
Time bar (total: 4.9s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 100% | 0% | 0% | 0% | 0% | 0 |
| 100% | 100% | 0% | 0% | 0% | 0% | 0% | 1 |
Compiled 7 to 7 computations (0% saved)
| 1.1s | 8 256× | 0 | valid |
ival-div: 94.0ms (61.9% of total)ival-sub: 42.0ms (27.7% of total)exact: 7.0ms (4.6% of total)ival-true: 6.0ms (4% of total)ival-assert: 3.0ms (2% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | #s(literal 3 binary64) |
| 0 | 0 | - | 0 | - | (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) |
| 0 | 0 | - | 0 | - | (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) |
| 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 |
| 138.0ms | 512× | 0 | valid |
Compiled 32 to 19 computations (40.6% saved)
ival-div: 4.0ms (54% of total)ival-sub: 2.0ms (27% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
| 16× | distribute-lft-neg-in |
| 14× | sub-neg |
| 12× | cancel-sign-sub-inv |
| 10× | associate--r+ |
| 10× | distribute-neg-in |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 9 |
| 1 | 18 | 9 |
| 2 | 39 | 6 |
| 3 | 63 | 6 |
| 4 | 96 | 6 |
| 5 | 104 | 6 |
| 6 | 106 | 6 |
| 0 | 5 | 3 |
| 0 | 8 | 3 |
| 1 | 13 | 3 |
| 2 | 14 | 3 |
| 0 | 14 | 3 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) |
| Outputs |
|---|
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) |
(-.f64 x #s(literal 1/3 binary64)) |
Compiled 6 to 5 computations (16.7% saved)
Compiled 1 to 1 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 100.0% | (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) |
Compiled 6 to 5 computations (16.7% saved)
| 1× | egg-herbie |
Found 2 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) | |
| cost-diff | 704 | (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) |
| 4× | lower-+.f64 |
| 4× | lower-+.f32 |
| 2× | lift-/.f64 |
| 2× | 1-exp |
| 2× | lift--.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 5 | 7 |
| 0 | 8 | 7 |
| 1 | 13 | 7 |
| 2 | 14 | 7 |
| 0 | 14 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) |
x |
(/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) |
#s(literal 1 binary64) |
#s(literal 3 binary64) |
| Outputs |
|---|
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) |
(-.f64 x #s(literal 1/3 binary64)) |
x |
(/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) |
#s(literal 1/3 binary64) |
#s(literal 1 binary64) |
#s(literal 3 binary64) |
Found 2 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) | |
| accuracy | 0.015625 | (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) |
| 8.0ms | 256× | 0 | valid |
Compiled 13 to 7 computations (46.2% saved)
ival-div: 2.0ms (53.5% of total)ival-sub: 1.0ms (26.7% 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 3 binary64)) (patch (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) #<representation binary64>) () ()) |
#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt -1/3 (taylor 0 x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 5.0ms | x | @ | 0 | ((/ 1 3) (- x (/ 1 3))) |
| 1.0ms | x | @ | inf | ((/ 1 3) (- x (/ 1 3))) |
| 0.0ms | x | @ | -inf | ((/ 1 3) (- x (/ 1 3))) |
| 1× | egg-herbie |
| 192× | lower-fma.f64 |
| 192× | lower-fma.f32 |
| 144× | lower-*.f64 |
| 144× | lower-*.f32 |
| 96× | times-frac |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 30 |
| 1 | 32 | 30 |
| 2 | 75 | 30 |
| 3 | 158 | 30 |
| 4 | 412 | 30 |
| 5 | 523 | 30 |
| 6 | 576 | 30 |
| 7 | 599 | 30 |
| 8 | 601 | 30 |
| 0 | 601 | 30 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
-1/3 |
(- x 1/3) |
(- x 1/3) |
(- x 1/3) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
| Outputs |
|---|
-1/3 |
#s(literal -1/3 binary64) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
| 6 912× | lower-fma.f64 |
| 6 912× | lower-fma.f32 |
| 4 474× | lower-*.f64 |
| 4 474× | lower-*.f32 |
| 3 944× | lower-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 5 | 4 |
| 0 | 8 | 4 |
| 1 | 27 | 4 |
| 2 | 129 | 4 |
| 3 | 979 | 4 |
| 0 | 8557 | 4 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) |
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) |
| Outputs |
|---|
#s(literal 1/3 binary64) |
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1/81 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64)))) |
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1/729 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64))))) |
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1/729 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))) |
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal -1/19683 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) (fma.f64 (*.f64 #s(literal 1/27 binary64) (*.f64 x x)) x #s(literal 1/729 binary64))))) |
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))) (+.f64 #s(literal 1/9 binary64) (*.f64 x (-.f64 x #s(literal 1/3 binary64))))) |
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (*.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64))))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (*.f64 (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))) (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x)))) |
