
Time bar (total: 6.6s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 0 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 1 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 2 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 3 |
| 50% | 49.9% | 49.9% | 0.1% | 0% | 0% | 0% | 4 |
| 50% | 49.9% | 49.9% | 0.1% | 0% | 0% | 0% | 5 |
| 50% | 49.9% | 49.9% | 0.1% | 0% | 0% | 0% | 6 |
| 66.7% | 49.9% | 25% | 0.1% | 0% | 25% | 0% | 7 |
| 66.7% | 49.9% | 25% | 0.1% | 0% | 25% | 0% | 8 |
| 66.7% | 49.9% | 25% | 0.1% | 0% | 25% | 0% | 9 |
| 80% | 49.9% | 12.5% | 0.1% | 0% | 37.4% | 0% | 10 |
| 80% | 49.9% | 12.5% | 0.1% | 0% | 37.4% | 0% | 11 |
| 80% | 49.9% | 12.5% | 0.1% | 0% | 37.4% | 0% | 12 |
Compiled 12 to 12 computations (0% saved)
| 478.0ms | 8 256× | 0 | valid |
| 124.0ms | 2 047× | 0 | invalid |
ival-mult: 120.0ms (35.1% of total)ival-div: 82.0ms (24% of total)ival-sqrt: 71.0ms (20.7% of total)ival-add: 48.0ms (14% of total)exact: 9.0ms (2.6% of total)ival-true: 8.0ms (2.3% of total)ival-assert: 4.0ms (1.2% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 0 | 0 | - | 0 | - | (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | z |
| 0 | 0 | - | 0 | - | (sqrt.f64 z) |
| 0 | 0 | - | 0 | - | (+.f64 x (*.f64 y (sqrt.f64 z))) |
| 0 | 0 | - | 0 | - | (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| 0 | 0 | - | 0 | - | y |
| 0 | 0 | - | 0 | - | #s(literal 2 binary64) |
| 0 | 0 | - | 0 | - | (*.f64 y (sqrt.f64 z)) |
| 0 | 0 | - | 0 | - | x |
| Predicted + | Predicted - | |
|---|---|---|
| + | 0 | 0 |
| - | 0 | 256 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 0 | 0 | 0 |
| - | 0 | 0 | 256 |
| number | freq |
|---|---|
| 0 | 256 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 0 | 0 | 0 |
| - | 0 | 0 | 1 |
| 32.0ms | 512× | 0 | valid |
Compiled 74 to 34 computations (54.1% saved)
ival-mult: 6.0ms (36.1% of total)ival-sqrt: 4.0ms (24.1% of total)ival-div: 3.0ms (18.1% of total)ival-add: 2.0ms (12% of total)exact: 1.0ms (6% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
| 482× | unsub-neg |
| 354× | distribute-lft-neg-in |
| 312× | cancel-sign-sub-inv |
| 270× | distribute-rgt-in |
| 236× | associate-*r* |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 35 | 78 |
| 1 | 112 | 74 |
| 2 | 311 | 74 |
| 3 | 600 | 74 |
| 4 | 932 | 74 |
| 5 | 1348 | 74 |
| 6 | 1744 | 74 |
| 7 | 2055 | 74 |
| 8 | 2168 | 74 |
| 9 | 2252 | 74 |
| 10 | 2288 | 74 |
| 11 | 2292 | 74 |
| 12 | 2292 | 74 |
| 0 | 10 | 8 |
| 0 | 16 | 8 |
| 1 | 27 | 8 |
| 2 | 37 | 8 |
| 3 | 39 | 8 |
| 0 | 39 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| Outputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
Compiled 10 to 10 computations (0% saved)
Compiled 0 to 3 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.8% | (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
Compiled 10 to 10 computations (0% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 y (sqrt.f64 z)) | |
| cost-diff | 0 | (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) | |
| cost-diff | 128 | (+.f64 x (*.f64 y (sqrt.f64 z))) | |
| cost-diff | 704 | (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) |
| 32× | lower-*.f32 |
| 28× | lower-*.f64 |
| 20× | lower-fma.f64 |
| 20× | lower-fma.f32 |
| 16× | *-commutative |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 10 | 26 |
| 0 | 16 | 26 |
| 1 | 27 | 26 |
| 2 | 37 | 26 |
| 3 | 39 | 26 |
| 0 | 39 | 24 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) |
#s(literal 1 binary64) |
#s(literal 2 binary64) |
(+.f64 x (*.f64 y (sqrt.f64 z))) |
x |
(*.f64 y (sqrt.f64 z)) |
y |
(sqrt.f64 z) |
z |
| Outputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) |
#s(literal 1/2 binary64) |
#s(literal 1 binary64) |
#s(literal 2 binary64) |
(+.f64 x (*.f64 y (sqrt.f64 z))) |
(fma.f64 (sqrt.f64 z) y x) |
x |
(*.f64 y (sqrt.f64 z)) |
(*.f64 (sqrt.f64 z) y) |
y |
(sqrt.f64 z) |
z |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) | |
| accuracy | 0 | (sqrt.f64 z) | |
| accuracy | 0.00390625 | (+.f64 x (*.f64 y (sqrt.f64 z))) | |
| accuracy | 0.23828125 | (*.f64 y (sqrt.f64 z)) |
| 25.0ms | 256× | 0 | valid |
Compiled 32 to 12 computations (62.5% saved)
ival-sqrt: 11.0ms (64.4% of total)ival-mult: 3.0ms (17.6% of total)ival-div: 2.0ms (11.7% of total)ival-add: 1.0ms (5.9% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (patch (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ()) |
#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ()) |
#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor inf z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z))) (taylor inf z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z))) (taylor inf z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z))) (taylor inf z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* y (sqrt z))) (taylor inf z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) (taylor inf z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) (taylor inf z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) (taylor inf z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor inf z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor inf z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor inf z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor inf z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt z) (taylor inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (sqrt z) (taylor inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (sqrt z) (taylor inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (sqrt z) (taylor inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) (taylor -inf z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) (taylor -inf z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) (taylor -inf z) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) (taylor -inf z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) (taylor -inf z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) (taylor -inf z) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt z) (pow (sqrt -1) 2))) (taylor -inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt z) (pow (sqrt -1) 2))) (taylor -inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt z) (pow (sqrt -1) 2))) (taylor -inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt z) (pow (sqrt -1) 2))) (taylor -inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor 0 y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor inf y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (sqrt z) (/ x y))) (taylor inf y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (sqrt z) (/ x y))) (taylor inf y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (sqrt z) (/ x y))) (taylor inf y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* y (sqrt z))) (taylor inf y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) (taylor inf y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) (taylor inf y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) (taylor inf y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor inf y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor inf y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor inf y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor inf y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor -inf y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) (taylor -inf y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) (taylor -inf y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) (taylor -inf y) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* y (sqrt z))) (taylor -inf y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) (taylor -inf y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) (taylor -inf y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) (taylor -inf y) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor -inf y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor -inf y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor -inf y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor -inf y) (#s(alt (*.f64 y (sqrt.f64 z)) (patch (*.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (* y (sqrt z))) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* (/ y x) (sqrt z)))) (taylor inf x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* (/ y x) (sqrt z)))) (taylor inf x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* (/ y x) (sqrt z)))) (taylor inf x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (+.f64 x (*.f64 y (sqrt.f64 z))) (patch (+.f64 x (*.f64 y (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) #<representation binary64>) () ())) ()) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | z | @ | -inf | ((/ 1 2) (+ x (* y (sqrt z))) (* (/ 1 2) (+ x (* y (sqrt z)))) (* y (sqrt z)) (sqrt z)) |
| 1.0ms | y | @ | -inf | ((/ 1 2) (+ x (* y (sqrt z))) (* (/ 1 2) (+ x (* y (sqrt z)))) (* y (sqrt z)) (sqrt z)) |
| 1.0ms | z | @ | 0 | ((/ 1 2) (+ x (* y (sqrt z))) (* (/ 1 2) (+ x (* y (sqrt z)))) (* y (sqrt z)) (sqrt z)) |
| 1.0ms | z | @ | inf | ((/ 1 2) (+ x (* y (sqrt z))) (* (/ 1 2) (+ x (* y (sqrt z)))) (* y (sqrt z)) (sqrt z)) |
| 1.0ms | y | @ | inf | ((/ 1 2) (+ x (* y (sqrt z))) (* (/ 1 2) (+ x (* y (sqrt z)))) (* y (sqrt z)) (sqrt z)) |
| 1× | egg-herbie |
| 5 642× | lower-fma.f64 |
| 5 642× | lower-fma.f32 |
| 3 660× | lower-*.f64 |
| 3 660× | lower-*.f32 |
| 1 856× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 75 | 646 |
| 1 | 251 | 646 |
| 2 | 797 | 646 |
| 3 | 2298 | 622 |
| 4 | 5069 | 622 |
| 5 | 7549 | 622 |
| 0 | 8141 | 566 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(* y (sqrt z)) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
x |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* 1/2 x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* 1/2 (* y (sqrt z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* 1/2 (* y (sqrt z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
| Outputs |
|---|
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* 1/2 (* y (sqrt z))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y)) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 (sqrt.f64 z) y) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y)) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 (sqrt.f64 z) y) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 (sqrt.f64 z) y) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 (sqrt.f64 z) y) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 (sqrt.f64 z) y) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(sqrt.f64 z) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(sqrt.f64 z) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(sqrt.f64 z) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(sqrt.f64 z) |
x |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (+ (sqrt z) (/ x y))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (+ (sqrt z) (/ x y))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (+ (sqrt z) (/ x y))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 (* y (sqrt z))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y)) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 (* y (sqrt z))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y)) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 (* y (sqrt z))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
| 7 460× | lower-fma.f64 |
| 7 460× | lower-fma.f32 |
| 4 298× | lower-*.f32 |
| 4 294× | lower-*.f64 |
| 4 222× | lower-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 10 | 21 |
| 0 | 16 | 21 |
| 1 | 41 | 21 |
| 2 | 234 | 21 |
| 3 | 2001 | 21 |
| 0 | 8162 | 19 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) |
(+.f64 x (*.f64 y (sqrt.f64 z))) |
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
(*.f64 y (sqrt.f64 z)) |
(sqrt.f64 z) |
| Outputs |
|---|
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Compiled 9 397 to 942 computations (90% saved)
10 alts after pruning (10 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 367 | 10 | 377 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 368 | 10 | 378 |
| Status | Accuracy | Program |
|---|---|---|
| 99.6% | (fma.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 y #s(literal 1/2 binary64))) (*.f64 x #s(literal 1/2 binary64))) | |
| ▶ | 54.1% | (/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) |
| 54.0% | (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 (sqrt.f64 z) y) x) (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)))) | |
| 99.6% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)))) | |
| ▶ | 99.8% | (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
| ▶ | 87.5% | (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))))) |
| 70.7% | (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (pow.f64 (*.f64 z z) #s(literal 1/4 binary64))))) | |
| ▶ | 95.2% | #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) |
| 52.2% | #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y))) | |
| ▶ | 49.5% | #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) |
Compiled 266 to 216 computations (18.8% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))))) | |
| cost-diff | 128 | (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))) | |
| cost-diff | 704 | (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) | |
| cost-diff | 1728 | (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))))) | |
| cost-diff | 0 | (*.f64 z y) | |
| cost-diff | 0 | (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) | |
| cost-diff | 0 | (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | (/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) | |
| cost-diff | 0 | (*.f64 z y) | |
| cost-diff | 0 | (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) | |
| cost-diff | 0 | (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) | |
| cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) x) | |
| cost-diff | 0 | #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) | |
| cost-diff | 0 | (sqrt.f64 z) | |
| cost-diff | 0 | (fma.f64 (sqrt.f64 z) y x) | |
| cost-diff | 0 | (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
| 3 560× | lower-fma.f32 |
| 3 552× | lower-fma.f64 |
| 2 480× | lower-*.f32 |
| 2 462× | lower-*.f64 |
| 1 280× | unsub-neg |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 37 | 263 |
| 0 | 65 | 254 |
| 1 | 125 | 254 |
| 2 | 257 | 252 |
| 3 | 586 | 246 |
| 4 | 1145 | 246 |
| 5 | 2094 | 246 |
| 6 | 3955 | 246 |
| 7 | 4750 | 246 |
