow (+ (/ 1 x) (/ 1 y)) 3)) (* 1/12 (/ (pow (+ x y) 3) (* (pow x 3) (pow y 3)))))))) (* (pow (* 1 (* x y)) 1/4) (+ (* -1/8 (/ (pow (+ x y) 2) (* (pow x 2) (pow y 2)))) (* 1/32 (pow (+ (/ 1 x) (/ 1 y)) 2)))))))) (pow (* 1 (* x y)) 1/4)) |
(* x y) |
(+ (* x y) (* z (+ x y))) |
(+ (* x y) (* z (+ x y))) |
(+ (* x y) (* z (+ x y))) |
(* 2 (sqrt (* x y))) |
(+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3)))))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(sqrt (* x y)) |
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(* -1 (* z (+ (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))) (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))))) |
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(* -1 (* z (+ (* -1/8 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/16 (* (/ (* (pow x 3) (pow y 3)) (pow (sqrt -1) 4)) (sqrt (/ 1 (* (pow z 7) (pow (+ x y) 5)))))) (+ (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))) (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))))))) |
(* z (+ x y)) |
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(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (* x y) z))))) |
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (* x y) z))))) |
(* x z) |
(* x z) |
(* x z) |
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(* -1 (* z (+ (* -1/4 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/8 (* (/ (* (pow x 3) (pow y 3)) (pow (sqrt -1) 4)) (sqrt (/ 1 (* (pow z 7) (pow (+ x y) 5)))))) (+ (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))))) |
(* -1 (* (sqrt (* z (+ x y))) (pow (sqrt -1) 2))) |
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(* -1 (* z (+ (* -1/8 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))) (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2)))))) |
(* -1 (* z (+ (* -1/8 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/16 (* (/ (* (pow x 3) (pow y 3)) (pow (sqrt -1) 4)) (sqrt (/ 1 (* (pow z 7) (pow (+ x y) 5)))))) (+ (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))) (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))))))) |
(* (sqrt (/ 1 (* z (+ x y)))) (pow (sqrt -1) 2)) |
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(+ (* -1 (/ (+ (* -1/2 (* (* (pow x 2) (pow y 2)) (sqrt (/ z (pow (+ x y) 5))))) (* 1/2 (* (sqrt (/ (+ x y) z)) (+ (* -1/4 (/ (* (pow x 2) (* (pow y 2) z)) (* (pow (sqrt -1) 2) (pow (+ x y) 3)))) (/ (* (pow x 3) (pow y 3)) (pow (+ x y) 4)))))) (pow z 3))) (+ (* -1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (pow (+ x y) 3)))))) (* (sqrt (/ 1 (* z (+ x y)))) (pow (sqrt -1) 2)))) |
(/ 1 (* z (+ x y))) |
(* -1 (/ (- (/ (* x y) (* z (pow (+ x y) 2))) (/ 1 (+ x y))) z)) |
(* -1 (/ (- (* -1 (/ (- (/ (* (pow x 2) (pow y 2)) (* z (pow (+ x y) 3))) (/ (* x y) (pow (+ x y) 2))) z)) (/ 1 (+ x y))) z)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (* (pow x 3) (pow y 3)) (* z (pow (+ x y) 4))) (/ (* (pow x 2) (pow y 2)) (pow (+ x y) 3))) z)) (/ (* x y) (pow (+ x y) 2))) z)) (/ 1 (+ x y))) z)) |
(* -1 (* z (+ (* 2 (* (sqrt (/ (pow x 3) z)) (pow (sqrt -1) 2))) (* (sqrt (/ x z)) (* y (pow (sqrt -1) 2)))))) |
(* -1 (* z (+ (* -1 (* (sqrt (/ (pow x 3) (pow z 3))) (* y (pow (sqrt -1) 2)))) (+ (* 2 (* (sqrt (/ (pow x 3) z)) (pow (sqrt -1) 2))) (* (sqrt (/ x z)) (* y (pow (sqrt -1) 2))))))) |
(* -1 (* z (+ (* -1 (* (sqrt (/ (pow x 3) (pow z 3))) (* y (pow (sqrt -1) 2)))) (+ (* 2 (* (sqrt (/ (pow x 3) z)) (pow (sqrt -1) 2))) (* (sqrt (/ x z)) (* y (pow (sqrt -1) 2))))))) |
(* -1 (* z (+ (* -1 (* (sqrt (/ (pow x 3) (pow z 3))) (* y (pow (sqrt -1) 2)))) (+ (* 2 (* (sqrt (/ (pow x 3) z)) (pow (sqrt -1) 2))) (* (sqrt (/ x z)) (* y (pow (sqrt -1) 2))))))) |
(* -2 (* (sqrt (* z (+ (* -1 x) (* -1 y)))) (sqrt -1))) |
(* -1 (* z (+ (* 2 (* (sqrt (/ (+ (* -1 x) (* -1 y)) z)) (sqrt -1))) (* (* x (* y (sqrt -1))) (sqrt (/ 1 (* (pow z 3) (+ (* -1 x) (* -1 y))))))))) |
(* -1 (* z (+ (* -1/4 (* (* (pow x 2) (* (pow y 2) (sqrt -1))) (sqrt (/ 1 (* (pow z 5) (pow (+ (* -1 x) (* -1 y)) 3)))))) (+ (* 2 (* (sqrt (/ (+ (* -1 x) (* -1 y)) z)) (sqrt -1))) (* (* x (* y (sqrt -1))) (sqrt (/ 1 (* (pow z 3) (+ (* -1 x) (* -1 y)))))))))) |
(* -1 (* z (+ (* -1/4 (* (* (pow x 2) (* (pow y 2) (sqrt -1))) (sqrt (/ 1 (* (pow z 5) (pow (+ (* -1 x) (* -1 y)) 3)))))) (+ (* 1/8 (* (* (pow x 3) (* (pow y 3) (sqrt -1))) (sqrt (/ 1 (* (pow z 7) (pow (+ (* -1 x) (* -1 y)) 5)))))) (+ (* 2 (* (sqrt (/ (+ (* -1 x) (* -1 y)) z)) (sqrt -1))) (* (* x (* y (sqrt -1))) (sqrt (/ 1 (* (pow z 3) (+ (* -1 x) (* -1 y))))))))))) |
(* -1 (* z (+ (* -1 (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ x z)) (pow (sqrt -1) 2)))))) |
(* -1 (* z (+ (* -1 (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))) (+ (* -1 (* (sqrt (/ x (pow z 3))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ x z)) (pow (sqrt -1) 2))))))) |
(* -1 (* z (+ (* -1 (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))) (+ (* -1 (* (sqrt (/ x (pow z 3))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ x z)) (pow (sqrt -1) 2))))))) |
(* -1 (* z (+ (* -1 (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))) (+ (* -1 (* (sqrt (/ x (pow z 3))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ x z)) (pow (sqrt -1) 2))))))) |
(* -1 (/ (* z (+ (* 2 (* (sqrt (/ (pow x 3) z)) (pow (sqrt -1) 2))) (* (sqrt (/ x z)) (* y (pow (sqrt -1) 2))))) x)) |
(* -1 (* z (+ (* -1 (* (sqrt (/ x (pow z 3))) (* y (pow (sqrt -1) 2)))) (+ (* 2 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2))))))) |
(* -1 (* z (+ (* -1 (* (sqrt (/ x (pow z 3))) (* y (pow (sqrt -1) 2)))) (+ (* 2 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2))))))) |
(* -1 (* z (+ (* -1 (* (sqrt (/ x (pow z 3))) (* y (pow (sqrt -1) 2)))) (+ (* 2 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2))))))) |
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(* -1 (* z (+ (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))) |
(* -1 (* z (+ (* -1/4 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y))))))))) |
(* -1 (* z (+ (* -1/4 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/8 (* (/ (* (pow x 3) (pow y 3)) (pow (sqrt -1) 4)) (sqrt (/ 1 (* (pow z 7) (pow (+ x y) 5)))))) (+ (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))))) |
(* 2 (* (sqrt (* z (+ x y))) (pow (sqrt -1) 2))) |
(* -1 (* z (+ (* -2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x (* y (pow (sqrt -1) 2))) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))) |
(* -1 (* z (+ (* -2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x (* y (pow (sqrt -1) 2))) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))) |
(* -1 (* z (+ (* -2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x (* y (pow (sqrt -1) 2))) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))) |
(* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) |
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(+ (* -1 (* (* x (* y (pow (sqrt -1) 2))) (sqrt (/ 1 (* (pow z 3) (+ x y)))))) (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2)))) |
(+ (* -1 (* (* x (* y (pow (sqrt -1) 2))) (sqrt (/ 1 (* (pow z 3) (+ x y)))))) (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2)))) |
(* -1 (* (sqrt (/ 1 (* (pow z 3) (+ x y)))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ 1 (* (pow z 3) (+ x y)))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ 1 (* (pow z 3) (+ x y)))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ 1 (* (pow z 3) (+ x y)))) (pow (sqrt -1) 2))) |
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(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (* x y) z))))) |
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (* x y) z))))) |
(* (sqrt (/ x z)) (pow (sqrt -1) 2)) |
(* (sqrt (/ x z)) (pow (sqrt -1) 2)) |
(* (sqrt (/ x z)) (pow (sqrt -1) 2)) |
(* (sqrt (/ x z)) (pow (sqrt -1) 2)) |
(* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2)) |
(* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2)) |
(* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2)) |
(* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2)) |
(sqrt (* x z)) |
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(+ (sqrt (* x z)) (* y (+ (* 1/2 (* (sqrt (/ 1 (* x z))) (+ x z))) (* y (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow (+ x z) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow z 5)))) (* y (pow (+ x z) 3))))))))) |
(* 2 (sqrt (* x z))) |
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(+ (* 2 (sqrt (* x z))) (* y (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (* y (pow (+ x z) 2)))) (* (sqrt (/ 1 (* x z))) (+ x z))))) |
(+ (* 2 (sqrt (* x z))) (* y (+ (* y (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow (+ x z) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow z 5)))) (* y (pow (+ x z) 3)))))) (* (sqrt (/ 1 (* x z))) (+ x z))))) |
(pow (* 1 (* x z)) 1/4) |
(+ (* 1/4 (* (pow (* 1 (* x z)) 1/4) (* y (+ (/ 1 x) (/ 1 z))))) (pow (* 1 (* x z)) 1/4)) |
(+ (* y (+ (* 1/4 (* (pow (* 1 (* x z)) 1/4) (+ (/ 1 x) (/ 1 z)))) (* (pow (* 1 (* x z)) 1/4) (* y (+ (* -1/8 (/ (pow (+ x z) 2) (* (pow x 2) (pow z 2)))) (* 1/32 (pow (+ (/ 1 x) (/ 1 z)) 2))))))) (pow (* 1 (* x z)) 1/4)) |
(+ (* y (+ (* 1/4 (* (pow (* 1 (* x z)) 1/4) (+ (/ 1 x) (/ 1 z)))) (* y (+ (* (pow (* 1 (* x z)) 1/4) (* y (+ (* -1/32 (/ (* (pow (+ x z) 2) (+ (/ 1 x) (/ 1 z))) (* (pow x 2) (pow z 2)))) (+ (* 1/384 (pow (+ (/ 1 x) (/ 1 z)) 3)) (* 1/12 (/ (pow (+ x z) 3) (* (pow x 3) (pow z 3)))))))) (* (pow (* 1 (* x z)) 1/4) (+ (* -1/8 (/ (pow (+ x z) 2) (* (pow x 2) (pow z 2)))) (* 1/32 (pow (+ (/ 1 x) (/ 1 z)) 2)))))))) (pow (* 1 (* x z)) 1/4)) |
(* x z) |
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(* 2 (sqrt (* x z))) |
(+ (* 2 (sqrt (* x z))) (* (sqrt (/ 1 (* x z))) (* y (+ x z)))) |
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(+ (* 2 (sqrt (* x z))) (* y (+ (* y (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow (+ x z) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow z 5)))) (* y (pow (+ x z) 3)))))) (* (sqrt (/ 1 (* x z))) (+ x z))))) |
(sqrt (* x z)) |
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(+ (sqrt (* x z)) (* y (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (* y (pow (+ x z) 2)))) (* 1/2 (* (sqrt (/ 1 (* x z))) (+ x z)))))) |
(+ (sqrt (* x z)) (* y (+ (* 1/2 (* (sqrt (/ 1 (* x z))) (+ x z))) (* y (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow (+ x z) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow z 5)))) (* y (pow (+ x z) 3))))))))) |
(* x z) |
(+ (* x z) (* y (+ x z))) |
(+ (* x z) (* y (+ x z))) |
(+ (* x z) (* y (+ x z))) |
(* 2 (sqrt (* x z))) |
(+ (* 2 (sqrt (* x z))) (* (sqrt (/ 1 (* x z))) (* y (+ x z)))) |
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(+ (* 2 (sqrt (* x z))) (* y (+ (* y (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow (+ x z) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow z 5)))) (* y (pow (+ x z) 3)))))) (* (sqrt (/ 1 (* x z))) (+ x z))))) |
(sqrt (* x z)) |
(+ (sqrt (* x z)) (* 1/2 (* (sqrt (/ 1 (* x z))) (* y (+ x z))))) |
(+ (sqrt (* x z)) (* y (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (* y (pow (+ x z) 2)))) (* 1/2 (* (sqrt (/ 1 (* x z))) (+ x z)))))) |
(+ (sqrt (* x z)) (* y (+ (* 1/2 (* (sqrt (/ 1 (* x z))) (+ x z))) (* y (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow (+ x z) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow z 5)))) (* y (pow (+ x z) 3))))))))) |
(sqrt (/ 1 (* x z))) |
(+ (sqrt (/ 1 (* x z))) (* -1/2 (* (sqrt (* x z)) (* y (+ (/ 1 (* x (pow z 2))) (/ 1 (* (pow x 2) z))))))) |
(+ (sqrt (/ 1 (* x z))) (* y (+ (* -1/2 (* (sqrt (* x z)) (* y (+ (* -1 (/ (* (+ x z) (+ (/ 1 (* x (pow z 2))) (/ 1 (* (pow x 2) z)))) (* x z))) (* 1/4 (* x (* z (pow (+ (/ 1 (* x (pow z 2))) (/ 1 (* (pow x 2) z))) 2)))))))) (* -1/2 (* (sqrt (* x z)) (+ (/ 1 (* x (pow z 2))) (/ 1 (* (pow x 2) z)))))))) |
(+ (sqrt (/ 1 (* x z))) (* y (+ (* -1/2 (* (sqrt (* x z)) (+ (/ 1 (* x (pow z 2))) (/ 1 (* (pow x 2) z))))) (* y (+ (* -1/2 (* (sqrt (* x z)) (* y (+ (* 1/2 (* x (* z (* (+ (* -1 (/ (* (+ x z) (+ (/ 1 (* x (pow z 2))) (/ 1 (* (pow x 2) z)))) (* x z))) (* 1/4 (* x (* z (pow (+ (/ 1 (* x (pow z 2))) (/ 1 (* (pow x 2) z))) 2))))) (+ (/ 1 (* x (pow z 2))) (/ 1 (* (pow x 2) z))))))) (/ (* (pow (+ x z) 2) (+ (/ 1 (* x (pow z 2))) (/ 1 (* (pow x 2) z)))) (* (pow x 2) (pow z 2))))))) (* -1/2 (* (sqrt (* x z)) (+ (* -1 (/ (* (+ x z) (+ (/ 1 (* x (pow z 2))) (/ 1 (* (pow x 2) z)))) (* x z))) (* 1/4 (* x (* z (pow (+ (/ 1 (* x (pow z 2))) (/ 1 (* (pow x 2) z))) 2)))))))))))) |
(/ 1 (* x z)) |
(+ (* -1 (* y (+ (/ 1 (* x (pow z 2))) (/ 1 (* (pow x 2) z))))) (/ 1 (* x z))) |
(+ (* y (- (/ (* y (* (+ x z) (+ (/ 1 (* x (pow z 2))) (/ 1 (* (pow x 2) z))))) (* x z)) (+ (/ 1 (* x (pow z 2))) (/ 1 (* (pow x 2) z))))) (/ 1 (* x z))) |
(+ (* y (- (* y (- (* -1 (/ (* y (* (pow (+ x z) 2) (+ (/ 1 (* x (pow z 2))) (/ 1 (* (pow x 2) z))))) (* (pow x 2) (pow z 2)))) (* -1 (/ (* (+ x z) (+ (/ 1 (* x (pow z 2))) (/ 1 (* (pow x 2) z)))) (* x z))))) (+ (/ 1 (* x (pow z 2))) (/ 1 (* (pow x 2) z))))) (/ 1 (* x z))) |
(* 2 (sqrt (* (pow x 3) z))) |
(+ (* 2 (sqrt (* (pow x 3) z))) (* y (+ (sqrt (* x z)) (sqrt (/ (pow x 3) z))))) |
(+ (* 2 (sqrt (* (pow x 3) z))) (* y (+ (sqrt (* x z)) (sqrt (/ (pow x 3) z))))) |
(+ (* 2 (sqrt (* (pow x 3) z))) (* y (+ (sqrt (* x z)) (sqrt (/ (pow x 3) z))))) |
(* 2 (sqrt (* x z))) |
(+ (* 2 (sqrt (* x z))) (* (sqrt (/ 1 (* x z))) (* y (+ x z)))) |
(+ (* 2 (sqrt (* x z))) (* y (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (* y (pow (+ x z) 2)))) (* (sqrt (/ 1 (* x z))) (+ x z))))) |
(+ (* 2 (sqrt (* x z))) (* y (+ (* y (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow (+ x z) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow z 5)))) (* y (pow (+ x z) 3)))))) (* (sqrt (/ 1 (* x z))) (+ x z))))) |
(* 2 (sqrt (* x z))) |
(+ (* 2 (sqrt (* x z))) (* (sqrt (/ 1 (* x z))) (* y (+ x z)))) |
(+ (* 2 (sqrt (* x z))) (* (sqrt (/ 1 (* x z))) (* y (+ x z)))) |
(+ (* 2 (sqrt (* x z))) (* (sqrt (/ 1 (* x z))) (* y (+ x z)))) |
(* 2 (sqrt (* x z))) |
(+ (* 2 (sqrt (* x z))) (* y (+ (sqrt (/ x z)) (sqrt (/ z x))))) |
(+ (* 2 (sqrt (* x z))) (* y (+ (sqrt (/ x z)) (sqrt (/ z x))))) |
(+ (* 2 (sqrt (* x z))) (* y (+ (sqrt (/ x z)) (sqrt (/ z x))))) |
(* 2 (sqrt (* x z))) |
(+ (* 2 (sqrt (* x z))) (* (sqrt (/ 1 (* x z))) (* y (+ x z)))) |
(+ (* 2 (sqrt (* x z))) (* y (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (* y (pow (+ x z) 2)))) (* (sqrt (/ 1 (* x z))) (+ x z))))) |
(+ (* 2 (sqrt (* x z))) (* y (+ (* y (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow (+ x z) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow z 5)))) (* y (pow (+ x z) 3)))))) (* (sqrt (/ 1 (* x z))) (+ x z))))) |
(* 2 (sqrt (* x z))) |
(+ (* 2 (sqrt (* x z))) (* y (* z (+ (sqrt (/ 1 (* x z))) (sqrt (/ x (pow z 3))))))) |
(+ (* 2 (sqrt (* x z))) (* y (+ (* y (* z (+ (* -1/2 (sqrt (/ 1 (* x (pow z 3))))) (* -1/4 (sqrt (/ 1 (* (pow x 3) z))))))) (* z (+ (sqrt (/ 1 (* x z))) (sqrt (/ x (pow z 3)))))))) |
(+ (* 2 (sqrt (* x z))) (* y (+ (* y (+ (* y (* z (+ (* 1/8 (sqrt (/ 1 (* (pow x 5) z)))) (* 3/8 (sqrt (/ 1 (* (pow x 3) (pow z 3)))))))) (* z (+ (* -1/2 (sqrt (/ 1 (* x (pow z 3))))) (* -1/4 (sqrt (/ 1 (* (pow x 3) z)))))))) (* z (+ (sqrt (/ 1 (* x z))) (sqrt (/ x (pow z 3)))))))) |
(* 2 (sqrt (/ x z))) |
(+ (* 2 (sqrt (/ x z))) (* y (+ (sqrt (/ 1 (* x z))) (sqrt (/ x (pow z 3)))))) |
(+ (* 2 (sqrt (/ x z))) (* y (+ (sqrt (/ 1 (* x z))) (+ (sqrt (/ x (pow z 3))) (* y (+ (* -1/2 (sqrt (/ 1 (* x (pow z 3))))) (* -1/4 (sqrt (/ 1 (* (pow x 3) z)))))))))) |
(+ (* 2 (sqrt (/ x z))) (* y (+ (sqrt (/ 1 (* x z))) (+ (sqrt (/ x (pow z 3))) (* y (+ (* -1/2 (sqrt (/ 1 (* x (pow z 3))))) (+ (* -1/4 (sqrt (/ 1 (* (pow x 3) z)))) (* y (+ (* 1/8 (sqrt (/ 1 (* (pow x 5) z)))) (* 3/8 (sqrt (/ 1 (* (pow x 3) (pow z 3)))))))))))))) |
(sqrt (/ 1 (* x (pow z 3)))) |
(+ (sqrt (/ 1 (* x (pow z 3)))) (* -1/2 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) y))) |
(+ (sqrt (/ 1 (* x (pow z 3)))) (* y (+ (* -1/2 (sqrt (/ 1 (* (pow x 3) (pow z 3))))) (* 3/8 (* (sqrt (/ 1 (* (pow x 5) (pow z 3)))) y))))) |
(+ (sqrt (/ 1 (* x (pow z 3)))) (* y (+ (* -1/2 (sqrt (/ 1 (* (pow x 3) (pow z 3))))) (* y (+ (* -5/16 (* (sqrt (/ 1 (* (pow x 7) (pow z 3)))) y)) (* 3/8 (sqrt (/ 1 (* (pow x 5) (pow z 3)))))))))) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* x z) |
(+ (* x z) (* y (+ x z))) |
(+ (* x z) (* y (+ x z))) |
(+ (* x z) (* y (+ x z))) |
(sqrt (/ x z)) |
(+ (sqrt (/ x z)) (* 1/2 (* (sqrt (/ 1 (* x z))) y))) |
(+ (sqrt (/ x z)) (* y (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) z))) y)) (* 1/2 (sqrt (/ 1 (* x z))))))) |
(+ (sqrt (/ x z)) (* y (+ (* 1/2 (sqrt (/ 1 (* x z)))) (* y (+ (* -1/8 (sqrt (/ 1 (* (pow x 3) z)))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) z))) y))))))) |
(sqrt (* y (+ x z))) |
(* y (+ (sqrt (/ (+ x z) y)) (* 1/2 (* (* x z) (sqrt (/ 1 (* (pow y 3) (+ x z)))))))) |