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))) (/.f64 #s(literal -1 binary64) (-.f64 x #s(literal -1/3 binary64)))) |
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1/81 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (-.f64 #s(literal -1/3 binary64) x))) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 x #s(literal -1/3 binary64)))) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1/81 binary64)) (/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (neg.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1/81 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1/81 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (*.f64 x (-.f64 x #s(literal 1/3 binary64))))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1/729 binary64)) (/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64)))) (neg.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1/729 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) |
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1/729 binary64)) (*.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1/729 binary64)) (*.f64 (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal -1/19683 binary64)) (*.f64 (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) (fma.f64 (*.f64 #s(literal 1/27 binary64) (*.f64 x x)) x #s(literal 1/729 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal -1/19683 binary64)) (*.f64 (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64)))) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) (fma.f64 (*.f64 #s(literal 1/27 binary64) (*.f64 x x)) x #s(literal 1/729 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal 1/3 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1/81 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (-.f64 x #s(literal -1/3 binary64)))) |
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1/729 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64)))) (-.f64 x #s(literal -1/3 binary64)))) |
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(+.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal -1/9 binary64) (-.f64 x #s(literal -1/3 binary64)))) |
(+.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))))) |
(+.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) |
(+.f64 #s(literal -1/3 binary64) (*.f64 x #s(literal 1 binary64))) |
(+.f64 #s(literal -1/3 binary64) (*.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal -1/3 binary64) x) |
(+.f64 x #s(literal -1/3 binary64)) |
Compiled 10 409 to 757 computations (92.7% saved)
4 alts after pruning (4 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 319 | 4 | 323 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 320 | 4 | 324 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 67.5% | (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) |
| ▶ | 100.0% | (-.f64 x #s(literal 1/3 binary64)) |
| ▶ | 77.0% | (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) |
| ▶ | 49.9% | #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) |
Compiled 32 to 22 computations (31.3% saved)
| 1× | egg-herbie |
Found 10 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) | |
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) | |
| cost-diff | 0 | (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) | |
| cost-diff | 0 | (-.f64 x #s(literal 1/3 binary64)) | |
| cost-diff | 0 | (-.f64 #s(literal -1/3 binary64) x) | |
| cost-diff | 0 | (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) | |
| cost-diff | 0 | (fma.f64 x x #s(literal -1/9 binary64)) | |
| cost-diff | 320 | (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) | |
| cost-diff | 0 | #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) |
| 1 128× | lower-fma.f32 |
| 1 122× | lower-fma.f64 |
| 632× | lower-*.f32 |
| 628× | lower-*.f64 |
| 362× | distribute-rgt-in |
Useful iterations: 5 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 22 | 72 |
| 0 | 33 | 72 |
| 1 | 49 | 70 |
| 2 | 69 | 69 |
| 3 | 102 | 69 |
| 4 | 126 | 69 |
| 5 | 169 | 68 |
| 6 | 326 | 68 |
| 7 | 797 | 68 |
| 8 | 1521 | 68 |
| 9 | 1694 | 68 |
| 10 | 1756 | 68 |
| 11 | 1865 | 68 |
| 12 | 2150 | 68 |
| 13 | 2356 | 68 |
| 14 | 2466 | 68 |
| 15 | 2696 | 68 |
| 16 | 2716 | 68 |
| 17 | 2716 | 68 |
| 0 | 2716 | 68 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) |
#s(literal -1/3 binary64) |
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
x |
#s(literal -1/9 binary64) |
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) |
#s(literal -1 binary64) |
(-.f64 #s(literal -1/3 binary64) x) |
#s(literal -1/3 binary64) |
(-.f64 x #s(literal 1/3 binary64)) |
x |
#s(literal 1/3 binary64) |
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(*.f64 x x) |
x |
#s(literal -1/27 binary64) |
(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) |
(-.f64 x #s(literal -1/3 binary64)) |
#s(literal -1/3 binary64) |
#s(literal 1/9 binary64) |
| Outputs |
|---|
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) |
#s(literal -1/3 binary64) |
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) |
(/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal -1/3 binary64))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
x |
#s(literal -1/9 binary64) |