| 8 | 5091 | 246 |
| 9 | 5272 | 246 |
| 10 | 5284 | 246 |
| 11 | 5296 | 246 |
| 12 | 5871 | 246 |
| 13 | 6078 | 246 |
| 14 | 6096 | 246 |
| 15 | 6100 | 246 |
| 16 | 6100 | 246 |
| 17 | 6100 | 246 |
| 18 | 6154 | 246 |
| 19 | 6285 | 246 |
| 20 | 6382 | 246 |
| 21 | 6382 | 246 |
| 0 | 6382 | 246 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(fma.f64 (sqrt.f64 z) y x) |
(sqrt.f64 z) |
z |
y |
x |
#s(literal 1/2 binary64) |
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(*.f64 z y) |
z |
y |
(sqrt.f64 (/.f64 #s(literal 1 binary64) z)) |
(/.f64 #s(literal 1 binary64) z) |
#s(literal 1 binary64) |
x |
#s(literal 1/2 binary64) |
(/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) |
(*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) |
(fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) |
(*.f64 z y) |
z |
y |
(*.f64 (neg.f64 x) x) |
(neg.f64 x) |
x |
#s(literal 1/2 binary64) |
(-.f64 (*.f64 (sqrt.f64 z) y) x) |
(*.f64 (sqrt.f64 z) y) |
(sqrt.f64 z) |
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))))) |
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) |
#s(literal 1 binary64) |
#s(literal 2 binary64) |
(fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))))) |
x |
(/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) |
(-.f64 x (*.f64 (sqrt.f64 z) y)) |
(*.f64 (sqrt.f64 z) y) |
(sqrt.f64 z) |
z |
y |
(neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))) |
(*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) |
(*.f64 z y) |
(/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) |
| Outputs |
|---|
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 y (sqrt.f64 z) x)) |
(fma.f64 (sqrt.f64 z) y x) |
(fma.f64 y (sqrt.f64 z) x) |
(sqrt.f64 z) |
z |
y |
x |
#s(literal 1/2 binary64) |
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) |
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z) x) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z) x) #s(literal 1/2 binary64)) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z) x) |
(*.f64 z y) |
(*.f64 y z) |
z |
y |
(sqrt.f64 (/.f64 #s(literal 1 binary64) z)) |
(/.f64 #s(literal 1 binary64) z) |
#s(literal 1 binary64) |
x |
#s(literal 1/2 binary64) |
(/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) |
(*.f64 (fma.f64 (*.f64 (neg.f64 y) y) z (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) (fma.f64 y (sqrt.f64 z) (neg.f64 x)))) |
(*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) |
(*.f64 (fma.f64 (*.f64 y z) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) |
(fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) |
(fma.f64 (*.f64 y z) y (*.f64 (neg.f64 x) x)) |
(*.f64 z y) |
(*.f64 y z) |
z |
y |
(*.f64 (neg.f64 x) x) |
(neg.f64 x) |
x |
#s(literal 1/2 binary64) |
(-.f64 (*.f64 (sqrt.f64 z) y) x) |
(fma.f64 y (sqrt.f64 z) (neg.f64 x)) |
(*.f64 (sqrt.f64 z) y) |
(*.f64 y (sqrt.f64 z)) |
(sqrt.f64 z) |
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))))) |
(*.f64 (fma.f64 (*.f64 (neg.f64 y) y) z (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) (fma.f64 y (sqrt.f64 z) (neg.f64 x)))) |
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) |
#s(literal 1/2 binary64) |
#s(literal 1 binary64) |
#s(literal 2 binary64) |
(fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))))) |
(/.f64 (fma.f64 (*.f64 (neg.f64 y) y) z (*.f64 x x)) (-.f64 x (*.f64 y (sqrt.f64 z)))) |
x |
(/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) |
(/.f64 x (-.f64 x (*.f64 y (sqrt.f64 z)))) |
(-.f64 x (*.f64 (sqrt.f64 z) y)) |
(-.f64 x (*.f64 y (sqrt.f64 z))) |
(*.f64 (sqrt.f64 z) y) |
(*.f64 y (sqrt.f64 z)) |
(sqrt.f64 z) |
z |
y |
(neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))) |
(*.f64 (/.f64 z (fma.f64 y (sqrt.f64 z) (neg.f64 x))) (*.f64 y y)) |
(*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) |
(*.f64 (/.f64 z (-.f64 x (*.f64 y (sqrt.f64 z)))) (*.f64 y y)) |
(*.f64 z y) |
(*.f64 y z) |
(/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) |
(/.f64 y (-.f64 x (*.f64 y (sqrt.f64 z)))) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.23828125 | (*.f64 (sqrt.f64 z) y) | |
| accuracy | 1.8625433899550892 | (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) | |
| accuracy | 4.416924135229649 | (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) | |
| accuracy | 4.947040889273882 | (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) | |
| accuracy | 0.01171875 | (-.f64 (*.f64 (sqrt.f64 z) y) x) | |
| accuracy | 0.23828125 | (*.f64 (sqrt.f64 z) y) | |
| accuracy | 1.5820257452111206 | (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) | |
| accuracy | 28.80863559915213 | (/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) | |
| accuracy | 0 | (*.f64 z y) | |
| accuracy | 0 | #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) | |
| accuracy | 0.14453125 | (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) | |
| accuracy | 3.0415992012567914 | (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) | |
| accuracy | 0 | (*.f64 #s(literal 1/2 binary64) x) | |
| accuracy | 32.313986461195164 | #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) | |
| accuracy | 0 | (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) | |
| accuracy | 0 | (sqrt.f64 z) | |
| accuracy | 0.12890625 | (fma.f64 (sqrt.f64 z) y x) |
| 83.0ms | 256× | 0 | valid |
Compiled 266 to 38 computations (85.7% saved)
ival-div: 24.0ms (40.9% of total)ival-mult: 20.0ms (34.1% of total)ival-add: 5.0ms (8.5% of total)ival-sqrt: 4.0ms (6.8% of total)ival-neg: 3.0ms (5.1% of total)ival-sub: 2.0ms (3.4% 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 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (sqrt.f64 z) y x) (patch (fma.f64 (sqrt.f64 z) y x) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ()) |
#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ()) |
#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) #<representation binary64>) () ()) |
#s(alt (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) (patch (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #<representation binary64>) () ()) |
#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) (patch (/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) #<representation binary64>) () ()) |
#s(alt (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) (patch (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #<representation binary64>) () ()) |
#s(alt (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))))) (patch (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (patch (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))) (patch (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))) #<representation binary64>) () ()) |
#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) #<representation binary64>) () ()) |
#s(alt (*.f64 (sqrt.f64 z) y) (patch (*.f64 (sqrt.f64 z) y) #<representation binary64>) () ()) |
#s(alt (-.f64 (*.f64 (sqrt.f64 z) y) x) (patch (-.f64 (*.f64 (sqrt.f64 z) y) x) #<representation binary64>) () ()) |
#s(alt (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ()) |
#s(alt (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) (patch (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) #<representation binary64>) () ()) |
#s(alt (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (sqrt.f64 z) y x) (patch (fma.f64 (sqrt.f64 z) y x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (sqrt.f64 z) y x) (patch (fma.f64 (sqrt.f64 z) y x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (sqrt.f64 z) y x) (patch (fma.f64 (sqrt.f64 z) y x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (sqrt.f64 z) y x) (patch (fma.f64 (sqrt.f64 z) y x) #<representation binary64>) () ())) ()) |
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) (patch #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) (patch (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) (patch (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) (patch (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) (patch (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #<representation binary64>) () ())) ()) |
#s(alt (* y z) (taylor 0 z) (#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ())) ()) |
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#s(alt (* y z) (taylor 0 z) (#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ())) ()) |
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#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))))) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 (*.f64 (sqrt.f64 z) y) x) (patch (-.f64 (*.f64 (sqrt.f64 z) y) x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) (taylor -inf x) (#s(alt (-.f64 (*.f64 (sqrt.f64 z) y) x) (patch (-.f64 (*.f64 (sqrt.f64 z) y) x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) (taylor -inf x) (#s(alt (-.f64 (*.f64 (sqrt.f64 z) y) x) (patch (-.f64 (*.f64 (sqrt.f64 z) y) x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) (taylor -inf x) (#s(alt (-.f64 (*.f64 (sqrt.f64 z) y) x) (patch (-.f64 (*.f64 (sqrt.f64 z) y) x) #<representation binary64>) () ())) ()) |
#s(alt (/ y x) (taylor -inf x) (#s(alt (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (+ (* -1 y) (* -1 (* (/ (pow y 2) x) (sqrt z)))) x)) (taylor -inf x) (#s(alt (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* (pow y 2) (sqrt z)) (/ (* (pow y 3) z) x)) x))) x)) (taylor -inf x) (#s(alt (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (/ (pow y 4) x) (sqrt (pow z 3)))) (* -1 (* (pow y 3) z))) x)) (* (pow y 2) (sqrt z))) x))) x)) (taylor -inf x) (#s(alt (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ()) |
#s(alt (/ (* (pow y 2) z) x) (taylor -inf x) (#s(alt (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) (patch (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (+ (* -1 (* (/ (pow y 3) x) (sqrt (pow z 3)))) (* -1 (* (pow y 2) z))) x)) (taylor -inf x) (#s(alt (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) (patch (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (+ (* -1 (* (pow y 2) z)) (* -1 (/ (+ (* (pow y 3) (sqrt (pow z 3))) (/ (* (pow y 4) (pow z 2)) x)) x))) x)) (taylor -inf x) (#s(alt (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) (patch (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (+ (* -1 (* (pow y 2) z)) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (/ (pow y 5) x) (sqrt (pow z 5)))) (* -1 (* (pow y 4) (pow z 2)))) x)) (* (pow y 3) (sqrt (pow z 3)))) x))) x)) (taylor -inf x) (#s(alt (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) (patch (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor -inf x) (#s(alt (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (/ y x) (sqrt z))) (taylor -inf x) (#s(alt (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1 (/ (- (* -1 (/ (* (pow y 2) z) x)) (* y (sqrt z))) x))) (taylor -inf x) (#s(alt (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1 (/ (- (* -1 (/ (- (* (/ (pow y 3) x) (sqrt (pow z 3))) (* -1 (* (pow y 2) z))) x)) (* y (sqrt z))) x))) (taylor -inf x) (#s(alt (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (patch (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) #<representation binary64>) () ())) ()) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 17.0ms | y | @ | inf | ((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (sqrt (/ 1 z))) x) 1/2) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y)))))) (/ 1 2) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))) (* (/ 1 2) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))))) (sqrt (/ 1 z)) (* (sqrt z) y) (- (* (sqrt z) y) x) (/ y (- x (* (sqrt z) y))) (* (* z y) (/ y (- x (* (sqrt z) y)))) (/ x (- x (* (sqrt z) y)))) |
| 11.0ms | z | @ | -inf | ((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (sqrt (/ 1 z))) x) 1/2) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y)))))) (/ 1 2) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))) (* (/ 1 2) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))))) (sqrt (/ 1 z)) (* (sqrt z) y) (- (* (sqrt z) y) x) (/ y (- x (* (sqrt z) y))) (* (* z y) (/ y (- x (* (sqrt z) y)))) (/ x (- x (* (sqrt z) y)))) |
| 9.0ms | x | @ | -inf | ((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (sqrt (/ 1 z))) x) 1/2) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y)))))) (/ 1 2) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))) (* (/ 1 2) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))))) (sqrt (/ 1 z)) (* (sqrt z) y) (- (* (sqrt z) y) x) (/ y (- x (* (sqrt z) y))) (* (* z y) (/ y (- x (* (sqrt z) y)))) (/ x (- x (* (sqrt z) y)))) |
| 6.0ms | z | @ | inf | ((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (sqrt (/ 1 z))) x) 1/2) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y)))))) (/ 1 2) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))) (* (/ 1 2) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))))) (sqrt (/ 1 z)) (* (sqrt z) y) (- (* (sqrt z) y) x) (/ y (- x (* (sqrt z) y))) (* (* z y) (/ y (- x (* (sqrt z) y)))) (/ x (- x (* (sqrt z) y)))) |
| 6.0ms | z | @ | 0 | ((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (/ 1 2) (+ x (* y (sqrt z)))) (* (+ (* (* z y) (sqrt (/ 1 z))) x) 1/2) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y)))))) (/ 1 2) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))) (* (/ 1 2) (+ (* x (/ x (- x (* (sqrt z) y)))) (neg (* (* z y) (/ y (- x (* (sqrt z) y))))))) (sqrt (/ 1 z)) (* (sqrt z) y) (- (* (sqrt z) y) x) (/ y (- x (* (sqrt z) y))) (* (* z y) (/ y (- x (* (sqrt z) y)))) (/ x (- x (* (sqrt z) y)))) |
| 1× | egg-herbie |
| 10 772× | lower-fma.f64 |
| 10 772× | lower-fma.f32 |
| 6 546× | lower-*.f64 |
| 6 546× | lower-*.f32 |
| 3 324× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 868 | 8527 |
| 1 | 2940 | 7807 |
| 0 | 8434 | 7444 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y z) |
(* y z) |
(* y z) |
(* y z) |
(* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) |
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x)))) |
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x)))) |
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x)))) |
(* -1/2 (pow x 2)) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(* -1 (pow x 2)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(/ (pow x 2) (- x (* y (sqrt z)))) |
(+ (* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (/ (pow x 2) (- x (* y (sqrt z))))) |
(+ (* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (/ (pow x 2) (- x (* y (sqrt z))))) |