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(* -1 (* y (+ (* -1 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (* y (pow z 3)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ (pow y 3) z)))) (* 1/2 (* (* x (+ (* -1/4 (/ (* (pow x 2) y) (* (pow z 3) (pow (sqrt -1) 2)))) (/ (pow x 3) (pow z 3)))) (sqrt (* y (pow z 3)))))) y)) (* 1/2 (* (pow x 3) (sqrt (/ y (pow z 3)))))) (pow y 3))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (+ (* 2 (* (sqrt (/ 1 (* y z))) (pow (sqrt -1) 2))) (* x (sqrt (/ 1 (* (pow y 3) z)))))))))) |
(* (sqrt (/ 1 (* y (pow z 3)))) (pow (sqrt -1) 2)) |
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(* x y) |
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(pow (* 1 (* y z)) 1/4) |
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(+ (* x (+ y z)) (* y z)) |
(* x z) |
(* x z) |
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(sqrt (* y z)) |
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(sqrt (/ 1 (* y z))) |
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(/ 1 (* y z)) |
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(+ (* x (- (* x (- (* -1 (/ (* x (* (pow (+ y z) 2) (+ (/ 1 (* y (pow z 2))) (/ 1 (* (pow y 2) z))))) (* (pow y 2) (pow z 2)))) (* -1 (/ (* (+ y z) (+ (/ 1 (* y (pow z 2))) (/ 1 (* (pow y 2) z)))) (* y z))))) (+ (/ 1 (* y (pow z 2))) (/ 1 (* (pow y 2) z))))) (/ 1 (* y z))) |
(* (sqrt (* x z)) y) |
(+ (* x (+ (* 2 (sqrt (* x z))) (* (sqrt (/ x z)) y))) (* (sqrt (* x z)) y)) |
(+ (* x (+ (* 2 (sqrt (* x z))) (* (sqrt (/ x z)) y))) (* (sqrt (* x z)) y)) |
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(* (sqrt (/ z x)) y) |
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(/ (+ (* x (+ (* 2 (sqrt (* x z))) (* (sqrt (/ x z)) y))) (* (sqrt (* x z)) y)) x) |
(/ (+ (* x (+ (* 2 (sqrt (* x z))) (* (sqrt (/ x z)) y))) (* (sqrt (* x z)) y)) x) |
(* (sqrt (/ z x)) y) |
(/ (+ (* x (+ (* 2 (sqrt (* x z))) (* (sqrt (/ x z)) y))) (* (sqrt (* x z)) y)) x) |
(/ (+ (* x (+ (* 2 (sqrt (* x z))) (* (sqrt (/ x z)) y))) (* (sqrt (* x z)) y)) x) |
(/ (+ (* x (+ (* 2 (sqrt (* x z))) (* (sqrt (/ x z)) y))) (* (sqrt (* x z)) y)) x) |
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(* 2 (sqrt (* y z))) |
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(+ (* 2 (sqrt (/ y z))) (* x (+ (sqrt (/ 1 (* y z))) (+ (sqrt (/ y (pow z 3))) (* x (+ (* -1/2 (sqrt (/ 1 (* y (pow z 3))))) (+ (* -1/4 (sqrt (/ 1 (* (pow y 3) z)))) (* x (+ (* 1/8 (sqrt (/ 1 (* (pow y 5) z)))) (* 3/8 (sqrt (/ 1 (* (pow y 3) (pow z 3)))))))))))))) |
(sqrt (/ 1 (* y (pow z 3)))) |
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(+ (sqrt (/ 1 (* y (pow z 3)))) (* x (+ (* -1/2 (sqrt (/ 1 (* (pow y 3) (pow z 3))))) (* 3/8 (* x (sqrt (/ 1 (* (pow y 5) (pow z 3))))))))) |
(+ (sqrt (/ 1 (* y (pow z 3)))) (* x (+ (* -1/2 (sqrt (/ 1 (* (pow y 3) (pow z 3))))) (* x (+ (* -5/16 (* x (sqrt (/ 1 (* (pow y 7) (pow z 3)))))) (* 3/8 (sqrt (/ 1 (* (pow y 5) (pow z 3)))))))))) |
(* x y) |
(* x y) |
(* x y) |
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(sqrt (/ x z)) |
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(+ (sqrt (/ y z)) (* x (+ (* 1/2 (sqrt (/ 1 (* y z)))) (* x (+ (* -1/8 (sqrt (/ 1 (* (pow y 3) z)))) (* 1/16 (* x (sqrt (/ 1 (* (pow y 5) z)))))))))) |
(sqrt (* x (+ y z))) |
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(* x (+ (sqrt (/ (+ y z) x)) (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))))) |
(* x (+ (sqrt (/ (+ y z) x)) (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) (pow (+ y z) 5)))) (* (pow y 3) (pow z 3)))) (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z))))))) |
(* 2 (sqrt (* x (+ y z)))) |
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(* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z))))) |
(* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow x 7) (pow (+ y z) 5)))) (* (pow y 3) (pow z 3)))) (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))))) |
(exp (* 1/4 (+ (log (+ y z)) (* -1 (log (/ 1 x)))))) |
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(* -1 (* (pow x 2) (+ (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))))) |
(* (pow x 2) (+ (* -1 (* (sqrt (/ z (pow x 3))) (* y (pow (sqrt -1) 2)))) (* -1 (+ (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2))))))) |
(* (pow x 2) (+ (* -1 (* (sqrt (/ z (pow x 3))) (* y (pow (sqrt -1) 2)))) (* -1 (+ (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2))))))) |
(* (pow x 2) (+ (* -1 (* (sqrt (/ z (pow x 3))) (* y (pow (sqrt -1) 2)))) (* -1 (+ (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2))))))) |
(* -2 (* (sqrt (* x (+ (* -1 y) (* -1 z)))) (sqrt -1))) |
(* -1 (* x (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1)))))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow x 7) (pow (+ (* -1 y) (* -1 z)) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))))))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))) (+ (* -1 (* (sqrt (/ z (pow x 3))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))) (+ (* -1 (* (sqrt (/ z (pow x 3))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))) (+ (* -1 (* (sqrt (/ z (pow x 3))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2))) (+ (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2))) (* (sqrt (/ z (pow x 3))) (* y (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2))) (+ (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2))) (* (sqrt (/ z (pow x 3))) (* y (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* 2 (* (sqrt (/ z x)) (pow (sqrt -1) 2))) (+ (* (sqrt (/ 1 (* x z))) (* y (pow (sqrt -1) 2))) (* (sqrt (/ z (pow x 3))) (* y (pow (sqrt -1) 2))))))) |
(* -2 (* (sqrt (* x (+ (* -1 y) (* -1 z)))) (sqrt -1))) |
(* -1 (* x (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1)))))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow x 7) (pow (+ (* -1 y) (* -1 z)) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 2 (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))) (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))))))) |
(* -1 (* x (* z (+ (* -1 (* (sqrt (/ 1 (* x (pow z 3)))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* z (+ (* -1 (* (sqrt (/ 1 (* x (pow z 3)))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))))) (/ (* z (+ (* 1/2 (* (sqrt (/ x (pow z 3))) (pow y 2))) (* (sqrt (/ x z)) y))) (pow x 2))))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (* (pow x 5) z))) (pow y 3))) (+ (* z (+ (* -1 (* (sqrt (/ 1 (* x (pow z 3)))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))))) (/ (* z (+ (* 1/2 (* (sqrt (/ x (pow z 3))) (pow y 2))) (* (sqrt (/ x z)) y))) (pow x 2)))))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (* z (+ (* -1/4 (* (sqrt (/ (pow x 3) z)) (/ (pow y 2) (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt (* x (pow z 3))) (* y (+ (* -1/4 (/ (* x (pow y 2)) (* (pow z 3) (pow (sqrt -1) 2)))) (/ (pow y 3) (pow z 3)))))))) x)) (* 1/2 (* (sqrt (/ x z)) (pow y 3)))) (pow x 3))) (+ (* z (+ (* -1 (* (sqrt (/ 1 (* x (pow z 3)))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))))) (/ (* z (+ (* 1/2 (* (sqrt (/ x (pow z 3))) (pow y 2))) (* (sqrt (/ x z)) y))) (pow x 2)))))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x (pow z 3)))) (* y (pow (sqrt -1) 2)))) (* 2 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x (pow z 3)))) (* y (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow y 2))) (+ (* 2 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (* (pow x 3) z))) y)))))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x (pow z 3)))) (* y (pow (sqrt -1) 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow x 5) (pow z 3)))) (pow y 3))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow y 2))) (+ (* 2 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (* (pow x 3) z))) y))))))) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x (pow z 3)))) (* y (pow (sqrt -1) 2)))) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ (pow x 3) z)) (/ (pow y 2) (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt (* x (pow z 3))) (* y (+ (* -1/4 (/ (* x (pow y 2)) (* (pow z 3) (pow (sqrt -1) 2)))) (/ (pow y 3) (pow z 3))))))) x)) (* 1/2 (* (sqrt (/ x (pow z 3))) (pow y 3)))) (pow x 3))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow y 2))) (+ (* 2 (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (* (pow x 3) z))) y))))))) |
(* (sqrt (/ 1 (* x (pow z 3)))) (pow (sqrt -1) 2)) |
(+ (* -1/2 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) y)) (* (sqrt (/ 1 (* x (pow z 3)))) (pow (sqrt -1) 2))) |
(+ (* -1/2 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) y)) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 5) (pow z 3)))) (pow y 2))) (* (sqrt (/ 1 (* x (pow z 3)))) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ x (pow z 3))) (pow y 2))) (* 1/2 (* (sqrt (/ (pow z 3) x)) (+ (* -1/4 (/ (* x (pow y 2)) (* (pow z 3) (pow (sqrt -1) 2)))) (/ (pow y 3) (pow z 3)))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) y)) (* (sqrt (/ 1 (* x (pow z 3)))) (pow (sqrt -1) 2)))) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(* -1 (* x (+ (* -1 y) (* -1 z)))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(* -1 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) z))) y)) (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) z))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) z))) y)) (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) z))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) z))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) z))) y)) (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))))))) |
| Outputs |
|---|
(sqrt (* x y)) |
(sqrt.f64 (*.f64 x y)) |
(+ (sqrt (* x y)) (* 1/2 (* (sqrt (/ 1 (* x y))) (* z (+ x y))))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y))) (*.f64 z (+.f64 y x))) (sqrt.f64 (*.f64 x y))) |
(+ (sqrt (* x y)) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y)))))) |
(fma.f64 z (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64)))) (*.f64 z (pow.f64 (+.f64 y x) #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y))) (+.f64 y x)))) (sqrt.f64 (*.f64 x y))) |
(+ (sqrt (* x y)) (* z (+ (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y))) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3))))))))) |
(fma.f64 z (fma.f64 z (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 y #s(literal 5 binary64))))) (*.f64 z (pow.f64 (+.f64 y x) #s(literal 3 binary64))) (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (pow.f64 (+.f64 y x) #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y))) (+.f64 y x)))) (sqrt.f64 (*.f64 x y))) |
(* 2 (sqrt (* x y))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 x y))) |
(+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) |
(fma.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 x y)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y))) (*.f64 z (+.f64 y x)))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(fma.f64 z (fma.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (*.f64 z (pow.f64 (+.f64 y x) #s(literal 2 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y))) (+.f64 y x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 x y)))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3)))))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(fma.f64 z (fma.f64 z (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 y #s(literal 5 binary64))))) (*.f64 z (pow.f64 (+.f64 y x) #s(literal 3 binary64))) (*.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (pow.f64 (+.f64 y x) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y))) (+.f64 y x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 x y)))) |
(pow (* 1 (* x y)) 1/4) |
(pow.f64 (*.f64 x y) #s(literal 1/4 binary64)) |
(+ (* 1/4 (* (pow (* 1 (* x y)) 1/4) (* z (+ (/ 1 x) (/ 1 y))))) (pow (* 1 (* x y)) 1/4)) |
(fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (pow.f64 (*.f64 x y) #s(literal 1/4 binary64)) z) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) x))) (pow.f64 (*.f64 x y) #s(literal 1/4 binary64))) |
(+ (* z (+ (* 1/4 (* (pow (* 1 (* x y)) 1/4) (+ (/ 1 x) (/ 1 y)))) (* (pow (* 1 (* x y)) 1/4) (* z (+ (* -1/8 (/ (pow (+ x y) 2) (* (pow x 2) (pow y 2)))) (* 1/32 (pow (+ (/ 1 x) (/ 1 y)) 2))))))) (pow (* 1 (* x y)) 1/4)) |
(fma.f64 z (fma.f64 (*.f64 (pow.f64 (*.f64 x y) #s(literal 1/4 binary64)) z) (fma.f64 #s(literal 1/32 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 (+.f64 y x) #s(literal 2 binary64))) (*.f64 (*.f64 x x) (*.f64 y y)))) (*.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 x y) #s(literal 1/4 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) x)))) (pow.f64 (*.f64 x y) #s(literal 1/4 binary64))) |
(+ (* z (+ (* 1/4 (* (pow (* 1 (* x y)) 1/4) (+ (/ 1 x) (/ 1 y)))) (* z (+ (* (pow (* 1 (* x y)) 1/4) (* z (+ (* -1/32 (/ (* (pow (+ x y) 2) (+ (/ 1 x) (/ 1 y))) (* (pow x 2) (pow y 2)))) (+ (* 1/384 (pow (+ (/ 1 x) (/ 1 y)) 3)) (* 1/12 (/ (pow (+ x y) 3) (* (pow x 3) (pow y 3)))))))) (* (pow (* 1 (* x y)) 1/4) (+ (* -1/8 (/ (pow (+ x y) 2) (* (pow x 2) (pow y 2)))) (* 1/32 (pow (+ (/ 1 x) (/ 1 y)) 2)))))))) (pow (* 1 (* x y)) 1/4)) |
(fma.f64 z (fma.f64 z (*.f64 (pow.f64 (*.f64 x y) #s(literal 1/4 binary64)) (fma.f64 z (fma.f64 (/.f64 #s(literal -1/32 binary64) (*.f64 x x)) (/.f64 (*.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) x))) (*.f64 y y)) (fma.f64 #s(literal 1/384 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (/.f64 (*.f64 #s(literal 1/12 binary64) (pow.f64 (+.f64 y x) #s(literal 3 binary64))) (*.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))))) (fma.f64 #s(literal 1/32 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 (+.f64 y x) #s(literal 2 binary64))) (*.f64 (*.f64 x x) (*.f64 y y)))))) (*.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 x y) #s(literal 1/4 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) x)))) (pow.f64 (*.f64 x y) #s(literal 1/4 binary64))) |
(* x y) |
(*.f64 x y) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 z (+.f64 y x) (*.f64 x y)) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 z (+.f64 y x) (*.f64 x y)) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 z (+.f64 y x) (*.f64 x y)) |
(* 2 (sqrt (* x y))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 x y))) |
(+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) |
(fma.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 x y)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y))) (*.f64 z (+.f64 y x)))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(fma.f64 z (fma.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (*.f64 z (pow.f64 (+.f64 y x) #s(literal 2 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y))) (+.f64 y x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 x y)))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3)))))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(fma.f64 z (fma.f64 z (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 y #s(literal 5 binary64))))) (*.f64 z (pow.f64 (+.f64 y x) #s(literal 3 binary64))) (*.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (pow.f64 (+.f64 y x) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y))) (+.f64 y x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 x y)))) |
(sqrt (* x y)) |
(sqrt.f64 (*.f64 x y)) |
(+ (sqrt (* x y)) (* 1/2 (* (sqrt (/ 1 (* x y))) (* z (+ x y))))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y))) (*.f64 z (+.f64 y x))) (sqrt.f64 (*.f64 x y))) |
(+ (sqrt (* x y)) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y)))))) |
(fma.f64 z (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64)))) (*.f64 z (pow.f64 (+.f64 y x) #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y))) (+.f64 y x)))) (sqrt.f64 (*.f64 x y))) |
(+ (sqrt (* x y)) (* z (+ (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y))) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3))))))))) |
(fma.f64 z (fma.f64 z (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 y #s(literal 5 binary64))))) (*.f64 z (pow.f64 (+.f64 y x) #s(literal 3 binary64))) (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (pow.f64 (+.f64 y x) #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y))) (+.f64 y x)))) (sqrt.f64 (*.f64 x y))) |
(* x y) |
(*.f64 x y) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 z (+.f64 y x) (*.f64 x y)) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 z (+.f64 y x) (*.f64 x y)) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 z (+.f64 y x) (*.f64 x y)) |
(* x z) |
(*.f64 x z) |
(* x z) |
(*.f64 x z) |
(* x z) |
(*.f64 x z) |
(* x z) |
(*.f64 x z) |
(* 2 (sqrt (* x y))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 x y))) |
(+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) |
(fma.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 x y)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y))) (*.f64 z (+.f64 y x)))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(fma.f64 z (fma.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (*.f64 z (pow.f64 (+.f64 y x) #s(literal 2 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y))) (+.f64 y x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 x y)))) |
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(/ 1 (* x z)) |
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(sqrt (* x (+ y z))) |
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(* (pow x 2) (+ (* 2 (sqrt (/ z x))) (* (sqrt (/ 1 (* x z))) y))) |