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) |
#s(literal -1 binary64) |
(-.f64 #s(literal -1/3 binary64) x) |
#s(literal -1/3 binary64) |
(-.f64 x #s(literal 1/3 binary64)) |
x |
#s(literal 1/3 binary64) |
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) |
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(*.f64 x x) |
x |
#s(literal -1/27 binary64) |
(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) |
(fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) |
(-.f64 x #s(literal -1/3 binary64)) |
#s(literal -1/3 binary64) |
#s(literal 1/9 binary64) |
Found 10 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.00390625 | (-.f64 x #s(literal -1/3 binary64)) | |
| accuracy | 0.0234375 | (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) | |
| accuracy | 0.04296875 | (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) | |
| accuracy | 20.3105395498375 | (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) | |
| accuracy | 0.015625 | (-.f64 x #s(literal 1/3 binary64)) | |
| accuracy | 0.00390625 | (fma.f64 x x #s(literal -1/9 binary64)) | |
| accuracy | 0.00390625 | (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) | |
| accuracy | 0.00390625 | (-.f64 #s(literal -1/3 binary64) x) | |
| accuracy | 14.698514384628556 | (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) | |
| accuracy | 32.04278354006126 | #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) |
| 63.0ms | 256× | 0 | valid |
Compiled 80 to 25 computations (68.8% saved)
const: 14.0ms (30% of total)ival-sub: 12.0ms (25.7% of total)ival-mult: 10.0ms (21.4% of total)ival-div: 7.0ms (15% of total)ival-add: 3.0ms (6.4% 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 #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ()) |
#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ()) |
#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ()) |
#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ()) |
#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ()) |
#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt -1/3 (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt -1/3 (taylor 0 x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt -1/9 (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt 3 (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 3 (* -9 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 3 (* x (- (* 27 x) 9))) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ 3 (* x (- (* x (+ 27 (* -81 x))) 9))) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) (patch (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt -1/3 (taylor 0 x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1 x) 1/3) (taylor 0 x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1 x) 1/3) (taylor 0 x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1 x) 1/3) (taylor 0 x) (#s(alt (-.f64 #s(literal -1/3 binary64) x) (patch (-.f64 #s(literal -1/3 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt -1/3 (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt -1/3 (taylor 0 x) (#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt -1/27 (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (pow x 3) 1/27) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (pow x 3) 1/27) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (pow x 3) 1/27) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (patch (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt 1/9 (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/9 (* 1/3 x)) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/9 (* x (+ 1/3 x))) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/9 (* x (+ 1/3 x))) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt 1/3 (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) (patch #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
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#s(alt (* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | x | @ | inf | ((- x (/ 1 3)) (* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (- -1/3 x) (- x 1/3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (* x x) (+ (* x (- x -1/3)) 1/9) (- x -1/3)) |
| 2.0ms | x | @ | -inf | ((- x (/ 1 3)) (* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (- -1/3 x) (- x 1/3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (* x x) (+ (* x (- x -1/3)) 1/9) (- x -1/3)) |
| 2.0ms | x | @ | 0 | ((- x (/ 1 3)) (* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (- -1/3 x) (- x 1/3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (* x x) (+ (* x (- x -1/3)) 1/9) (- x -1/3)) |
| 1× | egg-herbie |
| 8 024× | lower-fma.f64 |
| 8 024× | lower-fma.f32 |
| 3 062× | lower-*.f64 |
| 3 062× | lower-*.f32 |
| 1 470× | div-sub |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 91 | 515 |
| 1 | 257 | 507 |
| 2 | 639 | 490 |
| 3 | 1857 | 486 |
| 4 | 4563 | 486 |
| 0 | 8216 | 464 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
-1/3 |
(- x 1/3) |
(- x 1/3) |
(- x 1/3) |
-1/3 |
(- x 1/3) |
(- x 1/3) |
(- x 1/3) |
-1/9 |
(- (pow x 2) 1/9) |
(- (pow x 2) 1/9) |
(- (pow x 2) 1/9) |
3 |
(+ 3 (* -9 x)) |
(+ 3 (* x (- (* 27 x) 9))) |
(+ 3 (* x (- (* x (+ 27 (* -81 x))) 9))) |