(+ (* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (/ (pow x 2) (- x (* y (sqrt z))))) |
(* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) |
(* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) |
(* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) |
(* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) |
(* 1/2 (/ (pow x 2) (- x (* y (sqrt z))))) |
(+ (* -1/2 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (* 1/2 (/ (pow x 2) (- x (* y (sqrt z)))))) |
(+ (* -1/2 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (* 1/2 (/ (pow x 2) (- x (* y (sqrt z)))))) |
(+ (* -1/2 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (* 1/2 (/ (pow x 2) (- x (* y (sqrt z)))))) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(- (* y (sqrt z)) x) |
(- (* y (sqrt z)) x) |
(- (* y (sqrt z)) x) |
(- (* y (sqrt z)) x) |
(/ y (- x (* y (sqrt z)))) |
(/ y (- x (* y (sqrt z)))) |
(/ y (- x (* y (sqrt z)))) |
(/ y (- x (* y (sqrt z)))) |
(/ (* (pow y 2) z) (- x (* y (sqrt z)))) |
(/ (* (pow y 2) z) (- x (* y (sqrt z)))) |
(/ (* (pow y 2) z) (- x (* y (sqrt z)))) |
(/ (* (pow y 2) z) (- x (* y (sqrt z)))) |
(/ x (- x (* y (sqrt z)))) |
(/ x (- x (* y (sqrt z)))) |
(/ x (- x (* y (sqrt z)))) |
(/ x (- x (* y (sqrt z)))) |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* y (sqrt z)) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* y (sqrt z)) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* y z) |
(* y z) |
(* y z) |
(* y z) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 (* y (sqrt z))) (* 1/2 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z))) z))) |
(+ (* 1/2 (* y (sqrt z))) (+ (* 1/2 (* (/ (* x (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z)))) y) (sqrt (/ 1 (pow z 3))))) (* 1/2 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z))) z)))) |
(+ (* 1/2 (* y (sqrt z))) (+ (* 1/2 (* (/ (* x (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z)))) y) (sqrt (/ 1 (pow z 3))))) (+ (* 1/2 (/ (* (pow x 2) (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z)))) (* (pow y 2) (pow z 2)))) (* 1/2 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z))) z))))) |
(* 1/2 (* (pow y 2) z)) |
(* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2)))) |
(* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2)))) |
(* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2)))) |
(* (pow y 2) z) |
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2))) |
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2))) |
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2))) |
(* y (sqrt z)) |
(- (+ x (* -1 (* (/ (pow x 2) y) (sqrt (/ 1 z))))) (* -1 (* y (sqrt z)))) |
(- (+ x (+ (* -1 (* (/ (pow x 2) y) (sqrt (/ 1 z)))) (* (/ (pow x 2) y) (sqrt (/ 1 z))))) (+ (* -1 (* y (sqrt z))) (/ (pow x 3) (* (pow y 2) z)))) |
(- (+ x (+ (* -1 (* (/ (pow x 2) y) (sqrt (/ 1 z)))) (* (/ (pow x 2) y) (sqrt (/ 1 z))))) (+ (* -1 (* y (sqrt z))) (* (/ (pow x 4) (pow y 3)) (sqrt (/ 1 (pow z 3)))))) |
(* y (sqrt z)) |
(- x (* -1 (* y (sqrt z)))) |
(- (+ x (* (/ (pow x 2) y) (sqrt (/ 1 z)))) (* -1 (* y (sqrt z)))) |
(- (+ x (+ (* (/ (pow x 2) y) (sqrt (/ 1 z))) (/ (pow x 3) (* (pow y 2) z)))) (* -1 (* y (sqrt z)))) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 (* y (sqrt z))) (* 1/2 (/ (+ (* -1 (* (/ (pow x 2) y) (sqrt z))) (* x z)) z))) |
(+ (* 1/2 (* y (sqrt z))) (+ (* 1/2 (/ (+ (* -1 (* (/ (pow x 2) y) (sqrt z))) (* x z)) z)) (* 1/2 (/ (- (* (/ (pow x 2) y) (sqrt (pow z 3))) (/ (* (pow x 3) z) (pow y 2))) (pow z 2))))) |
(+ (* 1/2 (* y (sqrt z))) (+ (* 1/2 (/ (+ (* -1 (* (/ (pow x 2) y) (sqrt z))) (* x z)) z)) (+ (* 1/2 (/ (- (* (/ (pow x 2) y) (sqrt (pow z 3))) (/ (* (pow x 3) z) (pow y 2))) (pow z 2))) (* 1/2 (/ (- (/ (* (pow x 3) (pow z 2)) (pow y 2)) (* (/ (pow x 4) (pow y 3)) (sqrt (pow z 3)))) (pow z 3)))))) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(sqrt (/ 1 z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* z (+ (* -1 (/ x z)) (* y (sqrt (/ 1 z))))) |
(* z (+ (* -1 (/ x z)) (* y (sqrt (/ 1 z))))) |
(* z (+ (* -1 (/ x z)) (* y (sqrt (/ 1 z))))) |
(* -1 (sqrt (/ 1 z))) |
(/ (+ (* -1 (sqrt z)) (* -1 (/ x y))) z) |
(/ (- (+ (* -1 (sqrt z)) (* -1 (* (/ (pow x 2) (pow y 2)) (sqrt (/ 1 z))))) (/ x y)) z) |
(/ (- (+ (* -1 (sqrt z)) (* -1 (/ (pow x 3) (* (pow y 3) z)))) (+ (* (/ (pow x 2) (pow y 2)) (sqrt (/ 1 z))) (/ x y))) z) |
(* -1 (* y (sqrt z))) |
(+ (* -1 x) (* -1 (* y (sqrt z)))) |
(- (+ (* -1 (* y (sqrt z))) (* -1 (* (/ (pow x 2) y) (sqrt (/ 1 z))))) x) |
(- (+ (* -1 (* y (sqrt z))) (* -1 (/ (pow x 3) (* (pow y 2) z)))) (+ x (* (/ (pow x 2) y) (sqrt (/ 1 z))))) |
(* -1 (* (/ x y) (sqrt (/ 1 z)))) |
(/ (+ (* -1 (* (/ x y) (sqrt z))) (* -1 (/ (pow x 2) (pow y 2)))) z) |
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(+ (* -1 (sqrt (/ 1 z))) (* -1 (/ x (* y z)))) |
(+ (* -1 (sqrt (/ 1 z))) (* -1 (/ (- (* (/ (pow x 2) y) (sqrt (/ 1 (pow z 3)))) (* -1 (/ x z))) y))) |
(+ (* -1 (sqrt (/ 1 z))) (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow x 3) (* y (pow z 2)))) (* (pow x 2) (sqrt (/ 1 (pow z 3))))) y)) (* -1 (/ x z))) y))) |
(* -1 (* y (sqrt z))) |
(* -1 (* y (+ (sqrt z) (/ x y)))) |
(* -1 (* y (+ (sqrt z) (* -1 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt (/ 1 z)))) x) y))))) |
(* -1 (* y (+ (sqrt z) (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) (* y z)) (* -1 (* (pow x 2) (sqrt (/ 1 z))))) y)) x) y))))) |
(* -1 (* (/ x y) (sqrt (/ 1 z)))) |
(* -1 (/ (+ (* x (sqrt (/ 1 z))) (/ (pow x 2) (* y z))) y)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (* (/ (pow x 3) y) (sqrt (/ 1 (pow z 3))))) (/ (pow x 2) z)) y)) (* x (sqrt (/ 1 z)))) y)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (/ (pow x 4) (* y (pow z 2))) (* -1 (* (pow x 3) (sqrt (/ 1 (pow z 3)))))) y)) (/ (pow x 2) z)) y)) (* x (sqrt (/ 1 z)))) y)) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* y (sqrt z)) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* y (sqrt z)) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 (* (pow y 2) z)) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(* (pow y 2) z) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(* y (sqrt z)) |
(- x (* -1 (* y (sqrt z)))) |
(- (* x (+ 1 (* x (+ (* -1 (* (/ 1 y) (sqrt (/ 1 z)))) (* (/ 1 y) (sqrt (/ 1 z))))))) (* -1 (* y (sqrt z)))) |
(- (* x (+ 1 (* x (+ (* -1 (* (/ 1 y) (sqrt (/ 1 z)))) (* (/ 1 y) (sqrt (/ 1 z))))))) (* -1 (* y (sqrt z)))) |
(* y (sqrt z)) |
(- x (* -1 (* y (sqrt z)))) |
(- (* x (+ 1 (* (/ x y) (sqrt (/ 1 z))))) (* -1 (* y (sqrt z)))) |
(- (* x (+ 1 (* x (+ (* (/ 1 y) (sqrt (/ 1 z))) (/ x (* (pow y 2) z)))))) (* -1 (* y (sqrt z)))) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 (* y (sqrt z))) (* x (+ 1/2 (* 1/2 (* x (+ (* -1 (* (/ 1 y) (sqrt (/ 1 z)))) (* (/ 1 y) (sqrt (/ 1 z))))))))) |
(+ (* 1/2 (* y (sqrt z))) (* x (+ 1/2 (* 1/2 (* x (+ (* -1 (* (/ 1 y) (sqrt (/ 1 z)))) (* (/ 1 y) (sqrt (/ 1 z))))))))) |
(* y (sqrt z)) |
(+ (* -1 x) (* y (sqrt z))) |
(+ (* -1 x) (* y (sqrt z))) |
(+ (* -1 x) (* y (sqrt z))) |
(* -1 (sqrt (/ 1 z))) |
(+ (* -1 (sqrt (/ 1 z))) (* -1 (/ x (* y z)))) |
(+ (* -1 (sqrt (/ 1 z))) (* x (- (* -1 (* (/ x (pow y 2)) (sqrt (/ 1 (pow z 3))))) (/ 1 (* y z))))) |
(+ (* -1 (sqrt (/ 1 z))) (* x (- (* x (- (* -1 (/ x (* (pow y 3) (pow z 2)))) (* (/ 1 (pow y 2)) (sqrt (/ 1 (pow z 3)))))) (/ 1 (* y z))))) |
(* -1 (* y (sqrt z))) |
(+ (* -1 x) (* -1 (* y (sqrt z)))) |
(+ (* -1 (* y (sqrt z))) (* x (- (* -1 (* (/ x y) (sqrt (/ 1 z)))) 1))) |
(+ (* -1 (* y (sqrt z))) (* x (- (* x (- (* -1 (/ x (* (pow y 2) z))) (* (/ 1 y) (sqrt (/ 1 z))))) 1))) |
(* -1 (* (/ x y) (sqrt (/ 1 z)))) |
(* x (+ (* -1 (* (/ 1 y) (sqrt (/ 1 z)))) (* -1 (/ x (* (pow y 2) z))))) |
(* x (+ (* -1 (* (/ 1 y) (sqrt (/ 1 z)))) (* x (- (* -1 (* (/ x (pow y 3)) (sqrt (/ 1 (pow z 3))))) (/ 1 (* (pow y 2) z)))))) |
(* x (+ (* -1 (* (/ 1 y) (sqrt (/ 1 z)))) (* x (- (* x (- (* -1 (/ x (* (pow y 4) (pow z 2)))) (* (/ 1 (pow y 3)) (sqrt (/ 1 (pow z 3)))))) (/ 1 (* (pow y 2) z)))))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* -1 (pow x 2)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (- (+ 1 (* -1 (/ (+ (* -1 (* (pow y 2) z)) (* (pow y 2) z)) (pow x 2)))) (* -1 (* (/ y x) (sqrt z))))) |
(* x (- (+ 1 (* -1 (/ (+ (* -1 (* (pow y 2) z)) (* (pow y 2) z)) (pow x 2)))) (* -1 (* (/ y x) (sqrt z))))) |
(* -1 (/ (* (pow y 2) z) x)) |
(/ (- (* -1 (* (/ (pow y 3) x) (sqrt (pow z 3)))) (* (pow y 2) z)) x) |
(/ (- (+ (* -1 (* (/ (pow y 3) x) (sqrt (pow z 3)))) (* -1 (/ (* (pow y 4) (pow z 2)) (pow x 2)))) (* (pow y 2) z)) x) |
(/ (- (+ (* -1 (* (/ (pow y 3) x) (sqrt (pow z 3)))) (+ (* -1 (* (/ (pow y 5) (pow x 3)) (sqrt (pow z 5)))) (* -1 (/ (* (pow y 4) (pow z 2)) (pow x 2))))) (* (pow y 2) z)) x) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (+ (* -1/2 (/ (+ (* -1 (* (pow y 2) z)) (* (pow y 2) z)) (pow x 2))) (* 1/2 (* (/ y x) (sqrt z)))))) |
(* x (+ 1/2 (+ (* -1/2 (/ (+ (* -1 (* (pow y 2) z)) (* (pow y 2) z)) (pow x 2))) (* 1/2 (* (/ y x) (sqrt z)))))) |
(* -1 x) |
(* x (- (* (/ y x) (sqrt z)) 1)) |
(* x (- (* (/ y x) (sqrt z)) 1)) |
(* x (- (* (/ y x) (sqrt z)) 1)) |
(/ y x) |
(/ (+ y (* (/ (pow y 2) x) (sqrt z))) x) |
(/ (- (+ y (/ (* (pow y 3) z) (pow x 2))) (* -1 (* (/ (pow y 2) x) (sqrt z)))) x) |
(/ (- (+ y (* (/ (pow y 4) (pow x 3)) (sqrt (pow z 3)))) (+ (* -1 (* (/ (pow y 2) x) (sqrt z))) (* -1 (/ (* (pow y 3) z) (pow x 2))))) x) |
(/ (* (pow y 2) z) x) |
(/ (+ (* (/ (pow y 3) x) (sqrt (pow z 3))) (* (pow y 2) z)) x) |
(/ (- (+ (* (pow y 2) z) (/ (* (pow y 4) (pow z 2)) (pow x 2))) (* -1 (* (/ (pow y 3) x) (sqrt (pow z 3))))) x) |
(/ (- (+ (* (/ (pow y 5) (pow x 3)) (sqrt (pow z 5))) (* (pow y 2) z)) (+ (* -1 (* (/ (pow y 3) x) (sqrt (pow z 3)))) (* -1 (/ (* (pow y 4) (pow z 2)) (pow x 2))))) x) |
1 |
(+ 1 (* (/ y x) (sqrt z))) |
(- (+ 1 (/ (* (pow y 2) z) (pow x 2))) (* -1 (* (/ y x) (sqrt z)))) |
(- (+ 1 (* (/ (pow y 3) (pow x 3)) (sqrt (pow z 3)))) (+ (* -1 (* (/ y x) (sqrt z))) (* -1 (/ (* (pow y 2) z) (pow x 2))))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* -1 (pow x 2)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (/ (* (pow y 2) z) x)) |
(* -1 (/ (- (* (/ (pow y 3) x) (sqrt (pow z 3))) (* -1 (* (pow y 2) z))) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (* (pow y 4) (pow z 2)) x)) (* (pow y 3) (sqrt (pow z 3)))) x)) (* -1 (* (pow y 2) z))) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* (/ (pow y 5) x) (sqrt (pow z 5))) (* -1 (* (pow y 4) (pow z 2)))) x)) (* (pow y 3) (sqrt (pow z 3)))) x)) (* -1 (* (pow y 2) z))) x)) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 x) |
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) |
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) |
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) |
(/ y x) |
(* -1 (/ (+ (* -1 y) (* -1 (* (/ (pow y 2) x) (sqrt z)))) x)) |
(* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* (pow y 2) (sqrt z)) (/ (* (pow y 3) z) x)) x))) x)) |
(* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (/ (pow y 4) x) (sqrt (pow z 3)))) (* -1 (* (pow y 3) z))) x)) (* (pow y 2) (sqrt z))) x))) x)) |
(/ (* (pow y 2) z) x) |
(* -1 (/ (+ (* -1 (* (/ (pow y 3) x) (sqrt (pow z 3)))) (* -1 (* (pow y 2) z))) x)) |
(* -1 (/ (+ (* -1 (* (pow y 2) z)) (* -1 (/ (+ (* (pow y 3) (sqrt (pow z 3))) (/ (* (pow y 4) (pow z 2)) x)) x))) x)) |
(* -1 (/ (+ (* -1 (* (pow y 2) z)) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (/ (pow y 5) x) (sqrt (pow z 5)))) (* -1 (* (pow y 4) (pow z 2)))) x)) (* (pow y 3) (sqrt (pow z 3)))) x))) x)) |
1 |
(+ 1 (* (/ y x) (sqrt z))) |
(+ 1 (* -1 (/ (- (* -1 (/ (* (pow y 2) z) x)) (* y (sqrt z))) x))) |
(+ 1 (* -1 (/ (- (* -1 (/ (- (* (/ (pow y 3) x) (sqrt (pow z 3))) (* -1 (* (pow y 2) z))) x)) (* y (sqrt z))) x))) |
| Outputs |
|---|
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) |
(/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) |
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x)))) |
(fma.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) (/.f64 z (-.f64 (*.f64 (sqrt.f64 z) y) x)) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x))) |
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x)))) |
(fma.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) (/.f64 z (-.f64 (*.f64 (sqrt.f64 z) y) x)) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x))) |
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x)))) |
(fma.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) (/.f64 z (-.f64 (*.f64 (sqrt.f64 z) y) x)) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x))) |
(* -1/2 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/2 binary64)) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(fma.f64 (*.f64 (*.f64 y y) z) #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(fma.f64 (*.f64 (*.f64 y y) z) #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(fma.f64 (*.f64 (*.f64 y y) z) #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) |
(* -1 (pow x 2)) |
(*.f64 (neg.f64 x) x) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(fma.f64 (neg.f64 x) x (*.f64 (*.f64 y y) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(fma.f64 (neg.f64 x) x (*.f64 (*.f64 y y) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(fma.f64 (neg.f64 x) x (*.f64 (*.f64 y y) z)) |
(/ (pow x 2) (- x (* y (sqrt z)))) |
(/.f64 (*.f64 x x) (-.f64 x (*.f64 (sqrt.f64 z) y))) |
(+ (* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (/ (pow x 2) (- x (* y (sqrt z))))) |
(fma.f64 (*.f64 (neg.f64 y) y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y))) (/.f64 (*.f64 x x) (-.f64 x (*.f64 (sqrt.f64 z) y)))) |
(+ (* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (/ (pow x 2) (- x (* y (sqrt z))))) |
(fma.f64 (*.f64 (neg.f64 y) y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y))) (/.f64 (*.f64 x x) (-.f64 x (*.f64 (sqrt.f64 z) y)))) |
(+ (* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) (/ (pow x 2) (- x (* y (sqrt z))))) |
(fma.f64 (*.f64 (neg.f64 y) y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y))) (/.f64 (*.f64 x x) (-.f64 x (*.f64 (sqrt.f64 z) y)))) |
(* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) |
(*.f64 (*.f64 (neg.f64 y) y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y)))) |
(* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) |
(*.f64 (*.f64 (neg.f64 y) y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y)))) |
(* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) |