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(* (pow x 2) (+ (* 2 (sqrt (/ z x))) (+ (* (sqrt (/ 1 (* x z))) y) (* (sqrt (/ z (pow x 3))) y)))) |
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(* 2 (sqrt (* x (+ y z)))) |
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(* x (+ (* 2 (sqrt (/ z x))) (* (sqrt (/ 1 (* x z))) y))) |
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(* x (+ (* 2 (sqrt (/ z x))) (* (sqrt (/ 1 (* x z))) y))) |
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(* x (+ (* 2 (sqrt (/ z x))) (+ (* (sqrt (/ 1 (* x z))) y) (* (sqrt (/ z (pow x 3))) y)))) |
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(* 2 (sqrt (* x (+ y z)))) |
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(* x (+ (* 2 (sqrt (/ 1 (* x z)))) (* (sqrt (/ 1 (* x (pow z 3)))) y))) |
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(fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 z #s(literal 3 binary64))))) y (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 z #s(literal 3 binary64)))) (*.f64 y y)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (pow.f64 z #s(literal 3 binary64))))) #s(literal -1 binary64)))) |
(+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ x (pow z 3))) (pow y 2))) (* 1/2 (* (sqrt (/ (pow z 3) x)) (+ (* -1/4 (/ (* x (pow y 2)) (* (pow z 3) (pow (sqrt -1) 2)))) (/ (pow y 3) (pow z 3)))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) y)) (* (sqrt (/ 1 (* x (pow z 3)))) (pow (sqrt -1) 2)))) |
(-.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 z #s(literal 3 binary64))))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (pow.f64 z #s(literal 3 binary64))))) #s(literal -1 binary64))) (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 x (pow.f64 z #s(literal 3 binary64))))) (*.f64 y y) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (pow.f64 z #s(literal 3 binary64)) x))) (fma.f64 (/.f64 #s(literal -1/4 binary64) (pow.f64 z #s(literal 3 binary64))) (/.f64 (*.f64 x (*.f64 y y)) #s(literal -1 binary64)) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64)))))) (pow.f64 x #s(literal 3 binary64)))) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* x y) |
(*.f64 x y) |
(* -1 (* x (+ (* -1 y) (* -1 z)))) |
(*.f64 (neg.f64 x) (-.f64 (neg.f64 z) y)) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(*.f64 (neg.f64 x) (-.f64 (neg.f64 (fma.f64 y (/.f64 z x) z)) y)) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(*.f64 (neg.f64 x) (-.f64 (neg.f64 (fma.f64 y (/.f64 z x) z)) y)) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(*.f64 (neg.f64 x) (-.f64 (neg.f64 (fma.f64 y (/.f64 z x) z)) y)) |
(* -1 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 (/.f64 x z)) #s(literal 1 binary64)) |
(* -1 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 (/.f64 x z)) #s(literal 1 binary64)) |
(* -1 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 (/.f64 x z)) #s(literal 1 binary64)) |
(* -1 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 (/.f64 x z)) #s(literal 1 binary64)) |
(* -1 (* (sqrt (/ x z)) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 (/.f64 x z)) #s(literal 1 binary64)) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) z))) y)) (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))))) |
(*.f64 (neg.f64 x) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) z)))) y (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) z)) #s(literal -1 binary64)))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) z))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) z))) y)) (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2)))))) |
(*.f64 (neg.f64 x) (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) z)))) (/.f64 (*.f64 y y) #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) z)))) y (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) z)) #s(literal -1 binary64))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) z))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) z))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) z))) y)) (* (sqrt (/ 1 (* x z))) (pow (sqrt -1) 2))))))) |
(*.f64 (neg.f64 x) (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) z)))) (/.f64 (*.f64 y y) #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 7 binary64)) z)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) z)))) y (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) z)) #s(literal -1 binary64)))))) |
| 4 008× | lower-*.f32 |
| 3 988× | lower-*.f64 |
| 3 912× | lower-/.f32 |
| 3 898× | lower-/.f64 |
| 2 672× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 66 | 390 |
| 0 | 106 | 365 |
| 1 | 399 | 360 |
| 2 | 2518 | 360 |
| 0 | 8090 | 358 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(*.f64 (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) |
(fma.f64 z (+.f64 x y) (*.f64 x y)) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) |
(sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) |
#s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x)) |
(*.f64 z x) |
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x))))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x)))) |
(/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x))) |
(fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x))) |
#s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x)) |
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z)) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z) |
(fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) |
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) |
(*.f64 x y) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(sqrt.f64 (/.f64 x z)) |
(sqrt.f64 (/.f64 (+.f64 y x) z)) |
| Outputs |
|---|
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Compiled 52 966 to 6 264 computations (88.2% saved)
38 alts after pruning (35 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 642 | 18 | 1 660 |
| Fresh | 7 | 17 | 24 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 2 | 2 |
| Total | 1 653 | 38 | 1 691 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 70.3% | (*.f64 (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) #s(literal 2 binary64)) |
| 62.8% | (*.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)))) #s(literal 2 binary64)) #s(literal 2 binary64)) | |
| 36.6% | (*.f64 (pow.f64 (pow.f64 #s(approx (+ (* z (+ x y)) (* x y)) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) | |
| 37.9% | (*.f64 (pow.f64 (*.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) (fma.f64 z (+.f64 x y) (*.f64 x y))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) | |
| 5.8% | (*.f64 (pow.f64 (*.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 x z)) #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 x z))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) | |
| 43.3% | (*.f64 (pow.f64 #s(approx (pow (+ (* z (+ x y)) (* x y)) 1/4) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (-.f64 (log.f64 (-.f64 (neg.f64 z) y)) (log.f64 (/.f64 #s(literal -1 binary64) x))))) #s(literal 2 binary64)) #s(literal 2 binary64)) | |
| ▶ | 53.2% | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x))) #s(literal 2 binary64)) |
| 37.1% | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 y x) z))) #s(literal 2 binary64)) | |
| ▶ | 35.7% | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) |
| ✓ | 3.7% | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) |
| 19.1% | (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 x y)) #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 x y))) #s(literal 1/4 binary64))) | |
| 35.1% | (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 y z)))))) | |
| 36.3% | (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 x y)))))) | |
| 31.2% | (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (+ (* (+ y x) z) (* y x))) (/.f64 (fma.f64 (neg.f64 y) (/.f64 z (*.f64 x (pow.f64 (+.f64 z y) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 z y))) x))))) | |
| 56.2% | (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 #s(approx (/ (/ (pow (* z x) 2) x) (- y z)) (*.f64 (neg.f64 x) z)))) (*.f64 y z)))) | |
| ▶ | 35.4% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z)))))) |
| 37.8% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 z x (*.f64 x y))))) | |
| ✓ | 37.8% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) |
| ✓ | 36.8% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
| 22.5% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) #s(approx (* (+ z y) x) (*.f64 (fma.f64 x (/.f64 y z) x) z))))) | |
| ▶ | 30.4% | #s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y)))))) |
| 42.7% | #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (/.f64 (sqrt.f64 (+.f64 y x)) (sqrt.f64 z)) #s(literal 2 binary64))) z)) | |
| 37.2% | #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 z (+.f64 y x)))) #s(literal 2 binary64))) z)) | |
| 2.4% | #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 y x) z))) #s(literal -1 binary64))) z)) | |
| 31.8% | #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 y (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) z)) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (pow.f64 z #s(literal 3 binary64))))))))) z)) | |
| 44.4% | #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 y x) z)))) z)) | |
| 43.5% | #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 y z)))) z)) | |
| 35.3% | #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) #s(approx (* (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) z) (fma.f64 (*.f64 x z) (+.f64 (sqrt.f64 (/.f64 y (pow.f64 z #s(literal 3 binary64)))) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) z))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 y z)))))) | |
| 3.6% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (/.f64 (+.f64 z x) (sqrt.f64 (*.f64 z x))) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) | |
| 3.6% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 z x) #s(literal -1/4 binary64)) #s(literal 2 binary64)) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) | |
| 3.6% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 z x)) #s(literal -1/2 binary64))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) | |
| 3.4% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 #s(approx (* (sqrt (/ 1 (* z x))) (+ z x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 x z)))) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) | |
| 3.4% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64))) z (*.f64 (sqrt.f64 (*.f64 z x)) y)) z))) | |
| 3.3% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 #s(approx (sqrt (/ x z)) (*.f64 (sqrt.f64 (/.f64 x z)) #s(literal -1 binary64))) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x))) | |
| 2.2% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 (fma.f64 (sqrt.f64 (/.f64 x z)) #s(literal 2 binary64) (*.f64 y (+.f64 (sqrt.f64 (/.f64 x (pow.f64 z #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x)))))) z))) | |
| 3.2% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) y (*.f64 (sqrt.f64 (/.f64 z x)) #s(literal 2 binary64))) x))) | |
| 2.5% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 (sqrt.f64 (/.f64 z x)) y))) | |
| 3.2% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 x (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) z)) y (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 z x))))))) |
Compiled 1 251 to 983 computations (21.4% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 x z) | |
| cost-diff | 0 | (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y)))) | |
| cost-diff | 0 | (*.f64 y (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y))))) | |
| cost-diff | 0 | #s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y)))))) | |
| cost-diff | 128 | (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z)) | |
| cost-diff | 320 | (/.f64 x (*.f64 (-.f64 y z) x)) | |
| cost-diff | 320 | (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) | |
| cost-diff | 1088 | (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z))) | |
| cost-diff | 0 | #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x)) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x))) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x))) #s(literal 2 binary64)) | |
| cost-diff | 704 | (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x) | |
| cost-diff | 0 | (*.f64 z y) | |
| cost-diff | 0 | #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y)) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) | |
| cost-diff | 0 | (fma.f64 (+.f64 y x) z (*.f64 y x)) | |
| cost-diff | 0 | (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) | |
| cost-diff | 0 | (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) | |
| cost-diff | 0 | (*.f64 (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) #s(literal 2 binary64)) |
| 6 920× | lower-fma.f32 |
| 6 912× | lower-fma.f64 |
| 4 634× | lower-*.f32 |
| 4 604× | lower-*.f64 |
| 2 560× | lower-/.f32 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 66 | 525 |
| 0 | 109 | 513 |
| 1 | 184 | 511 |
| 2 | 340 | 490 |
| 3 | 709 | 457 |
| 4 | 1157 | 457 |
| 5 | 3123 | 457 |
| 6 | 5952 | 457 |
| 0 | 8347 | 457 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) |
(pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(+.f64 y x) |
y |
x |
z |
(*.f64 y x) |
#s(literal 1/8 binary64) |
#s(literal 4 binary64) |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) |
(sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) |
#s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y)) |
(*.f64 z y) |
z |
y |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x))) #s(literal 2 binary64)) |
(sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x))) |
#s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x)) |
(*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x) |
(+.f64 (fma.f64 y (/.f64 z x) z) y) |
(fma.f64 y (/.f64 z x) z) |
y |
(/.f64 z x) |
z |
x |
#s(literal 2 binary64) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z)))))) |
#s(literal 2 binary64) |
(sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z))))) |
#s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z)))) |
(fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z))) |
(*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) |
(/.f64 x (*.f64 (-.f64 y z) x)) |
x |
(*.f64 (-.f64 y z) x) |
(-.f64 y z) |
y |
z |
(*.f64 x y) |
(/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z)) |
(neg.f64 (*.f64 (*.f64 z z) x)) |
(*.f64 (*.f64 z z) x) |
(*.f64 z z) |
#s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y)))))) |
(*.f64 y (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y))))) |
y |
(fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y)))) |
(*.f64 x z) |
x |
z |
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x)) |
(/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) |
#s(literal 1 binary64) |
(pow.f64 y #s(literal 3 binary64)) |
#s(literal 3 binary64) |
(+.f64 z x) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y))) |
#s(literal 2 binary64) |
(sqrt.f64 (/.f64 (+.f64 z x) y)) |
(/.f64 (+.f64 z x) y) |
| Outputs |
|---|
(*.f64 (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (pow.f64 (pow.f64 (fma.f64 (+.f64 z y) x (*.f64 z y)) #s(literal 1/8 binary64)) #s(literal 4 binary64))) |
(pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) |
(pow.f64 (pow.f64 (fma.f64 (+.f64 z y) x (*.f64 z y)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) |
(pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) |
(pow.f64 (fma.f64 (+.f64 z y) x (*.f64 z y)) #s(literal 1/8 binary64)) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(fma.f64 (+.f64 z y) x (*.f64 z y)) |
(+.f64 y x) |
(+.f64 x y) |
y |
x |
z |
(*.f64 y x) |
(*.f64 x y) |
#s(literal 1/8 binary64) |
#s(literal 4 binary64) |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) |
(sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) |
#s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y)) |
(*.f64 z y) |
z |
y |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x))) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (fma.f64 (+.f64 z y) x (*.f64 z y)))) #s(literal 2 binary64)) |
(sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x))) |
(sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (fma.f64 (+.f64 z y) x (*.f64 z y)))) |
#s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x)) |
#s(approx (+ (* (+ y x) z) (* y x)) (fma.f64 (+.f64 z y) x (*.f64 z y))) |
(*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x) |
(fma.f64 (+.f64 z y) x (*.f64 z y)) |
(+.f64 (fma.f64 y (/.f64 z x) z) y) |
(fma.f64 (/.f64 z x) (+.f64 x y) y) |
(fma.f64 y (/.f64 z x) z) |
(fma.f64 (/.f64 z x) y z) |
y |
(/.f64 z x) |
z |
x |
#s(literal 2 binary64) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z)))))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (fma.f64 (neg.f64 y) y (*.f64 z z)) (/.f64 x (-.f64 z y))))) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z))))) |
(sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (fma.f64 (neg.f64 y) y (*.f64 z z)) (/.f64 x (-.f64 z y))))) |
#s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z)))) |