-1/3 |
(- (* -1 x) 1/3) |
(- (* -1 x) 1/3) |
(- (* -1 x) 1/3) |
-1/3 |
(- x 1/3) |
(- x 1/3) |
(- x 1/3) |
-1/3 |
(- x 1/3) |
(- x 1/3) |
(- x 1/3) |
-1/27 |
(- (pow x 3) 1/27) |
(- (pow x 3) 1/27) |
(- (pow x 3) 1/27) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
1/9 |
(+ 1/9 (* 1/3 x)) |
(+ 1/9 (* x (+ 1/3 x))) |
(+ 1/9 (* x (+ 1/3 x))) |
1/3 |
(+ 1/3 x) |
(+ 1/3 x) |
(+ 1/3 x) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(pow x 2) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(/ 1 x) |
(/ (- 1 (* 1/3 (/ 1 x))) x) |
(/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x) |
(/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) |
(* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) |
(* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(pow x 3) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
x |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(pow x 2) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(/ 1 x) |
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x)) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) |
(* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) |
(* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(pow x 3) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
x |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
| Outputs |
|---|
-1/3 |
#s(literal -1/3 binary64) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
-1/3 |
#s(literal -1/3 binary64) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
-1/9 |
#s(literal -1/9 binary64) |
(- (pow x 2) 1/9) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(- (pow x 2) 1/9) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(- (pow x 2) 1/9) |
(fma.f64 x x #s(literal -1/9 binary64)) |
3 |
#s(literal 3 binary64) |
(+ 3 (* -9 x)) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(+ 3 (* x (- (* 27 x) 9))) |
(fma.f64 (fma.f64 #s(literal 27 binary64) x #s(literal -9 binary64)) x #s(literal 3 binary64)) |
(+ 3 (* x (- (* x (+ 27 (* -81 x))) 9))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -81 binary64) x #s(literal 27 binary64)) x #s(literal -9 binary64)) x #s(literal 3 binary64)) |
-1/3 |
#s(literal -1/3 binary64) |
(- (* -1 x) 1/3) |
(-.f64 #s(literal -1/3 binary64) x) |
(- (* -1 x) 1/3) |
(-.f64 #s(literal -1/3 binary64) x) |
(- (* -1 x) 1/3) |
(-.f64 #s(literal -1/3 binary64) x) |
-1/3 |
#s(literal -1/3 binary64) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
-1/3 |
#s(literal -1/3 binary64) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
-1/27 |
#s(literal -1/27 binary64) |
(- (pow x 3) 1/27) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(- (pow x 3) 1/27) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(- (pow x 3) 1/27) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
1/9 |
#s(literal 1/9 binary64) |
(+ 1/9 (* 1/3 x)) |
(fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) |
(+ 1/9 (* x (+ 1/3 x))) |
(fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) |
(+ 1/9 (* x (+ 1/3 x))) |
(fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) |
1/3 |
#s(literal 1/3 binary64) |
(+ 1/3 x) |
(-.f64 x #s(literal -1/3 binary64)) |
(+ 1/3 x) |
(-.f64 x #s(literal -1/3 binary64)) |
(+ 1/3 x) |
(-.f64 x #s(literal -1/3 binary64)) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ (- 1 (* 1/3 (/ 1 x))) x) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 #s(literal 1/3 binary64) x)) |
(/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/9 binary64) x)) x)) |
(/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x) #s(literal -1/3 binary64)) x)) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) |
(-.f64 #s(literal -1/3 binary64) x) |
(* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) |
(-.f64 #s(literal -1/3 binary64) x) |
(* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) |
(-.f64 #s(literal -1/3 binary64) x) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(pow x 3) |
(*.f64 (*.f64 x x) x) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) |
(*.f64 (-.f64 x #s(literal -1/3 binary64)) x) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) |
x |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal -1/3 binary64)) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal -1/3 binary64)) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal -1/3 binary64)) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x)) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 #s(literal 1/3 binary64) x)) |
(* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x)) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/9 binary64) x)) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x)) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x) #s(literal -1/3 binary64)) x)) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) |
(-.f64 #s(literal -1/3 binary64) x) |
(* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) |
(-.f64 #s(literal -1/3 binary64) x) |
(* -1 (* x (+ 1 (* 1/3 (/ 1 x))))) |
(-.f64 #s(literal -1/3 binary64) x) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(pow x 3) |
(*.f64 (*.f64 x x) x) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) |