(*.f64 (*.f64 (neg.f64 y) y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y)))) |
(* -1 (/ (* (pow y 2) z) (- x (* y (sqrt z))))) |
(*.f64 (*.f64 (neg.f64 y) y) (/.f64 z (-.f64 x (*.f64 (sqrt.f64 z) y)))) |
(* 1/2 (/ (pow x 2) (- x (* y (sqrt z))))) |
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(*.f64 x #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (neg.f64 x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) #s(literal -1/2 binary64))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (neg.f64 x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) #s(literal -1/2 binary64))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (neg.f64 x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) #s(literal -1/2 binary64))) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (neg.f64 x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) #s(literal -1/2 binary64))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (neg.f64 x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) #s(literal -1/2 binary64))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (neg.f64 x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) #s(literal -1/2 binary64))) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (neg.f64 y) x) (sqrt.f64 z) #s(literal -1 binary64))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (neg.f64 y) x) (sqrt.f64 z) #s(literal -1 binary64))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (neg.f64 y) x) (sqrt.f64 z) #s(literal -1 binary64))) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (neg.f64 x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) #s(literal -1/2 binary64))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (neg.f64 x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) #s(literal -1/2 binary64))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (neg.f64 x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) #s(literal -1/2 binary64))) |
(* -1/2 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/2 binary64)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(*.f64 (*.f64 (fma.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) (/.f64 z (*.f64 x x)) #s(literal -1/2 binary64)) x) x) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(*.f64 (*.f64 (fma.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) (/.f64 z (*.f64 x x)) #s(literal -1/2 binary64)) x) x) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(*.f64 (*.f64 (fma.f64 (*.f64 (*.f64 y y) #s(literal 1/2 binary64)) (/.f64 z (*.f64 x x)) #s(literal -1/2 binary64)) x) x) |
(* -1 (pow x 2)) |
(*.f64 (neg.f64 x) x) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(*.f64 (*.f64 (fma.f64 (*.f64 y y) (/.f64 z (*.f64 x x)) #s(literal -1 binary64)) x) x) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(*.f64 (*.f64 (fma.f64 (*.f64 y y) (/.f64 z (*.f64 x x)) #s(literal -1 binary64)) x) x) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(*.f64 (*.f64 (fma.f64 (*.f64 y y) (/.f64 z (*.f64 x x)) #s(literal -1 binary64)) x) x) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (neg.f64 y) x) (sqrt.f64 z) #s(literal -1 binary64))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (neg.f64 y) x) (sqrt.f64 z) #s(literal -1 binary64))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (neg.f64 y) x) (sqrt.f64 z) #s(literal -1 binary64))) |
(* -1 (/ (* (pow y 2) z) x)) |
(*.f64 (*.f64 (neg.f64 y) y) (/.f64 z x)) |
(* -1 (/ (- (* (/ (pow y 3) x) (sqrt (pow z 3))) (* -1 (* (pow y 2) z))) x)) |
(/.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) x) (sqrt.f64 (pow.f64 z #s(literal 3 binary64))) (*.f64 (*.f64 y y) z)) (neg.f64 x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (* (pow y 4) (pow z 2)) x)) (* (pow y 3) (sqrt (pow z 3)))) x)) (* -1 (* (pow y 2) z))) x)) |
(/.f64 (fma.f64 (*.f64 y y) z (/.f64 (neg.f64 (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 (*.f64 z z) x) (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (neg.f64 x))) (neg.f64 x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* (/ (pow y 5) x) (sqrt (pow z 5))) (* -1 (* (pow y 4) (pow z 2)))) x)) (* (pow y 3) (sqrt (pow z 3)))) x)) (* -1 (* (pow y 2) z))) x)) |
(/.f64 (fma.f64 (/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 5 binary64)) x) (sqrt.f64 (pow.f64 z #s(literal 5 binary64))) (*.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) z) z)) (neg.f64 x)) (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64)))) x) #s(literal -1 binary64) (*.f64 (*.f64 y y) z)) (neg.f64 x)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (neg.f64 x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) #s(literal -1/2 binary64))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (neg.f64 x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) #s(literal -1/2 binary64))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (neg.f64 x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) #s(literal -1/2 binary64))) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) |
(*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 z) y) x))) |
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) |
(*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 z) y) x))) |
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) |
(*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 z) y) x))) |
(/ y x) |
(/.f64 y x) |
(* -1 (/ (+ (* -1 y) (* -1 (* (/ (pow y 2) x) (sqrt z)))) x)) |
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (*.f64 y y) x) (sqrt.f64 z) y)) x) |
(* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* (pow y 2) (sqrt z)) (/ (* (pow y 3) z) x)) x))) x)) |
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 y (/.f64 (fma.f64 (*.f64 (sqrt.f64 z) y) y (/.f64 (*.f64 (pow.f64 y #s(literal 3 binary64)) z) x)) x))) x) |
(* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (/ (pow y 4) x) (sqrt (pow z 3)))) (* -1 (* (pow y 3) z))) x)) (* (pow y 2) (sqrt z))) x))) x)) |
(/.f64 (-.f64 (/.f64 (fma.f64 (*.f64 y y) (sqrt.f64 z) (/.f64 (neg.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) z (*.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) x) (sqrt.f64 (pow.f64 z #s(literal 3 binary64)))))) (neg.f64 x))) (neg.f64 x)) y) (neg.f64 x)) |
(/ (* (pow y 2) z) x) |
(/.f64 (*.f64 (*.f64 y y) z) x) |
(* -1 (/ (+ (* -1 (* (/ (pow y 3) x) (sqrt (pow z 3)))) (* -1 (* (pow y 2) z))) x)) |
(/.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) x) (sqrt.f64 (pow.f64 z #s(literal 3 binary64))) (*.f64 (*.f64 y y) z)) x) |
(* -1 (/ (+ (* -1 (* (pow y 2) z)) (* -1 (/ (+ (* (pow y 3) (sqrt (pow z 3))) (/ (* (pow y 4) (pow z 2)) x)) x))) x)) |
(/.f64 (fma.f64 (*.f64 y y) z (/.f64 (neg.f64 (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 (*.f64 z z) x) (*.f64 (sqrt.f64 (pow.f64 z #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) (neg.f64 x))) x) |
(* -1 (/ (+ (* -1 (* (pow y 2) z)) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (/ (pow y 5) x) (sqrt (pow z 5)))) (* -1 (* (pow y 4) (pow z 2)))) x)) (* (pow y 3) (sqrt (pow z 3)))) x))) x)) |
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y y) z (/.f64 (fma.f64 (sqrt.f64 (pow.f64 z #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64)) (/.f64 (neg.f64 (fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) z) z (*.f64 (/.f64 (pow.f64 y #s(literal 5 binary64)) x) (sqrt.f64 (pow.f64 z #s(literal 5 binary64)))))) (neg.f64 x))) x))) x) |
1 |
#s(literal 1 binary64) |
(+ 1 (* (/ y x) (sqrt z))) |
(fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) |
(+ 1 (* -1 (/ (- (* -1 (/ (* (pow y 2) z) x)) (* y (sqrt z))) x))) |
(-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (fma.f64 y (*.f64 y (/.f64 z x)) (*.f64 (sqrt.f64 z) y))) x)) |
(+ 1 (* -1 (/ (- (* -1 (/ (- (* (/ (pow y 3) x) (sqrt (pow z 3))) (* -1 (* (pow y 2) z))) x)) (* y (sqrt z))) x))) |
(+.f64 (/.f64 (+.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) x) (sqrt.f64 (pow.f64 z #s(literal 3 binary64))) (*.f64 (*.f64 y y) z)) x) (*.f64 (sqrt.f64 z) y)) x) #s(literal 1 binary64)) |
| 6 688× | lower-fma.f32 |
| 6 680× | lower-fma.f64 |
| 4 894× | lower-/.f32 |
| 4 886× | lower-/.f64 |
| 4 100× | lower-*.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 37 | 214 |
| 0 | 65 | 157 |
| 1 | 227 | 155 |
| 2 | 1548 | 152 |
| 0 | 8808 | 152 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(fma.f64 (sqrt.f64 z) y x) |
(sqrt.f64 z) |
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(*.f64 z y) |
(/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) |
(*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) |
(fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) |
(fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))))) |
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) |
(neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))) |
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) z)) |
(*.f64 (sqrt.f64 z) y) |
(-.f64 (*.f64 (sqrt.f64 z) y) x) |
(/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))) |
(*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))) |
(/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) |
| Outputs |
|---|
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Compiled 96 289 to 5 545 computations (94.2% saved)
9 alts after pruning (6 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 2 823 | 6 | 2 829 |
| Fresh | 5 | 0 | 5 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 0 | 0 |
| Total | 2 830 | 9 | 2 839 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 53.8% | (/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x)) |
| ▶ | 25.0% | (/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) |
| ▶ | 92.2% | (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) |
| ✓ | 99.8% | (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
| 91.8% | (*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 y (sqrt.f64 z) x)) (fma.f64 y (sqrt.f64 z) x)) (fma.f64 y (sqrt.f64 z) x)) | |
| ▶ | 92.1% | (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) |
| ▶ | 52.2% | (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) |
| ✓ | 95.2% | #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) |
| ✓ | 49.5% | #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) |
Compiled 185 to 146 computations (21.1% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 z y) | |
| cost-diff | 0 | (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) | |
| cost-diff | 0 | (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | (/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x)) | |
| cost-diff | 0 | (*.f64 (*.f64 y y) z) | |
| cost-diff | 0 | #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | (/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) | |
| cost-diff | 0 | (+.f64 (/.f64 x y) (sqrt.f64 z)) | |
| cost-diff | 0 | #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) | |
| cost-diff | 832 | (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) | |
| cost-diff | 0 | (sqrt.f64 z) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 z) y) | |
| cost-diff | 0 | #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | (sqrt.f64 z) | |
| cost-diff | 0 | (/.f64 y (sqrt.f64 z)) | |
| cost-diff | 0 | (fma.f64 (/.f64 y (sqrt.f64 z)) z x) | |
| cost-diff | 0 | (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) |
| 5 074× | lower-fma.f32 |
| 5 070× | lower-fma.f64 |
| 3 326× | lower-*.f32 |
| 3 302× | lower-*.f64 |
| 1 026× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 39 | 266 |
| 0 | 65 | 266 |
| 1 | 99 | 266 |
| 2 | 140 | 266 |
| 3 | 226 | 266 |
| 4 | 419 | 266 |
| 5 | 676 | 260 |
| 6 | 1458 | 260 |
| 7 | 3761 | 260 |
| 8 | 5305 | 260 |
| 9 | 6454 | 260 |
| 10 | 7151 | 260 |
| 11 | 7506 | 260 |
| 12 | 7741 | 260 |
| 0 | 8009 | 253 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) |
(fma.f64 (/.f64 y (sqrt.f64 z)) z x) |
(/.f64 y (sqrt.f64 z)) |
y |
(sqrt.f64 z) |
z |
x |
#s(literal 1/2 binary64) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) |
#s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) |
(*.f64 (sqrt.f64 z) y) |
(sqrt.f64 z) |
z |
y |
#s(literal 1/2 binary64) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) |
#s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) |
(*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) |
(+.f64 (/.f64 x y) (sqrt.f64 z)) |
(/.f64 x y) |
x |
y |
(sqrt.f64 z) |
z |
#s(literal 1/2 binary64) |
(/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) |
(*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) |
#s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) |
(*.f64 (*.f64 y y) z) |
(*.f64 y y) |
y |
z |
#s(literal 1/2 binary64) |
(-.f64 (*.f64 (sqrt.f64 z) y) x) |
(*.f64 (sqrt.f64 z) y) |
(sqrt.f64 z) |
x |
(/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x)) |
(*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) |
(fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) |
(*.f64 z y) |
z |
y |
(*.f64 (neg.f64 x) x) |
(neg.f64 x) |
x |
#s(literal 1/2 binary64) |
(-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x) |
(/.f64 (*.f64 y z) (sqrt.f64 z)) |
(*.f64 y z) |
(sqrt.f64 z) |
| Outputs |
|---|
(*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 y (sqrt.f64 z)) z x)) |
(fma.f64 (/.f64 y (sqrt.f64 z)) z x) |
(/.f64 y (sqrt.f64 z)) |
y |
(sqrt.f64 z) |
z |
x |
#s(literal 1/2 binary64) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) |
#s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) |
(*.f64 (sqrt.f64 z) y) |
(sqrt.f64 z) |
z |
y |
#s(literal 1/2 binary64) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (fma.f64 (sqrt.f64 z) y x)) #s(literal 1/2 binary64)) |
#s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) |
#s(approx (+ (* (sqrt z) y) x) (fma.f64 (sqrt.f64 z) y x)) |
(*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) |
(fma.f64 (sqrt.f64 z) y x) |
(+.f64 (/.f64 x y) (sqrt.f64 z)) |
(/.f64 x y) |
x |
y |
(sqrt.f64 z) |
z |
#s(literal 1/2 binary64) |
(/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (sqrt.f64 z) y) x)) #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 z y) y))) |
(*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) |
(*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 z y) y)) #s(literal 1/2 binary64)) |
#s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) |
#s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 z y) y)) |
(*.f64 (*.f64 y y) z) |
(*.f64 (*.f64 z y) y) |
(*.f64 y y) |
y |
z |
#s(literal 1/2 binary64) |
(-.f64 (*.f64 (sqrt.f64 z) y) x) |
(*.f64 (sqrt.f64 z) y) |
(sqrt.f64 z) |
x |