#s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (fma.f64 (neg.f64 y) y (*.f64 z z)) (/.f64 x (-.f64 z y)))) |
(fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z))) |
(*.f64 (fma.f64 (neg.f64 y) y (*.f64 z z)) (/.f64 x (-.f64 z y))) |
(*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) |
(/.f64 y (-.f64 y z)) |
(/.f64 x (*.f64 (-.f64 y z) x)) |
(/.f64 #s(literal 1 binary64) (-.f64 y z)) |
x |
(*.f64 (-.f64 y z) x) |
(-.f64 y z) |
y |
z |
(*.f64 x y) |
(/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z)) |
(*.f64 (/.f64 z (-.f64 z y)) (*.f64 z x)) |
(neg.f64 (*.f64 (*.f64 z z) x)) |
(*.f64 (*.f64 (neg.f64 x) z) z) |
(*.f64 (*.f64 z z) x) |
(*.f64 z z) |
#s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y)))))) |
#s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 z x)) (pow.f64 y #s(literal 3 binary64)))) (*.f64 z x) (*.f64 (sqrt.f64 (/.f64 (+.f64 z x) y)) #s(literal 2 binary64))) y)) |
(*.f64 y (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 z x)) (pow.f64 y #s(literal 3 binary64)))) (*.f64 z x) (*.f64 (sqrt.f64 (/.f64 (+.f64 z x) y)) #s(literal 2 binary64))) y) |
y |
(fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y)))) |
(fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 z x)) (pow.f64 y #s(literal 3 binary64)))) (*.f64 z x) (*.f64 (sqrt.f64 (/.f64 (+.f64 z x) y)) #s(literal 2 binary64))) |
(*.f64 x z) |
(*.f64 z x) |
x |
z |
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) |
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 z x)) (pow.f64 y #s(literal 3 binary64)))) |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x)) |
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 z x)) (pow.f64 y #s(literal 3 binary64))) |
(/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) |
#s(literal 1 binary64) |
(pow.f64 y #s(literal 3 binary64)) |
#s(literal 3 binary64) |
(+.f64 z x) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y))) |
(*.f64 (sqrt.f64 (/.f64 (+.f64 z x) y)) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 (/.f64 (+.f64 z x) y)) |
(/.f64 (+.f64 z x) y) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 8.153019457215265 | (sqrt.f64 (/.f64 (+.f64 z x) y)) | |
| accuracy | 8.468516779600721 | (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y)))) | |
| accuracy | 18.792753313801654 | (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) | |
| accuracy | 31.93069365177588 | #s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y)))))) | |
| accuracy | 13.659016366163995 | (/.f64 x (*.f64 (-.f64 y z) x)) | |
| accuracy | 15.86109062638898 | (*.f64 (*.f64 z z) x) | |
| accuracy | 18.425324583112346 | (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z))))) | |
| accuracy | 29.12731062726915 | #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z)))) | |
| accuracy | 0 | #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x)) | |
| accuracy | 3.261471083434375 | (fma.f64 y (/.f64 z x) z) | |
| accuracy | 8.53715400889745 | (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x) | |
| accuracy | 18.425324583112346 | (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x))) | |
| accuracy | 0 | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) | |
| accuracy | 0 | (*.f64 z y) | |
| accuracy | 18.425324583112346 | (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) | |
| accuracy | 30.504607931133183 | #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y)) | |
| accuracy | 0 | (*.f64 y x) | |
| accuracy | 0.9486431154118479 | (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) | |
| accuracy | 1.0156139904222408 | (fma.f64 (+.f64 y x) z (*.f64 y x)) | |
| accuracy | 18.82639740503497 | (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) |
| 129.0ms | 256× | 0 | valid |
Compiled 401 to 60 computations (85% saved)
ival-mult: 34.0ms (33.3% of total)ival-add: 25.0ms (24.5% of total)ival-pow: 20.0ms (19.6% of total)ival-div: 11.0ms (10.8% of total)ival-sqrt: 6.0ms (5.9% of total)ival-pow2: 3.0ms (2.9% of total)ival-sub: 1.0ms (1% of total)exact: 1.0ms (1% of total)ival-neg: 1.0ms (1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (*.f64 (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) #s(literal 2 binary64)) (patch (*.f64 (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) #<representation binary64>) () ()) |
#s(alt (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) (patch (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (+.f64 y x) z (*.f64 y x)) (patch (fma.f64 (+.f64 y x) z (*.f64 y x)) #<representation binary64>) () ()) |
#s(alt (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) (patch (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) (patch (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y)) (patch #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y)) #<representation binary64>) () ()) |
#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ()) |
#s(alt (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x) (patch (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x) #<representation binary64>) () ()) |
#s(alt (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x))) #s(literal 2 binary64)) (patch (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x))) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x))) (patch (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x)) (patch #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z))) (patch (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z))) #<representation binary64>) () ()) |
#s(alt (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (patch (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) #<representation binary64>) () ()) |
#s(alt (/.f64 x (*.f64 (-.f64 y z) x)) (patch (/.f64 x (*.f64 (-.f64 y z) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z)) (patch (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z)) #<representation binary64>) () ()) |
#s(alt #s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y)))))) (patch #s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y)))))) #<representation binary64>) () ()) |
#s(alt (*.f64 y (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y))))) (patch (*.f64 y (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y))))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y)))) (patch (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y)))) #<representation binary64>) () ()) |
#s(alt (*.f64 x z) (patch (*.f64 x z) #<representation binary64>) () ()) |
#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ()) |
#s(alt (fma.f64 y (/.f64 z x) z) (patch (fma.f64 y (/.f64 z x) z) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z)))) (patch #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z)))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z))))) (patch (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z))))) #<representation binary64>) () ()) |
#s(alt (*.f64 (*.f64 z z) x) (patch (*.f64 (*.f64 z z) x) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (patch (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (/.f64 (+.f64 z x) y)) (patch (sqrt.f64 (/.f64 (+.f64 z x) y)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* 2 (sqrt (* x y))) (taylor 0 z) (#s(alt (*.f64 (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) #s(literal 2 binary64)) (patch (*.f64 (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) (taylor 0 z) (#s(alt (*.f64 (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) #s(literal 2 binary64)) (patch (*.f64 (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
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9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 56.0ms | x | @ | -inf | ((* (pow (pow (+ (* (+ y x) z) (* y x)) 1/8) 4) 2) (pow (pow (+ (* (+ y x) z) (* y x)) 1/8) 4) (pow (+ (* (+ y x) z) (* y x)) 1/8) (+ (* (+ y x) z) (* y x)) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (* z y) (* (+ (+ (* y (/ z x)) z) y) x) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (+ (* (* (/ x (* (- y z) x)) y) (* x y)) (/ (neg (* (* z z) x)) (- y z))) (* (/ x (* (- y z) x)) y) (/ x (* (- y z) x)) (/ (neg (* (* z z) x)) (- y z)) (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (* y (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y))))) (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (* x z) (* y x) (+ (* y (/ z x)) z) (+ (+ (* x y) (* x z)) (* y z)) (sqrt (+ (+ (* x y) (* x z)) (* y z))) (* (* z z) x) (sqrt (/ (/ 1 (pow y 3)) (+ z x))) (sqrt (/ (+ z x) y))) |
| 46.0ms | x | @ | 0 | ((* (pow (pow (+ (* (+ y x) z) (* y x)) 1/8) 4) 2) (pow (pow (+ (* (+ y x) z) (* y x)) 1/8) 4) (pow (+ (* (+ y x) z) (* y x)) 1/8) (+ (* (+ y x) z) (* y x)) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (* z y) (* (+ (+ (* y (/ z x)) z) y) x) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (+ (* (* (/ x (* (- y z) x)) y) (* x y)) (/ (neg (* (* z z) x)) (- y z))) (* (/ x (* (- y z) x)) y) (/ x (* (- y z) x)) (/ (neg (* (* z z) x)) (- y z)) (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (* y (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y))))) (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (* x z) (* y x) (+ (* y (/ z x)) z) (+ (+ (* x y) (* x z)) (* y z)) (sqrt (+ (+ (* x y) (* x z)) (* y z))) (* (* z z) x) (sqrt (/ (/ 1 (pow y 3)) (+ z x))) (sqrt (/ (+ z x) y))) |
| 32.0ms | z | @ | inf | ((* (pow (pow (+ (* (+ y x) z) (* y x)) 1/8) 4) 2) (pow (pow (+ (* (+ y x) z) (* y x)) 1/8) 4) (pow (+ (* (+ y x) z) (* y x)) 1/8) (+ (* (+ y x) z) (* y x)) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (* z y) (* (+ (+ (* y (/ z x)) z) y) x) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (+ (* (* (/ x (* (- y z) x)) y) (* x y)) (/ (neg (* (* z z) x)) (- y z))) (* (/ x (* (- y z) x)) y) (/ x (* (- y z) x)) (/ (neg (* (* z z) x)) (- y z)) (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (* y (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y))))) (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (* x z) (* y x) (+ (* y (/ z x)) z) (+ (+ (* x y) (* x z)) (* y z)) (sqrt (+ (+ (* x y) (* x z)) (* y z))) (* (* z z) x) (sqrt (/ (/ 1 (pow y 3)) (+ z x))) (sqrt (/ (+ z x) y))) |
| 20.0ms | y | @ | inf | ((* (pow (pow (+ (* (+ y x) z) (* y x)) 1/8) 4) 2) (pow (pow (+ (* (+ y x) z) (* y x)) 1/8) 4) (pow (+ (* (+ y x) z) (* y x)) 1/8) (+ (* (+ y x) z) (* y x)) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (* z y) (* (+ (+ (* y (/ z x)) z) y) x) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (+ (* (* (/ x (* (- y z) x)) y) (* x y)) (/ (neg (* (* z z) x)) (- y z))) (* (/ x (* (- y z) x)) y) (/ x (* (- y z) x)) (/ (neg (* (* z z) x)) (- y z)) (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (* y (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y))))) (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (* x z) (* y x) (+ (* y (/ z x)) z) (+ (+ (* x y) (* x z)) (* y z)) (sqrt (+ (+ (* x y) (* x z)) (* y z))) (* (* z z) x) (sqrt (/ (/ 1 (pow y 3)) (+ z x))) (sqrt (/ (+ z x) y))) |
| 16.0ms | x | @ | inf | ((* (pow (pow (+ (* (+ y x) z) (* y x)) 1/8) 4) 2) (pow (pow (+ (* (+ y x) z) (* y x)) 1/8) 4) (pow (+ (* (+ y x) z) (* y x)) 1/8) (+ (* (+ y x) z) (* y x)) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (* z y) (* (+ (+ (* y (/ z x)) z) y) x) (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (sqrt (+ (* (+ y x) z) (* y x))) (+ (* (+ y x) z) (* y x)) (+ (* (* (/ x (* (- y z) x)) y) (* x y)) (/ (neg (* (* z z) x)) (- y z))) (* (/ x (* (- y z) x)) y) (/ x (* (- y z) x)) (/ (neg (* (* z z) x)) (- y z)) (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (* y (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y))))) (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (* x z) (* y x) (+ (* y (/ z x)) z) (+ (+ (* x y) (* x z)) (* y z)) (sqrt (+ (+ (* x y) (* x z)) (* y z))) (* (* z z) x) (sqrt (/ (/ 1 (pow y 3)) (+ z x))) (sqrt (/ (+ z x) y))) |
| 1× | egg-herbie |
| 7 980× | lower-*.f64 |
| 7 980× | lower-*.f32 |
| 6 276× | lower-fma.f64 |
| 6 276× | lower-fma.f32 |
| 3 738× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1767 | 22861 |
| 1 | 6052 | 22030 |
| 0 | 8372 | 21182 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 2 (sqrt (* x y))) |
(+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) |
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(pow (* 1 (* x y)) 1/8) |
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(* x y) |
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(* x y) |
(+ (* x y) (* x z)) |
(+ (* x y) (* x z)) |
(+ (* x y) (* x z)) |
1 |
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(+ 1 (* z (+ (* z (+ (/ 1 (pow y 2)) (/ z (pow y 3)))) (/ 1 y)))) |
(/ 1 y) |
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(* (pow z 2) (+ (* -1 (/ x y)) (* -1 (/ (* x z) (pow y 2))))) |
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(/ (+ (* -1 y) (* -1 (/ (pow y 2) z))) z) |
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(/ (- (* -1 (/ (pow y 2) (pow z 2))) (+ 1 (/ y z))) z) |
(/ (- (* -1 (/ (pow y 3) (pow z 3))) (+ 1 (+ (/ y z) (/ (pow y 2) (pow z 2))))) z) |
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(* y (* z (+ (* 2 (sqrt (/ 1 (* y z)))) (* x (sqrt (/ 1 (* (pow y 3) z))))))) |
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(* z (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (+ (* 1/2 (* (pow x 3) (sqrt (/ 1 (* (pow y 3) (pow z 5)))))) (+ (* 2 (sqrt (/ 1 (* y z)))) (+ (* x (sqrt (/ 1 (* y (pow z 3))))) (* x (sqrt (/ 1 (* (pow y 3) z))))))))) |
(* z (+ (* -1/2 (* (* x (+ (* 1/4 (/ (* (pow x 2) z) (pow y 3))) (/ (pow x 3) (pow y 3)))) (sqrt (/ (pow y 3) (pow z 7))))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (+ (* -1/4 (* (pow x 2) (sqrt (/ 1 (* y (pow z 5)))))) (+ (* 1/2 (* (pow x 3) (sqrt (/ 1 (* (pow y 3) (pow z 5)))))) (+ (* 2 (sqrt (/ 1 (* y z)))) (+ (* x (sqrt (/ 1 (* y (pow z 3))))) (* x (sqrt (/ 1 (* (pow y 3) z))))))))))) |
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(sqrt (/ 1 (* (pow y 3) z))) |
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(sqrt (/ z y)) |
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(* -2 (* (sqrt (* z (+ x y))) (pow (sqrt -1) 2))) |
(* -1 (* z (+ (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))) |
(* -1 (* z (+ (* -1/4 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y))))))))) |
(* -1 (* z (+ (* -1/4 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/8 (* (/ (* (pow x 3) (pow y 3)) (pow (sqrt -1) 4)) (sqrt (/ 1 (* (pow z 7) (pow (+ x y) 5)))))) (+ (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))))) |
(* -1 (* (sqrt (* z (+ x y))) (pow (sqrt -1) 2))) |
(* -1 (* z (+ (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))) (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))))) |
(* -1 (* z (+ (* -1/8 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))) (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2)))))) |
(* -1 (* z (+ (* -1/8 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/16 (* (/ (* (pow x 3) (pow y 3)) (pow (sqrt -1) 4)) (sqrt (/ 1 (* (pow z 7) (pow (+ x y) 5)))))) (+ (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))) (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))))))) |
(exp (* 1/8 (+ (log (* -1 (+ x y))) (* -1 (log (/ -1 z)))))) |
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(* z (+ x y)) |
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(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (* x y) z))))) |
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (* x y) z))))) |
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(* -1 (* z (+ (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))) |
(* -1 (* z (+ (* -1/4 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y))))))))) |
(* -1 (* z (+ (* -1/4 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/8 (* (/ (* (pow x 3) (pow y 3)) (pow (sqrt -1) 4)) (sqrt (/ 1 (* (pow z 7) (pow (+ x y) 5)))))) (+ (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))))) |
(* -1 (* (sqrt (* z (+ x y))) (pow (sqrt -1) 2))) |
(* -1 (* z (+ (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))) (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))))) |
(* -1 (* z (+ (* -1/8 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))) (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2)))))) |
(* -1 (* z (+ (* -1/8 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/16 (* (/ (* (pow x 3) (pow y 3)) (pow (sqrt -1) 4)) (sqrt (/ 1 (* (pow z 7) (pow (+ x y) 5)))))) (+ (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))) (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))))))) |
(* z (+ x y)) |
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(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (* x y) z))))) |
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (* x y) z))))) |
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(* -1 (* z (+ (* -1 (/ (* x y) z)) (* x (- (* -1 (/ y x)) 1))))) |
(* -1 (* z (+ (* -1 (/ (* x y) z)) (* x (- (* -1 (/ y x)) 1))))) |
(* -1 (* z (+ (* -1 (/ (* x y) z)) (* x (- (* -1 (/ y x)) 1))))) |
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(* -1 (* z (+ (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))) |