(*.f64 (-.f64 x #s(literal -1/3 binary64)) x) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) |
x |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal -1/3 binary64)) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal -1/3 binary64)) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal -1/3 binary64)) |
| 5 516× | lower-fma.f32 |
| 5 510× | lower-fma.f64 |
| 4 694× | lower-*.f32 |
| 4 690× | lower-*.f64 |
| 3 668× | lower-/.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 22 | 61 |
| 0 | 33 | 64 |
| 1 | 131 | 61 |
| 2 | 898 | 43 |
| 0 | 9142 | 43 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) |
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) |
(-.f64 #s(literal -1/3 binary64) x) |
(-.f64 x #s(literal 1/3 binary64)) |
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(*.f64 x x) |
(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) |
(-.f64 x #s(literal -1/3 binary64)) |
| Outputs |
|---|
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) |
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(/.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 (neg.f64 x) x #s(literal -1/9 binary64)) (-.f64 x #s(literal 1/3 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal 1/19683 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x (+.f64 #s(literal 1/729 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal -1/27 binary64)))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) |
(/.f64 (*.f64 (-.f64 #s(literal 1/81 binary64) (*.f64 (*.f64 (*.f64 x x) x) x)) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal -1/9 binary64) (*.f64 x x)) (-.f64 x #s(literal 1/3 binary64)))) |
(/.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64))) #s(literal 1 binary64)) (*.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (-.f64 #s(literal 1/81 binary64) (*.f64 (*.f64 x x) #s(literal -1/9 binary64))))) (-.f64 x #s(literal 1/3 binary64)))) |
(/.f64 (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (neg.f64 x) x #s(literal 1/9 binary64))) (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (+.f64 (neg.f64 x) #s(literal 1/3 binary64)))) |
(/.f64 (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (neg.f64 x) (*.f64 x x) #s(literal -1/27 binary64))) (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (neg.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))) |
(/.f64 (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x x #s(literal -1/9 binary64))) (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal 1/3 binary64)))) |
(/.f64 (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))) (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x #s(literal 1/3 binary64))) (*.f64 (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (*.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) #s(literal -1/27 binary64))) (*.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) |
(/.f64 (fma.f64 (neg.f64 x) x #s(literal 1/9 binary64)) (-.f64 #s(literal 1/3 binary64) x)) |
(/.f64 (fma.f64 (neg.f64 x) x #s(literal 1/9 binary64)) (+.f64 (neg.f64 x) #s(literal 1/3 binary64))) |
(/.f64 (fma.f64 (neg.f64 x) (*.f64 x x) #s(literal -1/27 binary64)) (neg.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) |
(/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (-.f64 x #s(literal 1/3 binary64))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (-.f64 x #s(literal 1/3 binary64)))) |
(/.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal 1 binary64)) |
(/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (neg.f64 (neg.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))) |
(/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) (*.f64 (+.f64 #s(literal 1/81 binary64) (*.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)))) (-.f64 x #s(literal 1/3 binary64)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (-.f64 #s(literal 1/81 binary64) (*.f64 (*.f64 x x) #s(literal -1/9 binary64)))) (-.f64 x #s(literal 1/3 binary64)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) (*.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) |
(/.f64 (-.f64 #s(literal -1/3 binary64) x) #s(literal -1 binary64)) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 x #s(literal -1/3 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) |
(neg.f64 (-.f64 #s(literal -1/3 binary64) x)) |
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) #s(literal 1/3 binary64)) |
(fma.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 x (-.f64 x #s(literal 1/3 binary64))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))))) |
(fma.f64 (/.f64 x (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))) (/.f64 x (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))))) |
(fma.f64 (/.f64 x (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (/.f64 x (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal -1/3 binary64) x) x #s(literal -1/9 binary64)))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))))) |
(fma.f64 (/.f64 x (fma.f64 x x #s(literal -1/9 binary64))) (*.f64 (-.f64 x #s(literal -1/3 binary64)) x) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))))) |