(/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 y (sqrt.f64 z)) z (neg.f64 x))) (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x))) |
(*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) |
(fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) |
(*.f64 z y) |
z |
y |
(*.f64 (neg.f64 x) x) |
(neg.f64 x) |
x |
#s(literal 1/2 binary64) |
(-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x) |
(fma.f64 (/.f64 y (sqrt.f64 z)) z (neg.f64 x)) |
(/.f64 (*.f64 y z) (sqrt.f64 z)) |
(*.f64 (/.f64 y (sqrt.f64 z)) z) |
(*.f64 y z) |
(*.f64 z y) |
(sqrt.f64 z) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.01171875 | (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x) | |
| accuracy | 1.5820257452111206 | (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) | |
| accuracy | 6.486491170645028 | (/.f64 (*.f64 y z) (sqrt.f64 z)) | |
| accuracy | 28.80863559915213 | (/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x)) | |
| accuracy | 0.23828125 | (*.f64 (sqrt.f64 z) y) | |
| accuracy | 7.4748743680171135 | (*.f64 (*.f64 y y) z) | |
| accuracy | 27.212899386633868 | #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) | |
| accuracy | 28.80863559915213 | (/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) | |
| accuracy | 0 | (sqrt.f64 z) | |
| accuracy | 0 | #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) | |
| accuracy | 0.0078125 | (+.f64 (/.f64 x y) (sqrt.f64 z)) | |
| accuracy | 5.075735930260777 | (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) | |
| accuracy | 0 | (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) | |
| accuracy | 0 | (sqrt.f64 z) | |
| accuracy | 0.23828125 | (*.f64 (sqrt.f64 z) y) | |
| accuracy | 30.49993912766908 | #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) | |
| accuracy | 0 | (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) | |
| accuracy | 0 | (sqrt.f64 z) | |
| accuracy | 0.17578125 | (/.f64 y (sqrt.f64 z)) | |
| accuracy | 4.983146049881451 | (fma.f64 (/.f64 y (sqrt.f64 z)) z x) |
| 68.0ms | 256× | 0 | valid |
Compiled 230 to 31 computations (86.5% saved)
ival-mult: 20.0ms (50.6% of total)ival-div: 10.0ms (25.3% of total)ival-add: 4.0ms (10.1% of total)ival-sub: 2.0ms (5.1% of total)ival-sqrt: 2.0ms (5.1% of total)ival-neg: 1.0ms (2.5% 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 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (/.f64 y (sqrt.f64 z)) z x) (patch (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #<representation binary64>) () ()) |
#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #<representation binary64>) () ()) |
#s(alt (*.f64 (sqrt.f64 z) y) (patch (*.f64 (sqrt.f64 z) y) #<representation binary64>) () ()) |
#s(alt (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) (patch (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #<representation binary64>) () ()) |
#s(alt (+.f64 (/.f64 x y) (sqrt.f64 z)) (patch (+.f64 (/.f64 x y) (sqrt.f64 z)) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) (patch (/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) (patch #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #<representation binary64>) () ()) |
#s(alt (*.f64 (*.f64 y y) z) (patch (*.f64 (*.f64 y y) z) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x)) (patch (/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x)) #<representation binary64>) () ()) |
#s(alt (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) (patch (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #<representation binary64>) () ()) |
#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 y z) (sqrt.f64 z)) (patch (/.f64 (*.f64 y z) (sqrt.f64 z)) #<representation binary64>) () ()) |
#s(alt (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x) (patch (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) (patch (*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (/.f64 y (sqrt.f64 z)) z x) (patch (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (/.f64 y (sqrt.f64 z)) z x) (patch (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (/.f64 y (sqrt.f64 z)) z x) (patch (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (fma.f64 (/.f64 y (sqrt.f64 z)) z x) (patch (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 z) y) (patch (*.f64 (sqrt.f64 z) y) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 z) y) (patch (*.f64 (sqrt.f64 z) y) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 z) y) (patch (*.f64 (sqrt.f64 z) y) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 (sqrt.f64 z) y) (patch (*.f64 (sqrt.f64 z) y) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (sqrt z) (/ x y))) (taylor 0 z) (#s(alt (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) (patch (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (sqrt z) (/ x y))) (taylor 0 z) (#s(alt (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) (patch (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (sqrt z) (/ x y))) (taylor 0 z) (#s(alt (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) (patch (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) #<representation binary64>) () ())) ()) |
#s(alt (* y (+ (sqrt z) (/ x y))) (taylor 0 z) (#s(alt (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) (patch (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt z) (/ x y)) (taylor 0 z) (#s(alt (+.f64 (/.f64 x y) (sqrt.f64 z)) (patch (+.f64 (/.f64 x y) (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt z) (/ x y)) (taylor 0 z) (#s(alt (+.f64 (/.f64 x y) (sqrt.f64 z)) (patch (+.f64 (/.f64 x y) (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt z) (/ x y)) (taylor 0 z) (#s(alt (+.f64 (/.f64 x y) (sqrt.f64 z)) (patch (+.f64 (/.f64 x y) (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sqrt z) (/ x y)) (taylor 0 z) (#s(alt (+.f64 (/.f64 x y) (sqrt.f64 z)) (patch (+.f64 (/.f64 x y) (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (taylor 0 z) (#s(alt (/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) (patch (/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) #<representation binary64>) () ())) ()) |
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9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 7.0ms | z | @ | -inf | ((* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (/ x y) (sqrt z)) y) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (/ x y) (sqrt z)) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* (* y y) z) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (/ (* y z) (sqrt z)) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* z y) (/ (* y z) (sqrt z)) (- (/ (* y z) (sqrt z)) x)) |
| 3.0ms | y | @ | -inf | ((* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (/ x y) (sqrt z)) y) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (/ x y) (sqrt z)) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* (* y y) z) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (/ (* y z) (sqrt z)) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* z y) (/ (* y z) (sqrt z)) (- (/ (* y z) (sqrt z)) x)) |
| 2.0ms | z | @ | 0 | ((* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (/ x y) (sqrt z)) y) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (/ x y) (sqrt z)) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* (* y y) z) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (/ (* y z) (sqrt z)) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* z y) (/ (* y z) (sqrt z)) (- (/ (* y z) (sqrt z)) x)) |
| 2.0ms | y | @ | 0 | ((* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (/ x y) (sqrt z)) y) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (/ x y) (sqrt z)) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* (* y y) z) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (/ (* y z) (sqrt z)) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* z y) (/ (* y z) (sqrt z)) (- (/ (* y z) (sqrt z)) x)) |
| 2.0ms | y | @ | inf | ((* (+ (* (/ y (sqrt z)) z) x) 1/2) (+ (* (/ y (sqrt z)) z) x) (/ y (sqrt z)) (sqrt z) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (* (+ (/ x y) (sqrt z)) y) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (/ x y) (sqrt z)) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (* (sqrt z) y) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* (* y y) z) (/ (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (- (/ (* y z) (sqrt z)) x)) (* (+ (* (* z y) y) (* (neg x) x)) 1/2) (+ (* (* z y) y) (* (neg x) x)) (* z y) (/ (* y z) (sqrt z)) (- (/ (* y z) (sqrt z)) x)) |
| 1× | egg-herbie |
| 7 848× | lower-fma.f64 |
| 7 848× | lower-fma.f32 |
| 5 248× | lower-*.f64 |
| 5 248× | lower-*.f32 |
| 3 290× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 253 | 5866 |
| 1 | 834 | 5663 |
| 2 | 2969 | 5484 |
| 3 | 7096 | 5482 |
| 0 | 8151 | 5203 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) |
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x)))) |
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x)))) |
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x)))) |
(* -1/2 (pow x 2)) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(* -1 (pow x 2)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) |
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x)))) |
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x)))) |
(+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x)))) |
(* -1/2 (pow x 2)) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(* -1 (pow x 2)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(* y z) |
(* y z) |
(* y z) |
(* y z) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(- (* y (sqrt z)) x) |
(- (* y (sqrt z)) x) |
(- (* y (sqrt z)) x) |
(- (* y (sqrt z)) x) |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* y (sqrt z)) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* y (sqrt z)) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* y (sqrt z)) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(sqrt z) |
(* z (+ (sqrt (/ 1 z)) (/ x (* y z)))) |
(* z (+ (sqrt (/ 1 z)) (/ x (* y z)))) |
(* z (+ (sqrt (/ 1 z)) (/ x (* y z)))) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 (* y (sqrt z))) (* 1/2 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z))) z))) |
(+ (* 1/2 (* y (sqrt z))) (+ (* 1/2 (* (/ (* x (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z)))) y) (sqrt (/ 1 (pow z 3))))) (* 1/2 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z))) z)))) |
(+ (* 1/2 (* y (sqrt z))) (+ (* 1/2 (* (/ (* x (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z)))) y) (sqrt (/ 1 (pow z 3))))) (+ (* 1/2 (/ (* (pow x 2) (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z)))) (* (pow y 2) (pow z 2)))) (* 1/2 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z))) z))))) |
(* 1/2 (* (pow y 2) z)) |
(* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2)))) |
(* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2)))) |
(* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2)))) |
(* (pow y 2) z) |
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2))) |
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2))) |
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2))) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 (* y (sqrt z))) (* 1/2 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z))) z))) |
(+ (* 1/2 (* y (sqrt z))) (+ (* 1/2 (* (/ (* x (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z)))) y) (sqrt (/ 1 (pow z 3))))) (* 1/2 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z))) z)))) |
(+ (* 1/2 (* y (sqrt z))) (+ (* 1/2 (* (/ (* x (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z)))) y) (sqrt (/ 1 (pow z 3))))) (+ (* 1/2 (/ (* (pow x 2) (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z)))) (* (pow y 2) (pow z 2)))) (* 1/2 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (* x z))) z))))) |
(* 1/2 (* (pow y 2) z)) |
(* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2)))) |
(* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2)))) |
(* z (+ (* -1/2 (/ (pow x 2) z)) (* 1/2 (pow y 2)))) |
(* (pow y 2) z) |
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2))) |
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2))) |
(* z (+ (* -1 (/ (pow x 2) z)) (pow y 2))) |
(* y z) |
(* y z) |
(* y z) |
(* y z) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* z (+ (* -1 (/ x z)) (* y (sqrt (/ 1 z))))) |
(* z (+ (* -1 (/ x z)) (* y (sqrt (/ 1 z))))) |
(* z (+ (* -1 (/ x z)) (* y (sqrt (/ 1 z))))) |
(* 1/2 (* y (sqrt z))) |
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z))))) |
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z))))) |
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z))))) |
(* y (sqrt z)) |
(* -1 (* z (+ (* -1 (* y (sqrt (/ 1 z)))) (* -1 (/ x z))))) |
(* -1 (* z (+ (* -1 (* y (sqrt (/ 1 z)))) (* -1 (/ x z))))) |
(* -1 (* z (+ (* -1 (* y (sqrt (/ 1 z)))) (* -1 (/ x z))))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))))) |
(* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))))) |
(* -1 (* z (+ (* -1 (/ x (* y z))) (* (sqrt (/ 1 z)) (pow (sqrt -1) 2))))) |
(* -1/2 (* y (sqrt z))) |
(+ (* -1/2 (* y (sqrt z))) (* -1/2 (/ (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (/ (* x z) (pow (sqrt -1) 2)))) z))) |
(+ (* -1 (/ (+ (* -1/2 (* (/ (* x (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (/ (* x z) (pow (sqrt -1) 2))))) y) (sqrt (/ 1 z)))) (* 1/2 (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (/ (* x z) (pow (sqrt -1) 2)))))) z)) (* -1/2 (* y (sqrt z)))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (* (/ (* x (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (/ (* x z) (pow (sqrt -1) 2))))) y) (sqrt z))) (* 1/2 (/ (* (pow x 2) (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (/ (* x z) (pow (sqrt -1) 2))))) (* (pow y 2) (pow (sqrt -1) 2))))) z)) (* 1/2 (- (* -1 (* (/ (pow x 2) y) (sqrt z))) (* -1 (/ (* x z) (pow (sqrt -1) 2)))))) z)) (* -1/2 (* y (sqrt z)))) |
(* 1/2 (* (pow y 2) z)) |
(* -1 (* z (+ (* -1/2 (pow y 2)) (* 1/2 (/ (pow x 2) z))))) |
(* -1 (* z (+ (* -1/2 (pow y 2)) (* 1/2 (/ (pow x 2) z))))) |
(* -1 (* z (+ (* -1/2 (pow y 2)) (* 1/2 (/ (pow x 2) z))))) |
(* (pow y 2) z) |
(* -1 (* z (+ (* -1 (pow y 2)) (/ (pow x 2) z)))) |
(* -1 (* z (+ (* -1 (pow y 2)) (/ (pow x 2) z)))) |
(* -1 (* z (+ (* -1 (pow y 2)) (/ (pow x 2) z)))) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(+ (* -1/2 (/ (- (* (/ (* (pow x 2) (pow (sqrt -1) 2)) y) (sqrt z)) (* -1 (* x (* z (pow (sqrt -1) 2))))) z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))) |