(* -1 (* z (+ (* -1/4 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y))))))))) |
(* -1 (* z (+ (* -1/4 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/8 (* (/ (* (pow x 3) (pow y 3)) (pow (sqrt -1) 4)) (sqrt (/ 1 (* (pow z 7) (pow (+ x y) 5)))))) (+ (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))))) |
(* -1 (* (sqrt (* z (+ x y))) (pow (sqrt -1) 2))) |
(* -1 (* z (+ (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))) (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))))) |
(* -1 (* z (+ (* -1/8 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))) (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2)))))) |
(* -1 (* z (+ (* -1/8 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/16 (* (/ (* (pow x 3) (pow y 3)) (pow (sqrt -1) 4)) (sqrt (/ 1 (* (pow z 7) (pow (+ x y) 5)))))) (+ (* 1/2 (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))) (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))))))) |
(* z (+ x y)) |
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (* x y) z))))) |
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (* x y) z))))) |
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (* x y) z))))) |
(* x z) |
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(* -1 (* z (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* x (pow y 2))) (* x (pow y 2))) z)) (* x y)) z))))) |
(* -1 (* z (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* x (pow y 2))) (* x (pow y 2))) z)) (* x y)) z))))) |
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(* -1 (/ (+ y (/ (pow y 2) z)) z)) |
(* -1 (/ (+ y (* -1 (/ (- (* -1 (/ (pow y 3) z)) (pow y 2)) z))) z)) |
(* -1 (/ (+ y (* -1 (/ (- (* -1 (/ (- (/ (pow y 4) z) (* -1 (pow y 3))) z)) (pow y 2)) z))) z)) |
(/ -1 z) |
(* -1 (/ (+ 1 (/ y z)) z)) |
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) z)) y) z))) z)) |
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) z) (* -1 (pow y 2))) z)) y) z))) z)) |
(* x z) |
(* -1 (* z (+ (* -1 x) (* -1 (/ (* x y) z))))) |
(* -1 (* z (+ (* -1 x) (* -1 (/ (+ (* x y) (/ (* x (pow y 2)) z)) z))))) |
(* -1 (* z (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* x (pow y 2))) (* -1 (/ (* x (pow y 3)) z))) z)) (* x y)) z))))) |
(* -2 (* (sqrt (* z (+ x y))) (pow (sqrt -1) 2))) |
(* -1 (* z (+ (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))) |
(* -1 (* z (+ (* -1/4 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y))))))))) |
(* -1 (* z (+ (* -1/4 (* (/ (* (pow x 2) (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow z 5) (pow (+ x y) 3)))))) (+ (* 1/8 (* (/ (* (pow x 3) (pow y 3)) (pow (sqrt -1) 4)) (sqrt (/ 1 (* (pow z 7) (pow (+ x y) 5)))))) (+ (* 2 (* (sqrt (/ (+ x y) z)) (pow (sqrt -1) 2))) (* (* x y) (sqrt (/ 1 (* (pow z 3) (+ x y)))))))))) |
(* -1 (* y (* z (+ (* -1 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow y 3) z))))) (* 2 (* (sqrt (/ 1 (* y z))) (pow (sqrt -1) 2))))))) |
(* -1 (* z (+ (* y (+ (* -1 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow y 3) z))))) (* 2 (* (sqrt (/ 1 (* y z))) (pow (sqrt -1) 2))))) (/ (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ z (pow y 3))))) (* x (sqrt (/ z y))))) (pow z 2))))) |
(* -1 (* z (+ (* -1/2 (* (pow x 3) (sqrt (/ 1 (* y (pow z 5)))))) (+ (* y (+ (* -1 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow y 3) z))))) (* 2 (* (sqrt (/ 1 (* y z))) (pow (sqrt -1) 2))))) (/ (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ z (pow y 3))))) (* x (sqrt (/ z y))))) (pow z 2)))))) |
(* -1 (* z (+ (* -1 (/ (+ (* -1 (/ (* y (+ (* -1/4 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ (pow z 3) y)))) (* 1/2 (* (* x (+ (* -1/4 (/ (* (pow x 2) z) (* (pow y 3) (pow (sqrt -1) 2)))) (/ (pow x 3) (pow y 3)))) (sqrt (* (pow y 3) z)))))) z)) (* 1/2 (* (pow x 3) (sqrt (/ z y))))) (pow z 3))) (+ (* y (+ (* -1 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow y 3) z))))) (* 2 (* (sqrt (/ 1 (* y z))) (pow (sqrt -1) 2))))) (/ (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ z (pow y 3))))) (* x (sqrt (/ z y))))) (pow z 2)))))) |
(* -1 (* z (+ (* -1 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow y 3) z))))) (* 2 (* (sqrt (/ 1 (* y z))) (pow (sqrt -1) 2)))))) |
(* -1 (* z (+ (* -1 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow y 3) z))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (+ (* 2 (* (sqrt (/ 1 (* y z))) (pow (sqrt -1) 2))) (* x (sqrt (/ 1 (* y (pow z 3)))))))))) |
(* -1 (* z (+ (* -1 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow y 3) z))))) (+ (* -1/2 (* (pow x 3) (sqrt (/ 1 (* (pow y 3) (pow z 5)))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (+ (* 2 (* (sqrt (/ 1 (* y z))) (pow (sqrt -1) 2))) (* x (sqrt (/ 1 (* y (pow z 3))))))))))) |
(* -1 (* z (+ (* -1 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (* (pow y 3) z))))) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ (pow z 3) y)))) (* 1/2 (* (* x (+ (* -1/4 (/ (* (pow x 2) z) (* (pow y 3) (pow (sqrt -1) 2)))) (/ (pow x 3) (pow y 3)))) (sqrt (* (pow y 3) z))))) z)) (* 1/2 (* (pow x 3) (sqrt (/ z (pow y 3)))))) (pow z 3))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (+ (* 2 (* (sqrt (/ 1 (* y z))) (pow (sqrt -1) 2))) (* x (sqrt (/ 1 (* y (pow z 3))))))))))) |
(* x z) |
(* x z) |
(* x z) |
(* x z) |
(* -1 (* z (- (* -1 (/ y x)) 1))) |
(* -1 (* z (- (* -1 (/ y x)) 1))) |
(* -1 (* z (- (* -1 (/ y x)) 1))) |
(* -1 (* z (- (* -1 (/ y x)) 1))) |
(* -1 (* z (+ (* -1 x) (* -1 y)))) |
(* -1 (* z (+ (* -1 x) (+ (* -1 y) (* -1 (/ (* x y) z)))))) |
(* -1 (* z (+ (* -1 x) (+ (* -1 y) (* -1 (/ (* x y) z)))))) |
(* -1 (* z (+ (* -1 x) (+ (* -1 y) (* -1 (/ (* x y) z)))))) |
(* -1 (* (sqrt (* z (+ (* -1 x) (* -1 y)))) (sqrt -1))) |
(* -1 (* z (+ (* 1/2 (* (* x (* y (sqrt -1))) (sqrt (/ 1 (* (pow z 3) (+ (* -1 x) (* -1 y))))))) (* (sqrt (/ (+ (* -1 x) (* -1 y)) z)) (sqrt -1))))) |
(* -1 (* z (+ (* -1/8 (* (* (pow x 2) (* (pow y 2) (sqrt -1))) (sqrt (/ 1 (* (pow z 5) (pow (+ (* -1 x) (* -1 y)) 3)))))) (+ (* 1/2 (* (* x (* y (sqrt -1))) (sqrt (/ 1 (* (pow z 3) (+ (* -1 x) (* -1 y))))))) (* (sqrt (/ (+ (* -1 x) (* -1 y)) z)) (sqrt -1)))))) |
(* -1 (* z (+ (* -1/8 (* (* (pow x 2) (* (pow y 2) (sqrt -1))) (sqrt (/ 1 (* (pow z 5) (pow (+ (* -1 x) (* -1 y)) 3)))))) (+ (* 1/16 (* (* (pow x 3) (* (pow y 3) (sqrt -1))) (sqrt (/ 1 (* (pow z 7) (pow (+ (* -1 x) (* -1 y)) 5)))))) (+ (* 1/2 (* (* x (* y (sqrt -1))) (sqrt (/ 1 (* (pow z 3) (+ (* -1 x) (* -1 y))))))) (* (sqrt (/ (+ (* -1 x) (* -1 y)) z)) (sqrt -1))))))) |
(* x (pow z 2)) |
(* x (pow z 2)) |
(* x (pow z 2)) |
(* x (pow z 2)) |
(* (sqrt (/ 1 (* (pow y 3) z))) (pow (sqrt -1) 2)) |
(+ (* -1/2 (* x (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (* (sqrt (/ 1 (* (pow y 3) z))) (pow (sqrt -1) 2))) |
(+ (* -1/2 (* x (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (* (pow y 3) (pow z 5)))))) (* (sqrt (/ 1 (* (pow y 3) z))) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* -1/2 (* (pow x 2) (sqrt (/ z (pow y 3))))) (* 1/2 (* (sqrt (/ (pow y 3) z)) (+ (* -1/4 (/ (* (pow x 2) z) (* (pow y 3) (pow (sqrt -1) 2)))) (/ (pow x 3) (pow y 3)))))) (pow z 3))) (+ (* -1/2 (* x (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (* (sqrt (/ 1 (* (pow y 3) z))) (pow (sqrt -1) 2)))) |
(* -1 (* (sqrt (/ z y)) (pow (sqrt -1) 2))) |
(* -1 (* z (+ (* 1/2 (* x (sqrt (/ 1 (* y (pow z 3)))))) (* (sqrt (/ 1 (* y z))) (pow (sqrt -1) 2))))) |
(* -1 (* z (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (* y (pow z 5)))))) (+ (* 1/2 (* x (sqrt (/ 1 (* y (pow z 3)))))) (* (sqrt (/ 1 (* y z))) (pow (sqrt -1) 2)))))) |
(* -1 (* z (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (* y (pow z 5)))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (* y (pow z 7)))))) (+ (* 1/2 (* x (sqrt (/ 1 (* y (pow z 3)))))) (* (sqrt (/ 1 (* y z))) (pow (sqrt -1) 2))))))) |
(* 2 (sqrt (* x z))) |
(+ (* 2 (sqrt (* x z))) (* (sqrt (/ 1 (* x z))) (* y (+ x z)))) |
(+ (* 2 (sqrt (* x z))) (* y (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (* y (pow (+ x z) 2)))) (* (sqrt (/ 1 (* x z))) (+ x z))))) |
(+ (* 2 (sqrt (* x z))) (* y (+ (* y (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow (+ x z) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow z 5)))) (* y (pow (+ x z) 3)))))) (* (sqrt (/ 1 (* x z))) (+ x z))))) |
(sqrt (* x z)) |
(+ (sqrt (* x z)) (* 1/2 (* (sqrt (/ 1 (* x z))) (* y (+ x z))))) |
(+ (sqrt (* x z)) (* y (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (* y (pow (+ x z) 2)))) (* 1/2 (* (sqrt (/ 1 (* x z))) (+ x z)))))) |
(+ (sqrt (* x z)) (* y (+ (* 1/2 (* (sqrt (/ 1 (* x z))) (+ x z))) (* y (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow z 3)))) (pow (+ x z) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow z 5)))) (* y (pow (+ x z) 3))))))))) |
(pow (* 1 (* x z)) 1/8) |
(+ (* 1/8 (* (pow (* 1 (* x z)) 1/8) (* y (+ (/ 1 x) (/ 1 z))))) (pow (* 1 (* x z)) 1/8)) |
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1 |
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(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (* (pow z 2) (sqrt -1))) (sqrt (/ 1 (* (pow y 5) (pow (+ (* -1 x) (* -1 z)) 3)))))) (+ (* 1/2 (* (* x (* z (sqrt -1))) (sqrt (/ 1 (* (pow y 3) (+ (* -1 x) (* -1 z))))))) (* (sqrt (/ (+ (* -1 x) (* -1 z)) y)) (sqrt -1)))))) |
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(pow (* 1 (* y z)) 1/8) |
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(+ (* x (+ (* 1/8 (* (pow (* 1 (* y z)) 1/8) (+ (/ 1 y) (/ 1 z)))) (* (pow (* 1 (* y z)) 1/8) (* x (+ (* -1/16 (/ (pow (+ y z) 2) (* (pow y 2) (pow z 2)))) (* 1/128 (pow (+ (/ 1 y) (/ 1 z)) 2))))))) (pow (* 1 (* y z)) 1/8)) |
(+ (* x (+ (* 1/8 (* (pow (* 1 (* y z)) 1/8) (+ (/ 1 y) (/ 1 z)))) (* x (+ (* (pow (* 1 (* y z)) 1/8) (* x (+ (* -1/128 (/ (* (pow (+ y z) 2) (+ (/ 1 y) (/ 1 z))) (* (pow y 2) (pow z 2)))) (+ (* 1/3072 (pow (+ (/ 1 y) (/ 1 z)) 3)) (* 1/24 (/ (pow (+ y z) 3) (* (pow y 3) (pow z 3)))))))) (* (pow (* 1 (* y z)) 1/8) (+ (* -1/16 (/ (pow (+ y z) 2) (* (pow y 2) (pow z 2)))) (* 1/128 (pow (+ (/ 1 y) (/ 1 z)) 2)))))))) (pow (* 1 (* y z)) 1/8)) |
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(* 2 (sqrt (* y z))) |
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(+ (* 2 (sqrt (/ z y))) (* x (+ (sqrt (/ 1 (* y z))) (+ (sqrt (/ z (pow y 3))) (* x (+ (* -1/2 (sqrt (/ 1 (* (pow y 3) z)))) (+ (* -1/4 (sqrt (/ 1 (* y (pow z 3))))) (* x (+ (* 1/8 (sqrt (/ 1 (* y (pow z 5))))) (* 3/8 (sqrt (/ 1 (* (pow y 3) (pow z 3)))))))))))))) |
(* x z) |
(* x z) |
(* x z) |
(* x z) |
(* x y) |
(* x y) |
(* x y) |
(* x y) |
(/ (* y z) x) |
(/ (+ (* x z) (* y z)) x) |
(/ (+ (* x z) (* y z)) x) |
(/ (+ (* x z) (* y z)) x) |
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(+ (sqrt (* y z)) (* x (+ (* 1/2 (* (sqrt (/ 1 (* y z))) (+ y z))) (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow y 3) (pow z 3)))) (pow (+ y z) 2))) (* 1/16 (* (* x (pow (+ y z) 3)) (sqrt (/ 1 (* (pow y 5) (pow z 5))))))))))) |
(* x (pow z 2)) |
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(* x (pow z 2)) |
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(sqrt (/ 1 (* (pow y 3) z))) |
(+ (sqrt (/ 1 (* (pow y 3) z))) (* -1/2 (* x (sqrt (/ 1 (* (pow y 3) (pow z 3))))))) |
(+ (sqrt (/ 1 (* (pow y 3) z))) (* x (+ (* -1/2 (sqrt (/ 1 (* (pow y 3) (pow z 3))))) (* 3/8 (* x (sqrt (/ 1 (* (pow y 3) (pow z 5))))))))) |
(+ (sqrt (/ 1 (* (pow y 3) z))) (* x (+ (* -1/2 (sqrt (/ 1 (* (pow y 3) (pow z 3))))) (* x (+ (* -5/16 (* x (sqrt (/ 1 (* (pow y 3) (pow z 7)))))) (* 3/8 (sqrt (/ 1 (* (pow y 3) (pow z 5)))))))))) |
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(* 2 (sqrt (* x (+ y z)))) |
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(* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow x 7) (pow (+ y z) 5)))) (* (pow y 3) (pow z 3)))) (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))))) |
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(* x (+ (sqrt (/ (+ y z) x)) (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z)))))) |
(* x (+ (sqrt (/ (+ y z) x)) (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) (pow (+ y z) 5)))) (* (pow y 3) (pow z 3)))) (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z))))))) |
(exp (* 1/8 (+ (log (+ y z)) (* -1 (log (/ 1 x)))))) |
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(+ (exp (* 1/8 (+ (log (+ y z)) (* -1 (log (/ 1 x)))))) (+ (* 1/8 (/ (* y (* z (exp (* 1/8 (+ (log (+ y z)) (* -1 (log (/ 1 x)))))))) (* x (+ y z)))) (/ (* (exp (* 1/8 (+ (log (+ y z)) (* -1 (log (/ 1 x)))))) (+ (* -1/16 (/ (* (pow y 2) (pow z 2)) (pow (+ y z) 2))) (* 1/128 (/ (* (pow y 2) (pow z 2)) (pow (+ y z) 2))))) (pow x 2)))) |
(+ (exp (* 1/8 (+ (log (+ y z)) (* -1 (log (/ 1 x)))))) (+ (* 1/8 (/ (* y (* z (exp (* 1/8 (+ (log (+ y z)) (* -1 (log (/ 1 x)))))))) (* x (+ y z)))) (+ (/ (* (exp (* 1/8 (+ (log (+ y z)) (* -1 (log (/ 1 x)))))) (+ (* -1/16 (/ (* (pow y 2) (pow z 2)) (pow (+ y z) 2))) (* 1/128 (/ (* (pow y 2) (pow z 2)) (pow (+ y z) 2))))) (pow x 2)) (/ (* (exp (* 1/8 (+ (log (+ y z)) (* -1 (log (/ 1 x)))))) (+ (* -1/128 (/ (* (pow y 3) (pow z 3)) (pow (+ y z) 3))) (+ (* 1/3072 (/ (* (pow y 3) (pow z 3)) (pow (+ y z) 3))) (* 1/24 (/ (* (pow y 3) (pow z 3)) (pow (+ y z) 3)))))) (pow x 3))))) |
(* x (+ y z)) |
(* x (+ y (+ z (/ (* y z) x)))) |
(* x (+ y (+ z (/ (* y z) x)))) |
(* x (+ y (+ z (/ (* y z) x)))) |
(* 2 (sqrt (* x (+ y z)))) |
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(* x (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 5) (pow (+ y z) 3)))) (* (pow y 2) (pow z 2)))) (+ (* 2 (sqrt (/ (+ y z) x))) (* (sqrt (/ 1 (* (pow x 3) (+ y z)))) (* y z))))) |
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(+ z (/ (* y z) x)) |
(* -1 (* x (+ (* -1 y) (* -1 z)))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(* -1 (* (sqrt (* x (+ (* -1 y) (* -1 z)))) (sqrt -1))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) (pow (+ (* -1 y) (* -1 z)) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))))))) |
(* x (pow z 2)) |
(* x (pow z 2)) |
(* x (pow z 2)) |
(* x (pow z 2)) |
(* (sqrt (/ 1 (* x (pow y 3)))) (pow (sqrt -1) 2)) |
(+ (* -1/2 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) z)) (* (sqrt (/ 1 (* x (pow y 3)))) (pow (sqrt -1) 2))) |
(+ (* -1/2 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) z)) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 5) (pow y 3)))) (pow z 2))) (* (sqrt (/ 1 (* x (pow y 3)))) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ x (pow y 3))) (pow z 2))) (* 1/2 (* (sqrt (/ (pow y 3) x)) (+ (* -1/4 (/ (* x (pow z 2)) (* (pow y 3) (pow (sqrt -1) 2)))) (/ (pow z 3) (pow y 3)))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) z)) (* (sqrt (/ 1 (* x (pow y 3)))) (pow (sqrt -1) 2)))) |
(* -1 (* (sqrt (/ x y)) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) y))) z)) (* (sqrt (/ 1 (* x y))) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) y))) (/ (pow z 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) y))) z)) (* (sqrt (/ 1 (* x y))) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) y))) (/ (pow z 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) y))) (/ (pow z 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) y))) z)) (* (sqrt (/ 1 (* x y))) (pow (sqrt -1) 2))))))) |
| Outputs |
|---|
(* 2 (sqrt (* x y))) |
(*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64)) |
(+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) |
(fma.f64 (*.f64 (+.f64 y x) z) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))) (*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (*.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) z) (*.f64 (+.f64 y x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))))) z (*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3)))))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 y #s(literal 5 binary64))))) (*.f64 (pow.f64 (+.f64 y x) #s(literal 3 binary64)) z) (*.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (pow.f64 (+.f64 y x) #s(literal 2 binary64)))) z (*.f64 (+.f64 y x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))))) z (*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64))) |
(sqrt (* x y)) |
(sqrt.f64 (*.f64 y x)) |
(+ (sqrt (* x y)) (* 1/2 (* (sqrt (/ 1 (* x y))) (* z (+ x y))))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (+.f64 y x) z) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x)))) (sqrt.f64 (*.f64 y x))) |
(+ (sqrt (* x y)) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y)))))) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 y x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x)))))) z (sqrt.f64 (*.f64 y x))) |
(+ (sqrt (* x y)) (* z (+ (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y))) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 y #s(literal 5 binary64))))) (*.f64 (pow.f64 (+.f64 y x) #s(literal 3 binary64)) z) (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (pow.f64 (+.f64 y x) #s(literal 2 binary64)))) z (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 y x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x)))))) z (sqrt.f64 (*.f64 y x))) |
(pow (* 1 (* x y)) 1/8) |