(fma.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (fma.f64 x x #s(literal 1/9 binary64)) (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (*.f64 #s(literal 1/3 binary64) x))) |
(fma.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (*.f64 x x))) |
(fma.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (*.f64 x x) (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))) |
(fma.f64 (fma.f64 x x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (*.f64 (*.f64 #s(literal 1/3 binary64) x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))))) |
(fma.f64 (neg.f64 x) #s(literal -1 binary64) #s(literal 1/3 binary64)) |
(fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (*.f64 (*.f64 x x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))))) |
(fma.f64 (*.f64 (*.f64 x x) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))) |
(fma.f64 (*.f64 x x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (*.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))))) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))))) |
(fma.f64 #s(literal -1 binary64) (neg.f64 x) #s(literal 1/3 binary64)) |
(fma.f64 #s(literal 1 binary64) x #s(literal 1/3 binary64)) |
(fma.f64 x #s(literal 1 binary64) #s(literal 1/3 binary64)) |
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (fma.f64 x x #s(literal 1/9 binary64))) (-.f64 x #s(literal 1/3 binary64))) (/.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (-.f64 x #s(literal 1/3 binary64)))) |
(-.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 (neg.f64 x) #s(literal 1/3 binary64))) (/.f64 (*.f64 x x) (+.f64 (neg.f64 x) #s(literal 1/3 binary64)))) |
(-.f64 (/.f64 #s(literal -1/27 binary64) (neg.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 (*.f64 (*.f64 x x) x) (neg.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))) |
(-.f64 (/.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))) #s(literal -1 binary64)) (/.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 1/3 binary64))) #s(literal -1 binary64))) |
(-.f64 (/.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #s(literal -1 binary64)) (/.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #s(literal -1 binary64))) |
(-.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64)))) |
(-.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) |
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/3 binary64) x)) |
(-.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) |
(-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1 binary64))) |
(-.f64 #s(literal 1/3 binary64) (neg.f64 x)) |
(-.f64 x #s(literal -1/3 binary64)) |
(+.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64)))) (/.f64 (*.f64 x x) (-.f64 x #s(literal 1/3 binary64)))) |
(+.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) |
(+.f64 (*.f64 (fma.f64 x x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (*.f64 (*.f64 #s(literal 1/3 binary64) x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))))) |
(+.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (*.f64 (*.f64 x x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))))) |
(+.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (*.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))))) |
(+.f64 (*.f64 x #s(literal 1 binary64)) #s(literal 1/3 binary64)) |
(+.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) #s(literal 1/3 binary64)) |
(+.f64 (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (fma.f64 x x #s(literal 1/9 binary64))) (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (*.f64 #s(literal 1/3 binary64) x))) |
(+.f64 (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64))) (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (*.f64 x x))) |
(+.f64 (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (*.f64 x x)) (*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)))) |
(+.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 1/3 binary64))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))))) |
(+.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))) |
(+.f64 #s(literal 0 binary64) (-.f64 x #s(literal -1/3 binary64))) |
(+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1 binary64))) |
(+.f64 #s(literal 1/3 binary64) (*.f64 (neg.f64 x) #s(literal -1 binary64))) |
(+.f64 #s(literal 1/3 binary64) (neg.f64 (*.f64 x #s(literal -1 binary64)))) |
(+.f64 #s(literal 1/3 binary64) x) |
(+.f64 x #s(literal 1/3 binary64)) |
Compiled 42 231 to 2 333 computations (94.5% saved)
5 alts after pruning (2 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 524 | 2 | 1 526 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 3 | 4 |
| Done | 0 | 0 | 0 |
| Total | 1 525 | 5 | 1 530 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 67.5% | (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) |
| ▶ | 50.3% | (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) |
| ✓ | 100.0% | (-.f64 x #s(literal 1/3 binary64)) |
| ▶ | 49.2% | (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) |
| ✓ | 49.9% | #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) |
Compiled 42 to 28 computations (33.3% saved)
| 1× | egg-herbie |
Found 8 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (-.f64 x #s(literal -1/3 binary64)) | |