(+ (* -1 (/ (+ (* 1/2 (* (/ (* x (* (pow (sqrt -1) 2) (- (* (/ (* (pow x 2) (pow (sqrt -1) 2)) y) (sqrt z)) (* -1 (* x (* z (pow (sqrt -1) 2))))))) y) (sqrt (/ 1 z)))) (* 1/2 (- (* (/ (* (pow x 2) (pow (sqrt -1) 2)) y) (sqrt z)) (* -1 (* x (* z (pow (sqrt -1) 2))))))) z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (/ (* x (* (pow (sqrt -1) 2) (- (* (/ (* (pow x 2) (pow (sqrt -1) 2)) y) (sqrt z)) (* -1 (* x (* z (pow (sqrt -1) 2))))))) y) (sqrt z))) (* 1/2 (/ (* (pow x 2) (* (pow (sqrt -1) 2) (- (* (/ (* (pow x 2) (pow (sqrt -1) 2)) y) (sqrt z)) (* -1 (* x (* z (pow (sqrt -1) 2))))))) (pow y 2)))) z)) (* 1/2 (- (* (/ (* (pow x 2) (pow (sqrt -1) 2)) y) (sqrt z)) (* -1 (* x (* z (pow (sqrt -1) 2))))))) z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))) |
(* 1/2 (* (pow y 2) z)) |
(* -1 (* z (+ (* -1/2 (pow y 2)) (* 1/2 (/ (pow x 2) z))))) |
(* -1 (* z (+ (* -1/2 (pow y 2)) (* 1/2 (/ (pow x 2) z))))) |
(* -1 (* z (+ (* -1/2 (pow y 2)) (* 1/2 (/ (pow x 2) z))))) |
(* (pow y 2) z) |
(* -1 (* z (+ (* -1 (pow y 2)) (/ (pow x 2) z)))) |
(* -1 (* z (+ (* -1 (pow y 2)) (/ (pow x 2) z)))) |
(* -1 (* z (+ (* -1 (pow y 2)) (/ (pow x 2) z)))) |
(* y z) |
(* y z) |
(* y z) |
(* y z) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* -1 (* z (+ (* -1 (* y (sqrt (/ 1 z)))) (/ x z)))) |
(* -1 (* z (+ (* -1 (* y (sqrt (/ 1 z)))) (/ x z)))) |
(* -1 (* z (+ (* -1 (* y (sqrt (/ 1 z)))) (/ x z)))) |
(* 1/2 x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
x |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* 1/2 x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
x |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
x |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* 1/2 x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
x |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(/ x y) |
(/ (+ x (* y (sqrt z))) y) |
(/ (+ x (* y (sqrt z))) y) |
(/ (+ x (* y (sqrt z))) y) |
(* 1/2 x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* -1/2 (pow x 2)) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(* -1 (pow x 2)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* 1/2 x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* -1/2 (pow x 2)) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(* -1 (pow x 2)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(* y z) |
(* y z) |
(* y z) |
(* y z) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* -1 x) |
(- (* y (sqrt z)) x) |
(- (* y (sqrt z)) x) |
(- (* y (sqrt z)) x) |
(* 1/2 (* y (sqrt z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (sqrt z)) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* 1/2 (* y (sqrt z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (sqrt z)) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* 1/2 (* y (sqrt z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (sqrt z)) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(* y (+ (sqrt z) (/ x y))) |
(sqrt z) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(* 1/2 (* y (sqrt z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* 1/2 (* (pow y 2) z)) |
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z))) |
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z))) |
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z))) |
(* (pow y 2) z) |
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2))))) |
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2))))) |
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2))))) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* 1/2 (* y (sqrt z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* 1/2 (* (pow y 2) z)) |
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z))) |
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z))) |
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z))) |
(* (pow y 2) z) |
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2))))) |
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2))))) |
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2))))) |
(* y z) |
(* y z) |
(* y z) |
(* y z) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (+ (sqrt z) (* -1 (/ x y)))) |
(* y (+ (sqrt z) (* -1 (/ x y)))) |
(* y (+ (sqrt z) (* -1 (/ x y)))) |
(* 1/2 (* y (sqrt z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* y (sqrt z)) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* 1/2 (* y (sqrt z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* y (sqrt z)) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* 1/2 (* y (sqrt z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* y (sqrt z)) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(sqrt z) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(* 1/2 (* y (sqrt z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* 1/2 (* (pow y 2) z)) |
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z))) |
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z))) |
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z))) |
(* (pow y 2) z) |
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2))))) |
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2))))) |
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2))))) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* (pow y 2) z) |
(* 1/2 (* y (sqrt z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* 1/2 (* (pow y 2) z)) |
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z))) |
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z))) |
(* (pow y 2) (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* 1/2 z))) |
(* (pow y 2) z) |
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2))))) |
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2))))) |
(* (pow y 2) (+ z (* -1 (/ (pow x 2) (pow y 2))))) |
(* y z) |
(* y z) |
(* y z) |
(* y z) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* -1 (* y (+ (* -1 (sqrt z)) (/ x y)))) |
(* -1 (* y (+ (* -1 (sqrt z)) (/ x y)))) |
(* -1 (* y (+ (* -1 (sqrt z)) (/ x y)))) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* y (sqrt z)) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* y (sqrt z)) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* y (sqrt z)) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(sqrt z) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(+ (sqrt z) (/ x y)) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 (* (pow y 2) z)) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(* (pow y 2) z) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(* 1/2 (* (pow y 2) z)) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(* (pow y 2) z) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(* y (sqrt z)) |
(+ (* -1 x) (* y (sqrt z))) |
(+ (* -1 x) (* y (sqrt z))) |
(+ (* -1 x) (* y (sqrt z))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(/ x y) |
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y))) |
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y))) |
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* -1 (pow x 2)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* -1 (pow x 2)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(* -1 x) |
(* x (- (* (/ y x) (sqrt z)) 1)) |
(* x (- (* (/ y x) (sqrt z)) 1)) |
(* x (- (* (/ y x) (sqrt z)) 1)) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(/ x y) |
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y)))) |
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y)))) |
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y)))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* -1 (pow x 2)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(* -1 (pow x 2)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(* -1 x) |
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) |
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) |
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) |
| Outputs |
|---|
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (+ (sqrt z) (/ x y))) |
(*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) |
(* y (+ (sqrt z) (/ x y))) |
(*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) |
(* y (+ (sqrt z) (/ x y))) |
(*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) |
(* y (+ (sqrt z) (/ x y))) |
(*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ (sqrt z) (/ x y)) |
(+.f64 (/.f64 x y) (sqrt.f64 z)) |
(+ (sqrt z) (/ x y)) |
(+.f64 (/.f64 x y) (sqrt.f64 z)) |
(+ (sqrt z) (/ x y)) |
(+.f64 (/.f64 x y) (sqrt.f64 z)) |
(+ (sqrt z) (/ x y)) |
(+.f64 (/.f64 x y) (sqrt.f64 z)) |
(* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) |
(*.f64 (*.f64 #s(literal -1/2 binary64) x) (/.f64 x (-.f64 (*.f64 (sqrt.f64 z) y) x))) |
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(fma.f64 (sqrt.f64 z) y x) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 (* y (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(sqrt z) |
(sqrt.f64 z) |
(+ (sqrt z) (/ x y)) |
(+.f64 (/.f64 x y) (sqrt.f64 z)) |
(+ (sqrt z) (/ x y)) |
(+.f64 (/.f64 x y) (sqrt.f64 z)) |
(+ (sqrt z) (/ x y)) |
(+.f64 (/.f64 x y) (sqrt.f64 z)) |
(* 1/2 (* y (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (* (pow y 2) z)) |
(*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/2 binary64)) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/2 binary64))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/2 binary64))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/2 binary64))) |
(* (pow y 2) z) |
(*.f64 (*.f64 y y) z) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(fma.f64 (neg.f64 x) x (*.f64 (*.f64 y y) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(fma.f64 (neg.f64 x) x (*.f64 (*.f64 y y) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(fma.f64 (neg.f64 x) x (*.f64 (*.f64 y y) z)) |
(* 1/2 (* y (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (* (pow y 2) z)) |
(*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/2 binary64)) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/2 binary64))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/2 binary64))) |
(+ (* -1/2 (pow x 2)) (* 1/2 (* (pow y 2) z))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 y y) z) #s(literal 1/2 binary64))) |
(* (pow y 2) z) |
(*.f64 (*.f64 y y) z) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(fma.f64 (neg.f64 x) x (*.f64 (*.f64 y y) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(fma.f64 (neg.f64 x) x (*.f64 (*.f64 y y) z)) |
(+ (* -1 (pow x 2)) (* (pow y 2) z)) |
(fma.f64 (neg.f64 x) x (*.f64 (*.f64 y y) z)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(+ (* -1 x) (* y (sqrt z))) |
(-.f64 (*.f64 (sqrt.f64 z) y) x) |
(+ (* -1 x) (* y (sqrt z))) |
(-.f64 (*.f64 (sqrt.f64 z) y) x) |
(+ (* -1 x) (* y (sqrt z))) |
(-.f64 (*.f64 (sqrt.f64 z) y) x) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(/ x y) |
(/.f64 x y) |
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y))) |
(+.f64 (/.f64 x y) (sqrt.f64 z)) |
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y))) |
(+.f64 (/.f64 x y) (sqrt.f64 z)) |
(* x (+ (* (/ 1 x) (sqrt z)) (/ 1 y))) |
(+.f64 (/.f64 x y) (sqrt.f64 z)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1/2 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/2 binary64)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(*.f64 (fma.f64 (*.f64 (*.f64 z #s(literal 1/2 binary64)) y) (/.f64 y (*.f64 x x)) #s(literal -1/2 binary64)) (*.f64 x x)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(*.f64 (fma.f64 (*.f64 (*.f64 z #s(literal 1/2 binary64)) y) (/.f64 y (*.f64 x x)) #s(literal -1/2 binary64)) (*.f64 x x)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(*.f64 (fma.f64 (*.f64 (*.f64 z #s(literal 1/2 binary64)) y) (/.f64 y (*.f64 x x)) #s(literal -1/2 binary64)) (*.f64 x x)) |
(* -1 (pow x 2)) |
(*.f64 (neg.f64 x) x) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(*.f64 (fma.f64 (*.f64 y (/.f64 y x)) (/.f64 z x) #s(literal -1 binary64)) (*.f64 x x)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(*.f64 (fma.f64 (*.f64 y (/.f64 y x)) (/.f64 z x) #s(literal -1 binary64)) (*.f64 x x)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(*.f64 (fma.f64 (*.f64 y (/.f64 y x)) (/.f64 z x) #s(literal -1 binary64)) (*.f64 x x)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1/2 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/2 binary64)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(*.f64 (fma.f64 (*.f64 (*.f64 z #s(literal 1/2 binary64)) y) (/.f64 y (*.f64 x x)) #s(literal -1/2 binary64)) (*.f64 x x)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(*.f64 (fma.f64 (*.f64 (*.f64 z #s(literal 1/2 binary64)) y) (/.f64 y (*.f64 x x)) #s(literal -1/2 binary64)) (*.f64 x x)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(*.f64 (fma.f64 (*.f64 (*.f64 z #s(literal 1/2 binary64)) y) (/.f64 y (*.f64 x x)) #s(literal -1/2 binary64)) (*.f64 x x)) |
(* -1 (pow x 2)) |
(*.f64 (neg.f64 x) x) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(*.f64 (fma.f64 (*.f64 y (/.f64 y x)) (/.f64 z x) #s(literal -1 binary64)) (*.f64 x x)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(*.f64 (fma.f64 (*.f64 y (/.f64 y x)) (/.f64 z x) #s(literal -1 binary64)) (*.f64 x x)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(*.f64 (fma.f64 (*.f64 y (/.f64 y x)) (/.f64 z x) #s(literal -1 binary64)) (*.f64 x x)) |
(* -1 x) |
(neg.f64 x) |
(* x (- (* (/ y x) (sqrt z)) 1)) |
(-.f64 (*.f64 (sqrt.f64 z) y) x) |
(* x (- (* (/ y x) (sqrt z)) 1)) |
(-.f64 (*.f64 (sqrt.f64 z) y) x) |
(* x (- (* (/ y x) (sqrt z)) 1)) |
(-.f64 (*.f64 (sqrt.f64 z) y) x) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(/ x y) |
(/.f64 x y) |
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y)))) |
(+.f64 (/.f64 x y) (sqrt.f64 z)) |
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y)))) |
(+.f64 (/.f64 x y) (sqrt.f64 z)) |
(* -1 (* x (- (* -1 (* (/ 1 x) (sqrt z))) (/ 1 y)))) |
(+.f64 (/.f64 x y) (sqrt.f64 z)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1/2 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/2 binary64)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(*.f64 (fma.f64 (*.f64 (*.f64 z #s(literal 1/2 binary64)) y) (/.f64 y (*.f64 x x)) #s(literal -1/2 binary64)) (*.f64 x x)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(*.f64 (fma.f64 (*.f64 (*.f64 z #s(literal 1/2 binary64)) y) (/.f64 y (*.f64 x x)) #s(literal -1/2 binary64)) (*.f64 x x)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(*.f64 (fma.f64 (*.f64 (*.f64 z #s(literal 1/2 binary64)) y) (/.f64 y (*.f64 x x)) #s(literal -1/2 binary64)) (*.f64 x x)) |
(* -1 (pow x 2)) |