(pow.f64 (*.f64 y x) #s(literal 1/8 binary64)) |
(+ (* 1/8 (* (pow (* 1 (* x y)) 1/8) (* z (+ (/ 1 x) (/ 1 y))))) (pow (* 1 (* x y)) 1/8)) |
(fma.f64 (*.f64 (*.f64 (pow.f64 (*.f64 y x) #s(literal 1/8 binary64)) z) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) x))) #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 1/8 binary64))) |
(+ (* z (+ (* 1/8 (* (pow (* 1 (* x y)) 1/8) (+ (/ 1 x) (/ 1 y)))) (* (pow (* 1 (* x y)) 1/8) (* z (+ (* -1/16 (/ (pow (+ x y) 2) (* (pow x 2) (pow y 2)))) (* 1/128 (pow (+ (/ 1 x) (/ 1 y)) 2))))))) (pow (* 1 (* x y)) 1/8)) |
(fma.f64 (fma.f64 (*.f64 (pow.f64 (*.f64 y x) #s(literal 1/8 binary64)) z) (fma.f64 (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(literal 1/128 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 (+.f64 y x) #s(literal 2 binary64))) (*.f64 (*.f64 y y) (*.f64 x x)))) (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 1/8 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) x)))) z (pow.f64 (*.f64 y x) #s(literal 1/8 binary64))) |
(+ (* z (+ (* 1/8 (* (pow (* 1 (* x y)) 1/8) (+ (/ 1 x) (/ 1 y)))) (* z (+ (* (pow (* 1 (* x y)) 1/8) (* z (+ (* -1/128 (/ (* (pow (+ x y) 2) (+ (/ 1 x) (/ 1 y))) (* (pow x 2) (pow y 2)))) (+ (* 1/3072 (pow (+ (/ 1 x) (/ 1 y)) 3)) (* 1/24 (/ (pow (+ x y) 3) (* (pow x 3) (pow y 3)))))))) (* (pow (* 1 (* x y)) 1/8) (+ (* -1/16 (/ (pow (+ x y) 2) (* (pow x 2) (pow y 2)))) (* 1/128 (pow (+ (/ 1 x) (/ 1 y)) 2)))))))) (pow (* 1 (* x y)) 1/8)) |
(fma.f64 (fma.f64 (*.f64 (pow.f64 (*.f64 y x) #s(literal 1/8 binary64)) (fma.f64 (fma.f64 (/.f64 #s(literal -1/128 binary64) (*.f64 y y)) (/.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 y x) #s(literal 2 binary64))) (*.f64 x x)) (fma.f64 (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) #s(literal 1/3072 binary64) (/.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 (+.f64 y x) #s(literal 3 binary64))) (*.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))) z (fma.f64 (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) #s(literal 1/128 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 (+.f64 y x) #s(literal 2 binary64))) (*.f64 (*.f64 y y) (*.f64 x x)))))) z (*.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 y x) #s(literal 1/8 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) x)))) z (pow.f64 (*.f64 y x) #s(literal 1/8 binary64))) |
(* x y) |
(*.f64 y x) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(* 2 (sqrt (* x y))) |
(*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64)) |
(+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) |
(fma.f64 (*.f64 (+.f64 y x) z) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))) (*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (*.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) z) (*.f64 (+.f64 y x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))))) z (*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3)))))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 y #s(literal 5 binary64))))) (*.f64 (pow.f64 (+.f64 y x) #s(literal 3 binary64)) z) (*.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (pow.f64 (+.f64 y x) #s(literal 2 binary64)))) z (*.f64 (+.f64 y x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))))) z (*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64))) |
(sqrt (* x y)) |
(sqrt.f64 (*.f64 y x)) |
(+ (sqrt (* x y)) (* 1/2 (* (sqrt (/ 1 (* x y))) (* z (+ x y))))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (+.f64 y x) z) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x)))) (sqrt.f64 (*.f64 y x))) |
(+ (sqrt (* x y)) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y)))))) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 y x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x)))))) z (sqrt.f64 (*.f64 y x))) |
(+ (sqrt (* x y)) (* z (+ (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y))) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 y #s(literal 5 binary64))))) (*.f64 (pow.f64 (+.f64 y x) #s(literal 3 binary64)) z) (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (pow.f64 (+.f64 y x) #s(literal 2 binary64)))) z (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 y x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x)))))) z (sqrt.f64 (*.f64 y x))) |
(* x y) |
(*.f64 y x) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* x y) |
(*.f64 y x) |
(+ (* x y) (* x (* z (+ 1 (/ y x))))) |
(*.f64 x (+.f64 y (*.f64 (+.f64 (/.f64 y x) #s(literal 1 binary64)) z))) |
(+ (* x y) (* x (* z (+ 1 (/ y x))))) |
(*.f64 x (+.f64 y (*.f64 (+.f64 (/.f64 y x) #s(literal 1 binary64)) z))) |
(+ (* x y) (* x (* z (+ 1 (/ y x))))) |
(*.f64 x (+.f64 y (*.f64 (+.f64 (/.f64 y x) #s(literal 1 binary64)) z))) |
(* 2 (sqrt (* x y))) |
(*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64)) |
(+ (* 2 (sqrt (* x y))) (* (sqrt (/ 1 (* x y))) (* z (+ x y)))) |
(fma.f64 (*.f64 (+.f64 y x) z) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))) (*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (*.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) z) (*.f64 (+.f64 y x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))))) z (*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64))) |
(+ (* 2 (sqrt (* x y))) (* z (+ (* z (+ (* -1/4 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/8 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3)))))) (* (sqrt (/ 1 (* x y))) (+ x y))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 y #s(literal 5 binary64))))) (*.f64 (pow.f64 (+.f64 y x) #s(literal 3 binary64)) z) (*.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (pow.f64 (+.f64 y x) #s(literal 2 binary64)))) z (*.f64 (+.f64 y x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))))) z (*.f64 (sqrt.f64 (*.f64 y x)) #s(literal 2 binary64))) |
(sqrt (* x y)) |
(sqrt.f64 (*.f64 y x)) |
(+ (sqrt (* x y)) (* 1/2 (* (sqrt (/ 1 (* x y))) (* z (+ x y))))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (+.f64 y x) z) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x)))) (sqrt.f64 (*.f64 y x))) |
(+ (sqrt (* x y)) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (* z (pow (+ x y) 2)))) (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y)))))) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 y x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x)))))) z (sqrt.f64 (*.f64 y x))) |
(+ (sqrt (* x y)) (* z (+ (* 1/2 (* (sqrt (/ 1 (* x y))) (+ x y))) (* z (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow (+ x y) 2))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (pow y 5)))) (* z (pow (+ x y) 3))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 y #s(literal 5 binary64))))) (*.f64 (pow.f64 (+.f64 y x) #s(literal 3 binary64)) z) (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (pow.f64 (+.f64 y x) #s(literal 2 binary64)))) z (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 y x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x)))))) z (sqrt.f64 (*.f64 y x))) |
(* x y) |
(*.f64 y x) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(+ (* x y) (* z (+ x y))) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(* x y) |
(*.f64 y x) |
(+ (* x y) (* x z)) |
(*.f64 (+.f64 z y) x) |
(+ (* x y) (* x z)) |
(*.f64 (+.f64 z y) x) |
(+ (* x y) (* x z)) |
(*.f64 (+.f64 z y) x) |
1 |
#s(literal 1 binary64) |
(+ 1 (/ z y)) |
(+.f64 (/.f64 z y) #s(literal 1 binary64)) |
(+ 1 (* z (+ (/ 1 y) (/ z (pow y 2))))) |
(fma.f64 (+.f64 (/.f64 z (*.f64 y y)) (/.f64 #s(literal 1 binary64) y)) z #s(literal 1 binary64)) |
(+ 1 (* z (+ (* z (+ (/ 1 (pow y 2)) (/ z (pow y 3)))) (/ 1 y)))) |
(fma.f64 (fma.f64 (+.f64 (/.f64 z (pow.f64 y #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 y y))) z (/.f64 #s(literal 1 binary64) y)) z #s(literal 1 binary64)) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(+ (/ 1 y) (/ z (pow y 2))) |
(+.f64 (/.f64 z (*.f64 y y)) (/.f64 #s(literal 1 binary64) y)) |
(+ (* z (+ (/ 1 (pow y 2)) (/ z (pow y 3)))) (/ 1 y)) |
(fma.f64 (+.f64 (/.f64 z (pow.f64 y #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 y y))) z (/.f64 #s(literal 1 binary64) y)) |
(+ (* z (+ (* z (+ (/ 1 (pow y 3)) (/ z (pow y 4)))) (/ 1 (pow y 2)))) (/ 1 y)) |
(fma.f64 (fma.f64 (+.f64 (/.f64 z (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) z (/.f64 #s(literal 1 binary64) (*.f64 y y))) z (/.f64 #s(literal 1 binary64) y)) |
(* -1 (/ (* x (pow z 2)) y)) |
(*.f64 (neg.f64 x) (/.f64 (*.f64 z z) y)) |
(* (pow z 2) (+ (* -1 (/ x y)) (* -1 (/ (* x z) (pow y 2))))) |
(*.f64 (fma.f64 (neg.f64 x) (/.f64 z (*.f64 y y)) (/.f64 (neg.f64 x) y)) (*.f64 z z)) |
(* (pow z 2) (+ (* -1 (/ x y)) (* z (+ (* -1 (/ x (pow y 2))) (* -1 (/ (* x z) (pow y 3))))))) |
(*.f64 (fma.f64 (fma.f64 (neg.f64 x) (/.f64 z (pow.f64 y #s(literal 3 binary64))) (/.f64 (neg.f64 x) (*.f64 y y))) z (/.f64 (neg.f64 x) y)) (*.f64 z z)) |
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(* z (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (+ (* 2 (sqrt (/ 1 (* y z)))) (+ (* x (sqrt (/ 1 (* y (pow z 3))))) (* x (sqrt (/ 1 (* (pow y 3) z)))))))) |
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(* z (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (+ (* 1/2 (* (pow x 3) (sqrt (/ 1 (* (pow y 3) (pow z 5)))))) (+ (* 2 (sqrt (/ 1 (* y z)))) (+ (* x (sqrt (/ 1 (* y (pow z 3))))) (* x (sqrt (/ 1 (* (pow y 3) z))))))))) |
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(* z (+ (* -1/2 (* (* x (+ (* 1/4 (/ (* (pow x 2) z) (pow y 3))) (/ (pow x 3) (pow y 3)))) (sqrt (/ (pow y 3) (pow z 7))))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (* (pow y 3) (pow z 3)))))) (+ (* -1/4 (* (pow x 2) (sqrt (/ 1 (* y (pow z 5)))))) (+ (* 1/2 (* (pow x 3) (sqrt (/ 1 (* (pow y 3) (pow z 5)))))) (+ (* 2 (sqrt (/ 1 (* y z)))) (+ (* x (sqrt (/ 1 (* y (pow z 3))))) (* x (sqrt (/ 1 (* (pow y 3) z))))))))))) |
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(* x z) |
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(* x z) |
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(* z (+ x (+ y (/ (* x y) z)))) |
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(* x (pow z 2)) |
(*.f64 (*.f64 z z) x) |
(* x (pow z 2)) |
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(*.f64 (*.f64 z z) x) |
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(sqrt (/ 1 (* (pow y 3) z))) |
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) z)) |
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(* z (+ (sqrt (/ 1 (* y z))) (* 1/2 (* x (sqrt (/ 1 (* y (pow z 3)))))))) |
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(* z (+ (sqrt (/ 1 (* y z))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (* y (pow z 5)))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (* y (pow z 7)))))) (* 1/2 (* x (sqrt (/ 1 (* y (pow z 3)))))))))) |
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(* -2 (* (sqrt (* z (+ x y))) (pow (sqrt -1) 2))) |
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(exp (* 1/8 (+ (log (* -1 (+ x y))) (* -1 (log (/ -1 z)))))) |
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(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 y #s(literal 3 binary64)) x))) z (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (*.f64 z z) (fma.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x)))) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y))) z)))) (neg.f64 x)) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x (pow y 3)))) (* z (pow (sqrt -1) 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow x 5) (pow y 3)))) (pow z 3))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow z 2))) (+ (* 2 (* (sqrt (/ 1 (* x y))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (* (pow x 3) y))) z))))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 y #s(literal 3 binary64)) x))) z (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 y #s(literal 3 binary64))))) (pow.f64 z #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (*.f64 z z) (fma.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x)))) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y))) z))))) (neg.f64 x)) |
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 (* x (pow y 3)))) (* z (pow (sqrt -1) 2)))) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ (pow x 3) y)) (/ (pow z 2) (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt (* x (pow y 3))) (* z (+ (* -1/4 (/ (* x (pow z 2)) (* (pow y 3) (pow (sqrt -1) 2)))) (/ (pow z 3) (pow y 3))))))) x)) (* 1/2 (* (sqrt (/ x (pow y 3))) (pow z 3)))) (pow x 3))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) (pow z 2))) (+ (* 2 (* (sqrt (/ 1 (* x y))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (* (pow x 3) y))) z))))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 y #s(literal 3 binary64)) x))) z (-.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (*.f64 z z) (fma.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x)))) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y))) z))) (/.f64 (-.f64 (*.f64 (*.f64 (pow.f64 z #s(literal 3 binary64)) (sqrt.f64 (/.f64 x (pow.f64 y #s(literal 3 binary64))))) #s(literal 1/2 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) y))) (/.f64 (*.f64 z z) #s(literal -1 binary64)) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (pow.f64 y #s(literal 3 binary64)) x))) (*.f64 (fma.f64 (/.f64 (*.f64 (*.f64 z z) x) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/4 binary64) (/.f64 (pow.f64 z #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) z))) x)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 x)) |
(* x z) |
(*.f64 z x) |
(* x z) |
(*.f64 z x) |
(* x z) |
(*.f64 z x) |
(* x z) |
(*.f64 z x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
(* x y) |
(*.f64 y x) |
z |
(+ z (/ (* y z) x)) |
(fma.f64 y (/.f64 z x) z) |
(+ z (/ (* y z) x)) |
(fma.f64 y (/.f64 z x) z) |
(+ z (/ (* y z) x)) |
(fma.f64 y (/.f64 z x) z) |
(* -1 (* x (+ (* -1 y) (* -1 z)))) |
(*.f64 (-.f64 (neg.f64 z) y) (neg.f64 x)) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(*.f64 (neg.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y)) (neg.f64 x)) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(*.f64 (neg.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y)) (neg.f64 x)) |
(* -1 (* x (+ (* -1 y) (+ (* -1 z) (* -1 (/ (* y z) x)))))) |
(*.f64 (neg.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y)) (neg.f64 x)) |
(* -1 (* (sqrt (* x (+ (* -1 y) (* -1 z)))) (sqrt -1))) |
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (-.f64 (neg.f64 z) y) x))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (-.f64 (neg.f64 z) y)))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) z) y) (*.f64 (sqrt.f64 (/.f64 (-.f64 (neg.f64 z) y) x)) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 x)) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 (-.f64 (neg.f64 z) y) #s(literal 3 binary64))))) (*.f64 (*.f64 (*.f64 z z) (*.f64 y y)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (-.f64 (neg.f64 z) y)))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) z) y) (*.f64 (sqrt.f64 (/.f64 (-.f64 (neg.f64 z) y) x)) (sqrt.f64 #s(literal -1 binary64))))) (neg.f64 x)) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) (pow (+ (* -1 y) (* -1 z)) 3)))) (* (pow y 2) (* (pow z 2) (sqrt -1))))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) (pow (+ (* -1 y) (* -1 z)) 5)))) (* (pow y 3) (* (pow z 3) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) (+ (* -1 y) (* -1 z))))) (* y (* z (sqrt -1))))) (* (sqrt (/ (+ (* -1 y) (* -1 z)) x)) (sqrt -1))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 (-.f64 (neg.f64 z) y) #s(literal 3 binary64))))) (*.f64 (*.f64 (*.f64 z z) (*.f64 y y)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))) (pow.f64 (-.f64 (neg.f64 z) y) #s(literal 5 binary64))))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 z #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (-.f64 (neg.f64 z) y)))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) z) y) (*.f64 (sqrt.f64 (/.f64 (-.f64 (neg.f64 z) y) x)) (sqrt.f64 #s(literal -1 binary64)))))) (neg.f64 x)) |
(* x (pow z 2)) |
(*.f64 (*.f64 z z) x) |
(* x (pow z 2)) |
(*.f64 (*.f64 z z) x) |
(* x (pow z 2)) |
(*.f64 (*.f64 z z) x) |
(* x (pow z 2)) |
(*.f64 (*.f64 z z) x) |
(* (sqrt (/ 1 (* x (pow y 3)))) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 y #s(literal 3 binary64)) x)))) |
(+ (* -1/2 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) z)) (* (sqrt (/ 1 (* x (pow y 3)))) (pow (sqrt -1) 2))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) z (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 y #s(literal 3 binary64)) x))))) |
(+ (* -1/2 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) z)) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 5) (pow y 3)))) (pow z 2))) (* (sqrt (/ 1 (* x (pow y 3)))) (pow (sqrt -1) 2)))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) z (fma.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 y #s(literal 3 binary64)))) (*.f64 z z)) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 y #s(literal 3 binary64)) x)))))) |