| cost-diff | 0 | (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) | |
| cost-diff | 0 | #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) | |
| cost-diff | 0 | (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) | |
| cost-diff | 0 | (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) | |
| cost-diff | 0 | #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) | |
| cost-diff | 0 | (fma.f64 x x #s(literal -1/9 binary64)) | |
| cost-diff | 0 | (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) |
| 132× | lower-+.f64 |
| 132× | lower-+.f32 |
| 98× | lower-fma.f32 |
| 92× | lower-fma.f64 |
| 50× | lower-*.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 75 |
| 0 | 29 | 75 |
| 1 | 42 | 71 |
| 2 | 60 | 71 |
| 3 | 79 | 71 |
| 4 | 94 | 71 |
| 5 | 102 | 71 |
| 6 | 118 | 71 |
| 7 | 160 | 71 |
| 8 | 215 | 71 |
| 9 | 229 | 71 |
| 10 | 232 | 71 |
| 11 | 235 | 71 |
| 0 | 235 | 71 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
x |
#s(literal -1/9 binary64) |
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
#s(literal -9 binary64) |
#s(literal 3 binary64) |
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) |
#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) |
#s(literal -1/27 binary64) |
(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) |
x |
(-.f64 x #s(literal -1/3 binary64)) |
#s(literal -1/3 binary64) |
#s(literal 1/9 binary64) |
| Outputs |
|---|
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) |
(*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (fma.f64 x x #s(literal -1/9 binary64))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
x |
#s(literal -1/9 binary64) |
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
#s(literal -9 binary64) |
#s(literal 3 binary64) |
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) |
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) |
#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) |
#s(literal -1/27 binary64) |
(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) |
(fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) |
x |
(-.f64 x #s(literal -1/3 binary64)) |
#s(literal -1/3 binary64) |
#s(literal 1/9 binary64) |
Found 8 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.00390625 | (-.f64 x #s(literal -1/3 binary64)) | |
| accuracy | 0.0234375 | (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) | |
| accuracy | 20.3105395498375 | (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) | |
| accuracy | 31.82102830291946 | #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) | |
| accuracy | 0 | (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) | |
| accuracy | 0.00390625 | (fma.f64 x x #s(literal -1/9 binary64)) | |
| accuracy | 14.698514384628556 | (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) | |
| accuracy | 32.12210910256336 | #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) |
| 143.0ms | 248× | 0 | valid |
| 1.0ms | 5× | 1 | valid |
| 1.0ms | 3× | 2 | valid |
Compiled 68 to 23 computations (66.2% saved)
const: 13.0ms (36.9% of total)ival-mult: 8.0ms (22.7% of total)ival-div: 7.0ms (19.9% of total)ival-add: 5.0ms (14.2% of total)ival-sub: 2.0ms (5.7% of total)adjust: 0.0ms (0% 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 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ()) |
#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ()) |
#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt -1/3 (taylor 0 x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt -1/9 (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (pow x 2) 1/9) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt 3 (taylor 0 x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 3 (* -9 x)) (taylor 0 x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 3 (* x (- (* 27 x) 9))) (taylor 0 x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 3 (* x (- (* x (+ 27 (* -81 x))) 9))) (taylor 0 x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 3 (taylor 0 x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 3 (* -9 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 3 (* -9 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 3 (* -9 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt -1/3 (taylor 0 x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt -1/27 (taylor 0 x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (pow x 3) 1/27) (taylor 0 x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (pow x 3) 1/27) (taylor 0 x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (pow x 3) 1/27) (taylor 0 x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt 1/9 (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/9 (* 1/3 x)) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/9 (* x (+ 1/3 x))) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/9 (* x (+ 1/3 x))) (taylor 0 x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt 1/3 (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/3 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 x) (taylor inf x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- 1 (* 1/3 (/ 1 x))) x) (taylor inf x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x) (taylor inf