(*.f64 (neg.f64 x) x) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(*.f64 (fma.f64 (*.f64 y (/.f64 y x)) (/.f64 z x) #s(literal -1 binary64)) (*.f64 x x)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(*.f64 (fma.f64 (*.f64 y (/.f64 y x)) (/.f64 z x) #s(literal -1 binary64)) (*.f64 x x)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(*.f64 (fma.f64 (*.f64 y (/.f64 y x)) (/.f64 z x) #s(literal -1 binary64)) (*.f64 x x)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1/2 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/2 binary64)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(*.f64 (fma.f64 (*.f64 (*.f64 z #s(literal 1/2 binary64)) y) (/.f64 y (*.f64 x x)) #s(literal -1/2 binary64)) (*.f64 x x)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(*.f64 (fma.f64 (*.f64 (*.f64 z #s(literal 1/2 binary64)) y) (/.f64 y (*.f64 x x)) #s(literal -1/2 binary64)) (*.f64 x x)) |
(* (pow x 2) (- (* 1/2 (/ (* (pow y 2) z) (pow x 2))) 1/2)) |
(*.f64 (fma.f64 (*.f64 (*.f64 z #s(literal 1/2 binary64)) y) (/.f64 y (*.f64 x x)) #s(literal -1/2 binary64)) (*.f64 x x)) |
(* -1 (pow x 2)) |
(*.f64 (neg.f64 x) x) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(*.f64 (fma.f64 (*.f64 y (/.f64 y x)) (/.f64 z x) #s(literal -1 binary64)) (*.f64 x x)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(*.f64 (fma.f64 (*.f64 y (/.f64 y x)) (/.f64 z x) #s(literal -1 binary64)) (*.f64 x x)) |
(* (pow x 2) (- (/ (* (pow y 2) z) (pow x 2)) 1)) |
(*.f64 (fma.f64 (*.f64 y (/.f64 y x)) (/.f64 z x) #s(literal -1 binary64)) (*.f64 x x)) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) |
(-.f64 (*.f64 (sqrt.f64 z) y) x) |
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) |
(-.f64 (*.f64 (sqrt.f64 z) y) x) |
(* -1 (* x (+ 1 (* -1 (* (/ y x) (sqrt z)))))) |
(-.f64 (*.f64 (sqrt.f64 z) y) x) |
| 5 310× | lower-fma.f32 |
| 5 306× | lower-fma.f64 |
| 4 446× | lower-/.f32 |
| 4 436× | lower-/.f64 |
| 4 422× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 39 | 214 |
| 0 | 65 | 201 |
| 1 | 198 | 201 |
| 2 | 1316 | 196 |
| 0 | 9205 | 189 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) |
(fma.f64 (/.f64 y (sqrt.f64 z)) z x) |
(/.f64 y (sqrt.f64 z)) |
(sqrt.f64 z) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) |
#s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) |
(*.f64 (sqrt.f64 z) y) |
(*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) |
#s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) |
(+.f64 (/.f64 x y) (sqrt.f64 z)) |
(/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) |
(*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) |
#s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) |
(*.f64 (*.f64 y y) z) |
(/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x)) |
(*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) |
(fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) |
(*.f64 z y) |
(/.f64 (*.f64 y z) (sqrt.f64 z)) |
(-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x) |
| Outputs |
|---|
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Compiled 35 020 to 3 349 computations (90.4% saved)
8 alts after pruning (3 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 752 | 3 | 1 755 |
| Fresh | 1 | 0 | 1 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 3 | 3 |
| Total | 1 756 | 8 | 1 764 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.8% | (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
| ▶ | 47.8% | (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) |
| ▶ | 47.4% | (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) |
| ▶ | 46.8% | (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) |
| ✓ | 92.1% | (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) |
| ✓ | 52.2% | (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) |
| ✓ | 95.2% | #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) |
| ✓ | 49.5% | #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) |
Compiled 72 to 72 computations (0% saved)
| 1× | egg-herbie |
Found 12 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 z y) | |
| cost-diff | 0 | (/.f64 (*.f64 z y) (sqrt.f64 z)) | |
| cost-diff | 0 | #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) | |
| cost-diff | 320 | (*.f64 z #s(literal 1 binary64)) | |
| cost-diff | 1088 | (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) | |
| cost-diff | 0 | (/.f64 y (sqrt.f64 z)) | |
| cost-diff | 0 | (*.f64 (/.f64 y (sqrt.f64 z)) z) | |
| cost-diff | 0 | #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) |
| 148× | times-frac |
| 116× | lower-*.f32 |
| 108× | lower-*.f64 |
| 90× | lower-/.f32 |
| 80× | lower-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 23 | 152 |
| 0 | 35 | 136 |
| 1 | 54 | 136 |
| 2 | 81 | 136 |
| 3 | 102 | 136 |
| 4 | 123 | 136 |
| 5 | 124 | 136 |
| 6 | 165 | 136 |
| 7 | 235 | 136 |
| 8 | 317 | 136 |
| 9 | 318 | 136 |
| 0 | 318 | 130 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) |
#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) |
(*.f64 (/.f64 y (sqrt.f64 z)) z) |
(/.f64 y (sqrt.f64 z)) |
y |
(sqrt.f64 z) |
z |
#s(literal 1/2 binary64) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) |
#s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) |
#s(literal 1 binary64) |
(/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))) |
(/.f64 (sqrt.f64 z) y) |
(sqrt.f64 z) |
z |
y |
(*.f64 z #s(literal 1 binary64)) |
#s(literal 1/2 binary64) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) |
#s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) |
(/.f64 (*.f64 z y) (sqrt.f64 z)) |
(*.f64 z y) |
z |
y |
(sqrt.f64 z) |
#s(literal 1/2 binary64) |
| Outputs |
|---|
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z))) |
#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) |
(*.f64 (/.f64 y (sqrt.f64 z)) z) |
(/.f64 y (sqrt.f64 z)) |
y |
(sqrt.f64 z) |
z |
#s(literal 1/2 binary64) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z))) |
#s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) |
#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) |
(*.f64 (/.f64 y (sqrt.f64 z)) z) |
#s(literal 1 binary64) |
(/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))) |
(/.f64 (/.f64 (sqrt.f64 z) y) z) |
(/.f64 (sqrt.f64 z) y) |
(sqrt.f64 z) |
z |
y |
(*.f64 z #s(literal 1 binary64)) |
z |
#s(literal 1/2 binary64) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z))) |
#s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) |
#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) |
(/.f64 (*.f64 z y) (sqrt.f64 z)) |
(*.f64 (/.f64 y (sqrt.f64 z)) z) |
(*.f64 z y) |
(*.f64 y z) |
z |
y |
(sqrt.f64 z) |
#s(literal 1/2 binary64) |
Found 12 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (*.f64 z y) | |
| accuracy | 0 | (sqrt.f64 z) | |
| accuracy | 6.486491170645028 | (/.f64 (*.f64 z y) (sqrt.f64 z)) | |
| accuracy | 30.49993912766908 | #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) | |
| accuracy | 0.2421875 | (/.f64 (sqrt.f64 z) y) | |
| accuracy | 0.5019902531452896 | (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) | |
| accuracy | 7.113432028837478 | (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))) | |
| accuracy | 30.49993912766908 | #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) | |
| accuracy | 0 | (sqrt.f64 z) | |
| accuracy | 0.17578125 | (/.f64 y (sqrt.f64 z)) | |
| accuracy | 7.598177951658053 | (*.f64 (/.f64 y (sqrt.f64 z)) z) | |
| accuracy | 30.49993912766908 | #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) |
| 39.0ms | 256× | 0 | valid |
Compiled 104 to 19 computations (81.7% saved)
ival-div: 7.0ms (31% of total)ival-mult: 7.0ms (31% of total)ival-sqrt: 7.0ms (31% of total)ival-add: 1.0ms (4.4% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #<representation binary64>) () ()) |
#s(alt (*.f64 (/.f64 y (sqrt.f64 z)) z) (patch (*.f64 (/.f64 y (sqrt.f64 z)) z) #<representation binary64>) () ()) |
#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) #<representation binary64>) () ()) |
#s(alt (*.f64 z #s(literal 1 binary64)) (patch (*.f64 z #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 z y) (sqrt.f64 z)) (patch (/.f64 (*.f64 z y) (sqrt.f64 z)) #<representation binary64>) () ()) |
#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation binary64>) () ()) |
#s(alt (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))) (patch (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (/.f64 (sqrt.f64 z) y) (patch (/.f64 (sqrt.f64 z) y) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) (patch #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 (/.f64 y (sqrt.f64 z)) z) (patch (*.f64 (/.f64 y (sqrt.f64 z)) z) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 (/.f64 y (sqrt.f64 z)) z) (patch (*.f64 (/.f64 y (sqrt.f64 z)) z) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 (/.f64 y (sqrt.f64 z)) z) (patch (*.f64 (/.f64 y (sqrt.f64 z)) z) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (*.f64 (/.f64 y (sqrt.f64 z)) z) (patch (*.f64 (/.f64 y (sqrt.f64 z)) z) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt z (taylor 0 z) (#s(alt (*.f64 z #s(literal 1 binary64)) (patch (*.f64 z #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt z (taylor 0 z) (#s(alt (*.f64 z #s(literal 1 binary64)) (patch (*.f64 z #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt z (taylor 0 z) (#s(alt (*.f64 z #s(literal 1 binary64)) (patch (*.f64 z #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt z (taylor 0 z) (#s(alt (*.f64 z #s(literal 1 binary64)) (patch (*.f64 z #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
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#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
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#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) (patch (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) (patch #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #<representation binary64>) () ())) ()) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 81.0ms | y | @ | 0 | ((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (/ 1 (/ (/ (sqrt z) y) (* z 1))) (* z 1) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* z y) (sqrt z)) (* z y) (sqrt z) (/ (/ (sqrt z) y) (* z 1)) (/ (sqrt z) y)) |
| 3.0ms | z | @ | -inf | ((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (/ 1 (/ (/ (sqrt z) y) (* z 1))) (* z 1) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* z y) (sqrt z)) (* z y) (sqrt z) (/ (/ (sqrt z) y) (* z 1)) (/ (sqrt z) y)) |
| 2.0ms | y | @ | -inf | ((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (/ 1 (/ (/ (sqrt z) y) (* z 1))) (* z 1) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* z y) (sqrt z)) (* z y) (sqrt z) (/ (/ (sqrt z) y) (* z 1)) (/ (sqrt z) y)) |
| 2.0ms | z | @ | 0 | ((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (/ 1 (/ (/ (sqrt z) y) (* z 1))) (* z 1) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* z y) (sqrt z)) (* z y) (sqrt z) (/ (/ (sqrt z) y) (* z 1)) (/ (sqrt z) y)) |
| 1.0ms | y | @ | inf | ((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (/ 1 (/ (/ (sqrt z) y) (* z 1))) (* z 1) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* z y) (sqrt z)) (* z y) (sqrt z) (/ (/ (sqrt z) y) (* z 1)) (/ (sqrt z) y)) |
| 1× | egg-herbie |
| 4 106× | lower-*.f64 |
| 4 106× | lower-*.f32 |
| 3 286× | lower-fma.f64 |
| 3 286× | lower-fma.f32 |
| 1 958× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 84 | 2454 |
| 1 | 279 | 2358 |
| 2 | 874 | 2358 |
| 3 | 2828 | 2286 |
| 4 | 6247 | 2286 |
| 0 | 8275 | 2118 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
z |
z |
z |
z |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(* 1/2 (+ x (* y (sqrt z)))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y z) |
(* y z) |
(* y z) |
(* y z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt z)) |
(* (/ 1 y) (sqrt z)) |
(* (/ 1 y) (sqrt z)) |
(* (/ 1 y) (sqrt z)) |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
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(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
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(* y (sqrt z)) |
(* y (sqrt z)) |
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(* y (sqrt (/ 1 z))) |
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(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
z |
z |
z |
z |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* y (sqrt z)) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* 1/2 (* y (sqrt z))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(* y (sqrt z)) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y z) |
(* y z) |
(* y z) |
(* y z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(sqrt z) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt z)) |
(* (/ 1 y) (sqrt z)) |
(* (/ 1 y) (sqrt z)) |
(* (/ 1 y) (sqrt z)) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
z |
z |
z |
z |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
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(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y z) |
(* y z) |
(* y z) |
(* y z) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))) |
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))) |
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))) |
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))) |
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt z))) |
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt z))) |
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt z))) |
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt z))) |
(* 1/2 x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
x |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
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(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt (/ 1 z))) |
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(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* 1/2 x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
x |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* 1/2 x) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
x |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y z) |
(* y z) |
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(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt z)) |
(* (/ 1 y) (sqrt z)) |
(* (/ 1 y) (sqrt z)) |
(* (/ 1 y) (sqrt z)) |
(* 1/2 (* y (sqrt z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