(+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ x (pow y 3))) (pow z 2))) (* 1/2 (* (sqrt (/ (pow y 3) x)) (+ (* -1/4 (/ (* x (pow z 2)) (* (pow y 3) (pow (sqrt -1) 2)))) (/ (pow z 3) (pow y 3)))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow x 3) (pow y 3)))) z)) (* (sqrt (/ 1 (* x (pow y 3)))) (pow (sqrt -1) 2)))) |
(-.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) z (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 y #s(literal 3 binary64)) x))))) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) x))) (fma.f64 (/.f64 (*.f64 (*.f64 z z) x) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/4 binary64) (/.f64 (pow.f64 z #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 x (pow.f64 y #s(literal 3 binary64)))) (*.f64 z z)) #s(literal -1/2 binary64))) (pow.f64 x #s(literal 3 binary64)))) |
(* -1 (* (sqrt (/ x y)) (pow (sqrt -1) 2))) |
(*.f64 (sqrt.f64 (/.f64 x y)) #s(literal 1 binary64)) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) y))) z)) (* (sqrt (/ 1 (* x y))) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)))) z (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))))) (neg.f64 x)) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) y))) (/ (pow z 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) y))) z)) (* (sqrt (/ 1 (* x y))) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) y)))) (/.f64 (*.f64 z z) #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)))) z (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x)))))) (neg.f64 x)) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 5) y))) (/ (pow z 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow x 7) y))) (/ (pow z 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow x 3) y))) z)) (* (sqrt (/ 1 (* x y))) (pow (sqrt -1) 2))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) y)))) (/.f64 (*.f64 z z) #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 7 binary64)) y)))) (/.f64 (pow.f64 z #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)))) z (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y x))))))) (neg.f64 x)) |
| 4 656× | lower-*.f32 |
| 4 628× | lower-*.f64 |
| 3 860× | lower-/.f32 |
| 3 848× | lower-/.f64 |
| 3 184× | lower-fma.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 65 | 397 |
| 0 | 107 | 376 |
| 1 | 402 | 367 |
| 2 | 2615 | 367 |
| 0 | 8636 | 367 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) |
(pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) |
(fma.f64 (+.f64 y x) z (*.f64 y x)) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) |
(sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) |
#s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y)) |
(*.f64 z y) |
(*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x))) #s(literal 2 binary64)) |
(sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x))) |
#s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x)) |
(fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z))) |
(*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) |
(/.f64 x (*.f64 (-.f64 y z) x)) |
(/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z)) |
#s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y)))))) |
(*.f64 y (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y))))) |
(fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y)))) |
(*.f64 x z) |
(*.f64 y x) |
(fma.f64 y (/.f64 z x) z) |
#s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z)))) |
(sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z))))) |
(*.f64 (*.f64 z z) x) |
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) |
(sqrt.f64 (/.f64 (+.f64 z x) y)) |
| Outputs |
|---|
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Compiled 47 047 to 5 778 computations (87.7% saved)
21 alts after pruning (17 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 491 | 7 | 1 498 |
| Fresh | 20 | 10 | 30 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 3 | 3 |
| Total | 1 515 | 21 | 1 536 |
| Status | Accuracy | Program |
|---|---|---|
| 45.2% | (*.f64 (pow.f64 #s(approx (pow (+ (* (+ y x) z) (* y x)) 1/8) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (-.f64 (log.f64 (-.f64 (neg.f64 z) y)) (log.f64 (/.f64 #s(literal -1 binary64) x))))) #s(literal 4 binary64)) #s(literal 2 binary64)) | |
| 57.6% | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 (*.f64 z y) (pow.f64 x #s(literal -1 binary64)) z) y) x))) #s(literal 2 binary64)) | |
| 37.1% | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 y x) z))) #s(literal 2 binary64)) | |
| ✓ | 35.7% | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) |
| ✓ | 3.7% | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) |
| 23.6% | (*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) #s(approx (* (+ (+ (* y (/ z x)) z) y) x) (*.f64 (*.f64 (+.f64 (/.f64 y x) #s(literal 1 binary64)) z) x)))) #s(literal 2 binary64)) | |
| 19.1% | (*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 x y)) #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 x y))) #s(literal 1/4 binary64))) | |
| 35.1% | (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 y z)))))) | |
| 36.3% | (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 x y)))))) | |
| 56.2% | (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 #s(approx (/ (/ (pow (* z x) 2) x) (- y z)) (*.f64 (neg.f64 x) z)))) (*.f64 y z)))) | |
| 37.8% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 z x (*.f64 x y))))) | |
| ✓ | 37.8% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) |
| ✓ | 36.8% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
| 22.5% | (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) #s(approx (+ (* (* (/ x (* (- y z) x)) y) (* x y)) (/ (neg (* (* z z) x)) (- y z))) (*.f64 (fma.f64 x (/.f64 y z) x) z))))) | |
| 31.8% | #s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 (+.f64 z x)) (sqrt.f64 y)))))) | |
| 42.7% | #s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y #s(approx (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 z x) y)) #s(literal -1 binary64)) #s(literal 2 binary64))))) | |
| 43.7% | #s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y #s(approx (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (*.f64 (sqrt.f64 (/.f64 z y)) #s(literal 2 binary64))))) | |
| 42.7% | #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (/.f64 (sqrt.f64 (+.f64 y x)) (sqrt.f64 z)) #s(literal 2 binary64))) z)) | |
| 44.4% | #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 y x) z)))) z)) | |
| 43.5% | #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 y z)))) z)) | |
| 2.5% | #s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 (sqrt.f64 (/.f64 z x)) y))) |
Compiled 1 492 to 665 computations (55.4% saved)
| Inputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z y)))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 y x) z))) #s(literal 2 binary64)) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 (sqrt.f64 (/.f64 z x)) y))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 z x (*.f64 x y))))) |
(*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 y z)))) z)) |
#s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y #s(approx (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (*.f64 (sqrt.f64 (/.f64 z y)) #s(literal 2 binary64))))) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 y x) z)))) z)) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) #s(approx (* (+ z y) x) (*.f64 (fma.f64 x (/.f64 y z) x) z))))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) #s(approx (+ (* (* (/ x (* (- y z) x)) y) (* x y)) (/ (neg (* (* z z) x)) (- y z))) (*.f64 (fma.f64 x (/.f64 y z) x) z))))) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 y x) z))) #s(literal -1 binary64))) z)) |
#s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y #s(approx (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 z x) y)) #s(literal -1 binary64)) #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) #s(approx (* (+ (+ (* y (/ z x)) z) y) x) (*.f64 (*.f64 (+.f64 (/.f64 y x) #s(literal 1 binary64)) z) x)))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (fma.f64 (+.f64 (/.f64 y z) #s(literal 1 binary64)) x y) z)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (fma.f64 (+.f64 (/.f64 z x) #s(literal 1 binary64)) y z) x)))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 y (/.f64 z x) z) y) x))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 x y)))))) |
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 y z)))))) |
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y x) z (*.f64 y x)))))) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 #s(approx (* (sqrt (/ 1 (* z x))) (+ z x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 x z)))) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (/.f64 (+.f64 z x) (sqrt.f64 (*.f64 z x))) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x))) y (*.f64 (sqrt.f64 (/.f64 z x)) #s(literal 2 binary64))) x))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 #s(approx (/ (/ (pow (* z x) 2) x) (- y z)) (*.f64 (neg.f64 x) z)))) (*.f64 y z)))) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 x (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) z)) y (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 z x))))))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 (*.f64 (/.f64 x (*.f64 (-.f64 y z) x)) y) (*.f64 x y) (/.f64 (neg.f64 (*.f64 (*.f64 z z) x)) (-.f64 y z)))))) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (/.f64 (fma.f64 z (sqrt.f64 (*.f64 z x)) (*.f64 (sqrt.f64 (*.f64 z x)) x)) (*.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 x z)) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x))) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64))) z (*.f64 (sqrt.f64 (*.f64 z x)) y)) z))) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64) (*.f64 #s(approx (sqrt (/ x z)) (*.f64 (sqrt.f64 (/.f64 x z)) #s(literal -1 binary64))) y)) x (*.f64 (sqrt.f64 (*.f64 z x)) y)) x))) |
(*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 x y)) #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 x y))) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 (*.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 x z)) #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 x z))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)) #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x))) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 (fma.f64 (*.f64 z y) (pow.f64 x #s(literal -1 binary64)) z) y) x))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 (*.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) (fma.f64 z (+.f64 x y) (*.f64 x y))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 z)) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) |
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (+ (* (+ y x) z) (* y x))) (/.f64 (fma.f64 (neg.f64 y) (/.f64 z (*.f64 x (pow.f64 (+.f64 z y) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 z y))) x))))) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 y (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) z)) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (pow.f64 z #s(literal 3 binary64))))))))) z)) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) (pow.f64 z #s(literal 3 binary64)))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z)) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 z x)) (pow.f64 y #s(literal 3 binary64)))) (*.f64 z x) (*.f64 (sqrt.f64 (/.f64 (+.f64 z x) y)) #s(literal 2 binary64))) y)) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 z x) (*.f64 (sqrt.f64 (/.f64 (+.f64 z x) y)) #s(literal 2 binary64))) y)) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (sqrt.f64 (/.f64 (+.f64 y x) z)) #s(literal 2 binary64))) z)) |
#s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 z x) y)))))) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 (fma.f64 (sqrt.f64 (/.f64 x z)) #s(literal 2 binary64) (*.f64 y (+.f64 (sqrt.f64 (/.f64 x (pow.f64 z #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 z x)))))) z))) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) #s(approx (* (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) z) (fma.f64 (*.f64 x z) (+.f64 (sqrt.f64 (/.f64 y (pow.f64 z #s(literal 3 binary64)))) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) z))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 y z)))))) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (/.f64 (sqrt.f64 (+.f64 y x)) (sqrt.f64 z)) #s(literal 2 binary64))) z)) |
#s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y (fma.f64 (*.f64 x z) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 z x))) (*.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 (+.f64 z x)) (sqrt.f64 y)))))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (fma.f64 (*.f64 (*.f64 y y) x) (/.f64 x (*.f64 (-.f64 y z) x)) (neg.f64 (/.f64 (/.f64 (pow.f64 (*.f64 z x) #s(literal 2 binary64)) x) (-.f64 y z)))) (*.f64 y z)))) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 (fma.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64))) (+.f64 y x))) (*.f64 y x) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 z (+.f64 y x)))) #s(literal 2 binary64))) z)) |
(*.f64 #s(literal 2 binary64) (pow.f64 (pow.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (pow.f64 #s(approx (+ (* z (+ x y)) (* x y)) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (pow.f64 (fma.f64 z (+.f64 x y) (*.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) |
(*.f64 (pow.f64 (pow.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) #s(literal 2 binary64)) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 z x) #s(literal -1/4 binary64)) #s(literal 2 binary64)) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 z x)) #s(literal -1/2 binary64))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) |
(*.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 (-.f64 (pow.f64 (*.f64 z y) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 z y) x) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 (*.f64 z y) (*.f64 (+.f64 z y) x))))) |
(*.f64 (/.f64 (sqrt.f64 (-.f64 (pow.f64 (*.f64 z (+.f64 x y)) #s(literal 2 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 z (+.f64 x y) (*.f64 (neg.f64 x) y)))) #s(literal 2 binary64)) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) (fma.f64 (*.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 z x)) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 (*.f64 z x)) #s(literal -1/2 binary64))) (+.f64 z x)) y (*.f64 (sqrt.f64 (*.f64 z x)) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 (fma.f64 (+.f64 y x) z (*.f64 y x)))) #s(literal 2 binary64)) #s(literal 2 binary64)) |
(*.f64 (pow.f64 #s(approx (pow (+ (* z (+ x y)) (* x y)) 1/4) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (-.f64 (log.f64 (-.f64 (neg.f64 z) y)) (log.f64 (/.f64 #s(literal -1 binary64) x))))) #s(literal 2 binary64)) #s(literal 2 binary64)) |
(*.f64 (pow.f64 #s(approx (pow (+ (* (+ y x) z) (* y x)) 1/8) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (-.f64 (log.f64 (-.f64 (neg.f64 z) y)) (log.f64 (/.f64 #s(literal -1 binary64) x))))) #s(literal 4 binary64)) #s(literal 2 binary64)) |
| Outputs |
|---|
#s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y #s(approx (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 z x) y)) #s(literal -1 binary64)) #s(literal 2 binary64))))) |
(*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 y x) z)))) z)) |
6 calls:
| 22.0ms | (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) |
| 21.0ms | y |
| 20.0ms | x |
| 19.0ms | z |
| 19.0ms | (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 86.4% | 4 | x |
| 97.2% | 3 | y |
| 87.2% | 3 | z |
| 84.1% | 2 | (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) |
| 84.1% | 2 | (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) |
| 84.1% | 2 | (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) |
Compiled 40 to 37 computations (7.5% saved)
| Inputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z y)))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 y x) z))) #s(literal 2 binary64)) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 (sqrt.f64 (/.f64 z x)) y))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 z x (*.f64 x y))))) |
(*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 y z)))) z)) |
#s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y #s(approx (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (*.f64 (sqrt.f64 (/.f64 z y)) #s(literal 2 binary64))))) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 y x) z)))) z)) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) #s(approx (* (+ z y) x) (*.f64 (fma.f64 x (/.f64 y z) x) z))))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) #s(approx (+ (* (* (/ x (* (- y z) x)) y) (* x y)) (/ (neg (* (* z z) x)) (- y z))) (*.f64 (fma.f64 x (/.f64 y z) x) z))))) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 y x) z))) #s(literal -1 binary64))) z)) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 y x) z)))) z)) |
2 calls:
| 6.0ms | z |
| 6.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 79.1% | 2 | z |
| 84.7% | 2 | y |
Compiled 2 to 6 computations (-200% saved)
| Inputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z y)))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 y x) z))) #s(literal 2 binary64)) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 (sqrt.f64 (/.f64 z x)) y))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 z x (*.f64 x y))))) |
(*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 y z)))) z)) |
#s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y #s(approx (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (*.f64 (sqrt.f64 (/.f64 z y)) #s(literal 2 binary64))))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
#s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y #s(approx (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (*.f64 (sqrt.f64 (/.f64 z y)) #s(literal 2 binary64))))) |
1 calls:
| 4.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 84.5% | 2 | y |
Compiled 1 to 3 computations (-200% saved)
| Inputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z y)))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 y x) z))) #s(literal 2 binary64)) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 (sqrt.f64 (/.f64 z x)) y))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 z x (*.f64 x y))))) |
(*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 y z)))) z)) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
#s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 y z)))) z)) |
1 calls:
| 4.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 84.5% | 2 | y |
Compiled 1 to 3 computations (-200% saved)
| Inputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z y)))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 y x) z))) #s(literal 2 binary64)) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 (sqrt.f64 (/.f64 z x)) y))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 z x (*.f64 x y))))) |
(*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
6 calls:
| 6.0ms | y |
| 5.0ms | x |
| 4.0ms | (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) |
| 4.0ms | z |
| 4.0ms | (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 71.1% | 1 | z |
| 71.1% | 1 | x |
| 71.1% | 1 | (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) |
| 71.1% | 1 | (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) |
| 71.1% | 1 | (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) |
| 71.1% | 1 | y |
Compiled 40 to 37 computations (7.5% saved)
| Inputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z y)))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 y x) z))) #s(literal 2 binary64)) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 (sqrt.f64 (/.f64 z x)) y))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 z x (*.f64 x y))))) |
| Outputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 z x (*.f64 x y))))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z)))) |
6 calls:
| 5.0ms | x |
| 4.0ms | (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) |
| 4.0ms | (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) |
| 4.0ms | (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) |
| 4.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 66.6% | 2 | x |
| 71.2% | 2 | y |
| 69.6% | 2 | z |
| 42.8% | 2 | (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) |
| 42.8% | 2 | (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) |
| 42.8% | 2 | (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) |
Compiled 40 to 37 computations (7.5% saved)
| Inputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z y)))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 (+.f64 y x) z))) #s(literal 2 binary64)) |
#s(approx (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))) #s(approx (+ (* (* (sqrt (/ 1 (* z x))) (+ z x)) y) (* (sqrt (* z x)) 2)) (*.f64 (sqrt.f64 (/.f64 z x)) y))) |
| Outputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z)))) |
1 calls:
| 3.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 71.2% | 2 | y |
Compiled 1 to 3 computations (-200% saved)
| Inputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z y)))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z)))) |
| Outputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z)))) |
1 calls:
| 3.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 70.5% | 2 | y |
Compiled 1 to 3 computations (-200% saved)
| Inputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z y)))) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z x))) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 #s(approx (+ (* (+ y x) z) (* y x)) (*.f64 z y))) #s(literal 2 binary64)) |
| Outputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z y)))) |
2 calls:
| 2.0ms | z |
| 2.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 67.9% | 2 | z |
| 69.5% | 2 | y |
Compiled 2 to 6 computations (-200% saved)
Total -21.5b remaining (-53.1%)
Threshold costs -21.5b (-53.1%)
| Inputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z x)))) |
| Outputs |
|---|
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
6 calls:
| 3.0ms | z |
| 2.0ms | (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) |
| 2.0ms | x |
| 2.0ms | y |
| 2.0ms | (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 36.8% | 1 | (*.f64 #s(literal 2 binary64) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)))) |
| 36.8% | 1 | (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z))) |
| 36.8% | 1 | (+.f64 (+.f64 (*.f64 x y) (*.f64 x z)) (*.f64 y z)) |
| 36.8% | 1 | x |
| 36.8% | 1 | z |
| 36.8% | 1 | y |
Compiled 40 to 37 computations (7.5% saved)
| 2× | binary-search |
| 1× | predicate-same |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 9.0ms | 8412.488505943667 | 7124129.463513828 |
| 31.0ms | -1.3385160098785532e+51 | -4.0370705786106133e+42 |
| 14.0ms | 209× | 0 | invalid |
| 13.0ms | 192× | 0 | valid |
Compiled 311 to 299 computations (3.9% saved)
ival-mult: 9.0ms (59.6% of total)ival-add: 3.0ms (19.9% of total)ival-sqrt: 2.0ms (13.3% 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 | 8412.488505943667 | 7124129.463513828 |
Compiled 86 to 83 computations (3.5% saved)
| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 32.0ms | 40361908.78120335 | 1641655754334.4597 |
| 11.0ms | 173× | 0 | invalid |
| 8.0ms | 128× | 0 | valid |
Compiled 185 to 185 computations (0% saved)
ival-mult: 6.0ms (53.6% of total)ival-add: 2.0ms (17.9% of total)ival-sqrt: 2.0ms (17.9% 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 | 8412.488505943667 | 7124129.463513828 |
Compiled 80 to 80 computations (0% saved)
| 1× | binary-search |
| 1× | predicate-same |
| Time | Left | Right |
|---|---|---|
| 3.0ms | -2.619738052618674e-282 | 1.8741906885658115e-286 |
| 1.0ms | 17× | 0 | invalid |
| 1.0ms | 16× | 0 | valid |
Compiled 36 to 37 computations (-2.8% saved)
ival-mult: 1.0ms (82.4% of total)ival-true: 0.0ms (0% of total)ival-add: 0.0ms (0% of total)ival-sqrt: 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 | -2.619738052618674e-282 | 1.8741906885658115e-286 |
Compiled 35 to 37 computations (-5.7% saved)
| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 33.0ms | -2.619738052618674e-282 | 1.8741906885658115e-286 |
| 11.0ms | 176× | 0 | valid |
| 11.0ms | 155× | 0 | invalid |
Compiled 209 to 245 computations (-17.2% saved)
ival-mult: 7.0ms (55.1% of total)ival-add: 3.0ms (23.6% of total)ival-sqrt: 2.0ms (15.7% 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× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 37.0ms | -2.619738052618674e-282 | 1.8741906885658115e-286 |
| 14.0ms | 184× | 0 | invalid |
| 11.0ms | 176× | 0 | valid |
Compiled 185 to 233 computations (-25.9% saved)
ival-mult: 8.0ms (50.5% of total)ival-sqrt: 5.0ms (31.5% of total)ival-add: 3.0ms (18.9% 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 |
| 44× | *-commutative-binary64-*.f64 |
| 12× | +-commutative-binary64-+.f64 |
| 8× | neg-sub0-binary64--.f64-neg.f64 |
| 6× | neg-mul-1-binary64-*.f64-neg.f64 |
| 6× | sub-neg-binary64-neg.f64-+.f64--.f64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 116 | 503 |
| 1 | 141 | 502 |
| 2 | 142 | 502 |
| 3 | 147 | 502 |
| 4 | 155 | 502 |
| 5 | 160 | 502 |
| 6 | 163 | 502 |
| 7 | 164 | 502 |
| 1× | saturated |
| Inputs |
|---|
(if (<=.f64 y #s(literal -4100000000000000044763167560505977894600704 binary64)) #s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y #s(approx (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 z x) y)) #s(literal -1 binary64)) #s(literal 2 binary64))))) (if (<=.f64 y #s(literal 2000000 binary64)) (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 y x) z)))) z)))) |
(if (<=.f64 y #s(literal 2000000 binary64)) (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 y x) z)))) z))) |
(if (<=.f64 y #s(literal 520000000000 binary64)) (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) #s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y #s(approx (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (*.f64 (sqrt.f64 (/.f64 z y)) #s(literal 2 binary64)))))) |
(if (<=.f64 y #s(literal 2000000 binary64)) (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 y z)))) z))) |
(*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
(if (<=.f64 y #s(literal -653996952628337/326998476314168493941780105303955630664491214509745363599777340200912796363811072538207513066313433266477866490952498420772444240018406385375505907430986779905229729456305877240633380281444431820005925969026076507067319984967003404515550047182527554765966689382523869862684015858539562586584645632 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 z x (*.f64 x y))))) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z))))) |
(if (<=.f64 y #s(literal -653996952628337/326998476314168493941780105303955630664491214509745363599777340200912796363811072538207513066313433266477866490952498420772444240018406385375505907430986779905229729456305877240633380281444431820005925969026076507067319984967003404515550047182527554765966689382523869862684015858539562586584645632 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z))))) |
(if (<=.f64 y #s(literal -6801568307334705/2615987810513347951534240842431645045315929716077962908798218721607302370910488580305660104530507466131822931927619987366179553920147251083004047259447894239241837835650447017925067042251555454560047407752208612056538559879736027236124400377460220438127733515060190958901472126868316500692677165056 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z))))) |
(if (<=.f64 y #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z y))))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
| Outputs |
|---|
(if (<=.f64 y #s(literal -4100000000000000044763167560505977894600704 binary64)) #s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y #s(approx (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 z x) y)) #s(literal -1 binary64)) #s(literal 2 binary64))))) (if (<=.f64 y #s(literal 2000000 binary64)) (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 y x) z)))) z)))) |
(if (<=.f64 y #s(literal -4100000000000000044763167560505977894600704 binary64)) #s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 #s(approx (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (*.f64 (neg.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (+.f64 x z) y)))) y)) (if (<=.f64 y #s(literal 2000000 binary64)) (*.f64 (sqrt.f64 (fma.f64 (+.f64 x y) z (*.f64 x y))) #s(literal 2 binary64)) #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 (sqrt.f64 (/.f64 (+.f64 x y) z)) #s(literal 2 binary64))) z)))) |
(if (<=.f64 y #s(literal 2000000 binary64)) (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 (+.f64 y x) z)))) z))) |
(if (<=.f64 y #s(literal 2000000 binary64)) (*.f64 (sqrt.f64 (fma.f64 (+.f64 x y) z (*.f64 x y))) #s(literal 2 binary64)) #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 (sqrt.f64 (/.f64 (+.f64 x y) z)) #s(literal 2 binary64))) z))) |
(if (<=.f64 y #s(literal 520000000000 binary64)) (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) #s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 y #s(approx (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (*.f64 (sqrt.f64 (/.f64 z y)) #s(literal 2 binary64)))))) |
(if (<=.f64 y #s(literal 520000000000 binary64)) (*.f64 (sqrt.f64 (fma.f64 (+.f64 x y) z (*.f64 x y))) #s(literal 2 binary64)) #s(approx (* (pow (pow (+ (* z (+ x y)) (* x y)) 1/4) 2) 2) (*.f64 #s(approx (+ (* (* x z) (sqrt (/ (/ 1 (pow y 3)) (+ z x)))) (* 2 (sqrt (/ (+ z x) y)))) (*.f64 (sqrt.f64 (/.f64 z y)) #s(literal 2 binary64))) y))) |
(if (<=.f64 y #s(literal 2000000 binary64)) (*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 y z)))) z))) |
(if (<=.f64 y #s(literal 2000000 binary64)) (*.f64 (sqrt.f64 (fma.f64 (+.f64 x y) z (*.f64 x y))) #s(literal 2 binary64)) #s(approx (* (sqrt (+ (* (+ y x) z) (* y x))) 2) (*.f64 #s(approx (+ (* (sqrt (/ (/ 1 (pow z 3)) (+ y x))) (* y x)) (* (sqrt (/ (+ y x) z)) 2)) (*.f64 (sqrt.f64 (/.f64 y z)) #s(literal 2 binary64))) z))) |
(*.f64 (sqrt.f64 (fma.f64 (+.f64 y x) z (*.f64 y x))) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 (fma.f64 (+.f64 x y) z (*.f64 x y))) #s(literal 2 binary64)) |
(if (<=.f64 y #s(literal -653996952628337/326998476314168493941780105303955630664491214509745363599777340200912796363811072538207513066313433266477866490952498420772444240018406385375505907430986779905229729456305877240633380281444431820005925969026076507067319984967003404515550047182527554765966689382523869862684015858539562586584645632 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 z x (*.f64 x y))))) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z))))) |
(if (<=.f64 y #s(literal -653996952628337/326998476314168493941780105303955630664491214509745363599777340200912796363811072538207513066313433266477866490952498420772444240018406385375505907430986779905229729456305877240633380281444431820005925969026076507067319984967003404515550047182527554765966689382523869862684015858539562586584645632 binary64)) (*.f64 (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (fma.f64 z x (*.f64 x y)))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 x y) z))) #s(literal 2 binary64))) |
(if (<=.f64 y #s(literal -653996952628337/326998476314168493941780105303955630664491214509745363599777340200912796363811072538207513066313433266477866490952498420772444240018406385375505907430986779905229729456305877240633380281444431820005925969026076507067319984967003404515550047182527554765966689382523869862684015858539562586584645632 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z))))) |
(if (<=.f64 y #s(literal -653996952628337/326998476314168493941780105303955630664491214509745363599777340200912796363811072538207513066313433266477866490952498420772444240018406385375505907430986779905229729456305877240633380281444431820005925969026076507067319984967003404515550047182527554765966689382523869862684015858539562586584645632 binary64)) (*.f64 (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 z y) x))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 x y) z))) #s(literal 2 binary64))) |
(if (<=.f64 y #s(literal -6801568307334705/2615987810513347951534240842431645045315929716077962908798218721607302370910488580305660104530507466131822931927619987366179553920147251083004047259447894239241837835650447017925067042251555454560047407752208612056538559879736027236124400377460220438127733515060190958901472126868316500692677165056 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 y x) z))))) |
(if (<=.f64 y #s(literal -6801568307334705/2615987810513347951534240842431645045315929716077962908798218721607302370910488580305660104530507466131822931927619987366179553920147251083004047259447894239241837835650447017925067042251555454560047407752208612056538559879736027236124400377460220438127733515060190958901472126868316500692677165056 binary64)) (*.f64 (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 x y))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 (+.f64 x y) z))) #s(literal 2 binary64))) |
(if (<=.f64 y #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z y))))) |
(if (<=.f64 y #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) (*.f64 (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 x y))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 z y))) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 y x)))) |
(*.f64 (sqrt.f64 #s(approx (+ (+ (* x y) (* x z)) (* y z)) (*.f64 x y))) #s(literal 2 binary64)) |
| 11 034× | lower-fma.f64 |
| 11 034× | lower-fma.f32 |
| 8 534× | lower-fma.f64 |
| 8 534× | lower-fma.f32 |
| 7 980× | lower-*.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 2012 | 26214 |
| 1 | 5980 | 25054 |
| 0 | 8232 | 24109 |
| 0 | 1767 | 22861 |
| 1 | 6052 | 22030 |
| 0 | 8372 | 21182 |
| 0 | 501 | 3429 |
| 1 | 1684 | 3363 |
| 2 | 6236 | 3318 |
| 0 | 8106 | 3177 |
| 0 | 47 | 323 |
| 0 | 82 | 247 |
| 1 | 306 | 233 |
| 2 | 2320 | 229 |
| 0 | 9928 | 229 |
| 0 | 11 | 44 |
| 0 | 18 | 36 |
| 1 | 55 | 36 |
| 2 | 435 | 36 |
| 3 | 6667 | 36 |
| 0 | 8469 | 33 |
| 0 | 1158 | 17035 |
| 1 | 3844 | 16312 |
| 0 | 8186 | 15684 |
| 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× | node limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 865 to 428 computations (50.5% saved)
Compiled 866 to 402 computations (53.6% saved)
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