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(* y (+ (sqrt z) (/ x y))) |
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(* y (sqrt z)) |
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(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
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(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
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(* 1/2 (* y (sqrt z))) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
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(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
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(* y z) |
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(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(* (/ 1 y) (sqrt (/ 1 z))) |
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(* (/ 1 y) (sqrt z)) |
(* (/ 1 y) (sqrt z)) |
(* 1/2 (* y (sqrt z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* y (sqrt z)) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt z)) |
(* y (sqrt (/ 1 z))) |
(* y (sqrt (/ 1 z))) |
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(* y (sqrt z)) |
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(* y (sqrt z)) |
(* 1/2 (* y (sqrt z))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
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(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
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(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(* y (sqrt z)) |
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(* y z) |
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(* (/ 1 y) (sqrt (/ 1 z))) |
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(* (/ 1 y) (sqrt z)) |
(* (/ 1 y) (sqrt z)) |
(* (/ 1 y) (sqrt z)) |
(* 1/2 (* y (sqrt z))) |
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(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
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(* 1/2 (* y (sqrt z))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
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(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
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(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(+ x (* y (sqrt z))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* 1/2 x) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
| Outputs |
|---|
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
z |
z |
z |
z |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* 1/2 (+ x (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* 1/2 (* y (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
z |
z |
z |
z |
(* 1/2 (* y (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* 1/2 (* y (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* z (+ (* y (sqrt (/ 1 z))) (/ x z))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(sqrt z) |
(sqrt.f64 z) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 (sqrt.f64 z) y) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
z |
z |
z |
z |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 (sqrt.f64 z) y) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) |
(*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)) |
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) |
(*.f64 (sqrt.f64 z) y) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) |
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(sqrt.f64 z) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(sqrt.f64 z) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(sqrt.f64 z) |
(* -1 (* (sqrt z) (pow (sqrt -1) 2))) |
(sqrt.f64 z) |
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt (/ 1 z)))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt z))) |
(/.f64 (sqrt.f64 z) y) |
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt z))) |
(/.f64 (sqrt.f64 z) y) |
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt z))) |
(/.f64 (sqrt.f64 z) y) |
(* -1 (* (/ (pow (sqrt -1) 2) y) (sqrt z))) |
(/.f64 (sqrt.f64 z) y) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
x |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
x |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
x |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* 1/2 (* y (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (+ (sqrt z) (/ x y))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (+ (sqrt z) (/ x y))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (+ (sqrt z) (/ x y))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* 1/2 (* y (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (+ (sqrt z) (/ x y))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (+ (sqrt z) (/ x y))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (+ (sqrt z) (/ x y))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 (* y (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (+ (sqrt z) (/ x y))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (+ (sqrt z) (/ x y))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (+ (sqrt z) (/ x y))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* 1/2 (* y (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt (/ 1 z))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* 1/2 (* y (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 (* y (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) |
(fma.f64 (sqrt.f64 z) y x) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* y z) |
(*.f64 z y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt (/ 1 z))) |
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* (/ 1 y) (sqrt z)) |
(/.f64 (sqrt.f64 z) y) |
(* 1/2 (* y (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 (* y (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 (* y (sqrt z))) |
(*.f64 (*.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* y (sqrt z)) |
(*.f64 (sqrt.f64 z) y) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(+ x (* y (sqrt z))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
x |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* x (+ 1 (* (/ y x) (sqrt z)))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
x |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) |
(fma.f64 (sqrt.f64 z) y x) |
| 3 958× | lower-fma.f64 |
| 3 958× | lower-fma.f32 |
| 3 634× | lower-*.f32 |
| 3 626× | lower-*.f64 |
| 2 688× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 23 | 138 |
| 0 | 35 | 122 |
| 1 | 97 | 122 |
| 2 | 433 | 103 |
| 3 | 3215 | 103 |
| 0 | 8149 | 97 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) |
#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) |
(*.f64 (/.f64 y (sqrt.f64 z)) z) |
(/.f64 y (sqrt.f64 z)) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64)))) |
(*.f64 z #s(literal 1 binary64)) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) |
#s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) |
#s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) |
(/.f64 (*.f64 z y) (sqrt.f64 z)) |
(*.f64 z y) |
(sqrt.f64 z) |
(/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))) |
(/.f64 (sqrt.f64 z) y) |
| Outputs |
|---|
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Compiled 16 474 to 2 741 computations (83.4% saved)
8 alts after pruning (1 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 206 | 1 | 1 207 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 2 | 3 |
| Done | 0 | 5 | 5 |
| Total | 1 207 | 8 | 1 215 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.8% | (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
| ✓ | 47.8% | (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) |
| 52.1% | (*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64)) | |
| ✓ | 46.8% | (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) |
| ✓ | 92.1% | (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) |
| ✓ | 52.2% | (*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) |
| ✓ | 95.2% | #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) |
| ✓ | 49.5% | #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) |
Compiled 334 to 164 computations (50.9% saved)
| Inputs |
|---|
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) |
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y))) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) |
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 z y) (sqrt.f64 z))) #s(literal 1/2 binary64)) |
(*.f64 (fma.f64 (/.f64 y (sqrt.f64 z)) z x) #s(literal 1/2 binary64)) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (+.f64 (/.f64 x y) (sqrt.f64 z)) y)) #s(literal 1/2 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64))) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) (sqrt.f64 z)))) #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)))) |
(/.f64 (*.f64 #s(approx (+ (* (* z y) y) (* (neg x) x)) (*.f64 (*.f64 y y) z)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) |
(/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) x)) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 z) y) (*.f64 z #s(literal 1 binary64))))) #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 (sqrt.f64 z) y) x) (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 z y) y (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 y z) (sqrt.f64 z)) x)) |
(*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 y (sqrt.f64 z) x)) (fma.f64 y (sqrt.f64 z) x)) (fma.f64 y (sqrt.f64 z) x)) |
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))) (neg.f64 (*.f64 (*.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y))))))) |
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (pow.f64 (*.f64 z z) #s(literal 1/4 binary64))))) |
(fma.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 y #s(literal 1/2 binary64))) (*.f64 x #s(literal 1/2 binary64))) |
| Outputs |
|---|
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
7 calls:
| 34.0ms | (*.f64 y (sqrt.f64 z)) |
| 18.0ms | z |
| 7.0ms | (sqrt.f64 z) |
| 7.0ms | y |
| 6.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | x |
| 99.8% | 1 | y |
| 99.8% | 1 | z |
| 99.8% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| 99.8% | 1 | (+.f64 x (*.f64 y (sqrt.f64 z))) |
| 99.8% | 1 | (*.f64 y (sqrt.f64 z)) |
| 99.8% | 1 | (sqrt.f64 z) |
Compiled 25 to 34 computations (-36% saved)
| Inputs |
|---|
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) |
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y))) |
(*.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) |
| Outputs |
|---|
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y))) |
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) |
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y))) |
7 calls:
| 10.0ms | z |
| 2.0ms | (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| 2.0ms | (sqrt.f64 z) |
| 2.0ms | (*.f64 y (sqrt.f64 z)) |
| 2.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 76.1% | 3 | x |
| 75.4% | 3 | y |
| 65.5% | 2 | z |
| 66.1% | 5 | (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| 66.1% | 5 | (+.f64 x (*.f64 y (sqrt.f64 z))) |
| 76.8% | 3 | (*.f64 y (sqrt.f64 z)) |
| 65.5% | 2 | (sqrt.f64 z) |
Compiled 25 to 34 computations (-36% saved)
Total 0.0b remaining (0%)
Threshold costs 0b (0%)
| Inputs |
|---|
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) |
| Outputs |
|---|
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) |
7 calls:
| 4.0ms | (+.f64 x (*.f64 y (sqrt.f64 z))) |
| 1.0ms | (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| 1.0ms | (sqrt.f64 z) |
| 1.0ms | x |
| 1.0ms | z |
| Accuracy | Segments | Branch |
|---|---|---|
| 49.5% | 1 | (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (*.f64 y (sqrt.f64 z)))) |
| 49.5% | 1 | (+.f64 x (*.f64 y (sqrt.f64 z))) |
| 49.5% | 1 | z |
| 49.5% | 1 | (sqrt.f64 z) |
| 49.5% | 1 | y |
| 49.5% | 1 | x |
| 49.5% | 1 | (*.f64 y (sqrt.f64 z)) |
Compiled 25 to 34 computations (-36% saved)
| 2× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 2.109919871678362e-93 | 1.1254345654938374e-89 |
| 0.0ms | -1.7159403214766657e-15 | -6.5161860743525674e-21 |
Compiled 13 to 16 computations (-23.1% saved)
| 1× | egg-herbie |
| 8× | *-commutative-binary64-*.f64 |
| 2× | 1-exp-binary32-exp.f32 |
| 2× | 1-exp-binary64-exp.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 26 | 75 |
| 1 | 33 | 75 |
| 1× | saturated |
| Inputs |
|---|
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(if (<=.f64 (*.f64 y (sqrt.f64 z)) #s(literal -2535301200456459/2535301200456458802993406410752 binary64)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y))) (if (<=.f64 (*.f64 y (sqrt.f64 z)) #s(literal 2348542582773833/587135645693458306972370149197334256843920637227079967676822742883052256278652110865924749596192175757983744 binary64)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y))))) |
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) |
| Outputs |
|---|
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 z) y x)) |
(if (<=.f64 (*.f64 y (sqrt.f64 z)) #s(literal -2535301200456459/2535301200456458802993406410752 binary64)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y))) (if (<=.f64 (*.f64 y (sqrt.f64 z)) #s(literal 2348542582773833/587135645693458306972370149197334256843920637227079967676822742883052256278652110865924749596192175757983744 binary64)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 z) y))))) |
(if (<=.f64 (*.f64 y (sqrt.f64 z)) #s(literal -2535301200456459/2535301200456458802993406410752 binary64)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (*.f64 y (sqrt.f64 z)) #s(literal 1/2 binary64))) (if (<=.f64 (*.f64 y (sqrt.f64 z)) #s(literal 2348542582773833/587135645693458306972370149197334256843920637227079967676822742883052256278652110865924749596192175757983744 binary64)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 (*.f64 y (sqrt.f64 z)) #s(literal 1/2 binary64))))) |
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x)) |
| 7 460× | lower-fma.f64 |
| 7 460× | lower-fma.f32 |
| 5 642× | lower-fma.f64 |
| 5 642× | lower-fma.f32 |
| 4 298× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 10 | 21 |
| 0 | 16 | 21 |
| 1 | 41 | 21 |
| 2 | 234 | 21 |
| 3 | 2001 | 21 |
| 0 | 8162 | 19 |
| 0 | 75 | 646 |
| 1 | 251 | 646 |
| 2 | 797 | 646 |
| 3 | 2298 | 622 |
| 4 | 5069 | 622 |
| 5 | 7549 | 622 |
| 0 | 8141 | 566 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 91 to 50 computations (45.1% saved)
Compiled 106 to 56 computations (47.2% saved)
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