x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x) (taylor inf x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -9 x) (taylor inf x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (* 3 (/ 1 x)) 9)) (taylor inf x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (* 3 (/ 1 x)) 9)) (taylor inf x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (* 3 (/ 1 x)) 9)) (taylor inf x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 3) (taylor inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) (taylor inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) (taylor inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) (taylor inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1/9 binary64)) (patch (fma.f64 x x #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 x) (taylor -inf x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (- (* 1/3 (/ 1 x)) 1) x)) (taylor -inf x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x)) (taylor -inf x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x)) (taylor -inf x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -9 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- 9 (* 3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- 9 (* 3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- 9 (* 3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 3) (taylor -inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1/3 binary64)) (patch (-.f64 x #s(literal -1/3 binary64)) #<representation binary64>) () ())) ()) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 18.0ms | x | @ | inf | ((* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (+ (* -9 x) 3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9) (- x -1/3)) |
| 1.0ms | x | @ | -inf | ((* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (+ (* -9 x) 3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9) (- x -1/3)) |
| 1.0ms | x | @ | 0 | ((* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (+ (* -9 x) 3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9) (- x -1/3)) |
| 1× | egg-herbie |
| 7 720× | lower-fma.f64 |
| 7 720× | lower-fma.f32 |
| 3 206× | lower-*.f64 |
| 3 206× | lower-*.f32 |
| 1 476× | div-sub |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 94 | 430 |
| 1 | 270 | 422 |
| 2 | 659 | 414 |
| 3 | 1994 | 410 |
| 4 | 4709 | 410 |
| 0 | 8237 | 379 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
-1/3 |
(- x 1/3) |
(- x 1/3) |
(- x 1/3) |
-1/9 |
(- (pow x 2) 1/9) |
(- (pow x 2) 1/9) |
(- (pow x 2) 1/9) |
3 |
(+ 3 (* -9 x)) |
(+ 3 (* x (- (* 27 x) 9))) |
(+ 3 (* x (- (* x (+ 27 (* -81 x))) 9))) |
3 |
(+ 3 (* -9 x)) |
(+ 3 (* -9 x)) |
(+ 3 (* -9 x)) |
-1/3 |
(- x 1/3) |
(- x 1/3) |
(- x 1/3) |
-1/27 |
(- (pow x 3) 1/27) |
(- (pow x 3) 1/27) |
(- (pow x 3) 1/27) |
1/9 |
(+ 1/9 (* 1/3 x)) |
(+ 1/9 (* x (+ 1/3 x))) |
(+ 1/9 (* x (+ 1/3 x))) |
1/3 |
(+ 1/3 x) |
(+ 1/3 x) |
(+ 1/3 x) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(pow x 2) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(/ 1 x) |
(/ (- 1 (* 1/3 (/ 1 x))) x) |
(/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x) |
(/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x) |
(* -9 x) |
(* x (- (* 3 (/ 1 x)) 9)) |
(* x (- (* 3 (/ 1 x)) 9)) |
(* x (- (* 3 (/ 1 x)) 9)) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(pow x 3) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
x |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(pow x 2) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(/ 1 x) |
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x)) |
(* -9 x) |
(* -1 (* x (- 9 (* 3 (/ 1 x))))) |
(* -1 (* x (- 9 (* 3 (/ 1 x))))) |
(* -1 (* x (- 9 (* 3 (/ 1 x))))) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(pow x 3) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
x |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
| Outputs |
|---|
-1/3 |
#s(literal -1/3 binary64) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
-1/9 |
#s(literal -1/9 binary64) |
(- (pow x 2) 1/9) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(- (pow x 2) 1/9) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(- (pow x 2) 1/9) |
(fma.f64 x x #s(literal -1/9 binary64)) |
3 |
#s(literal 3 binary64) |
(+ 3 (* -9 x)) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(+ 3 (* x (- (* 27 x) 9))) |
(fma.f64 (fma.f64 #s(literal 27 binary64) x #s(literal -9 binary64)) x #s(literal 3 binary64)) |
(+ 3 (* x (- (* x (+ 27 (* -81 x))) 9))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -81 binary64) x #s(literal 27 binary64)) x #s(literal -9 binary64)) x #s(literal 3 binary64)) |
3 |
#s(literal 3 binary64) |
(+ 3 (* -9 x)) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(+ 3 (* -9 x)) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(+ 3 (* -9 x)) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
-1/3 |
#s(literal -1/3 binary64) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
-1/27 |
#s(literal -1/27 binary64) |
(- (pow x 3) 1/27) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(- (pow x 3) 1/27) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(- (pow x 3) 1/27) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
1/9 |
#s(literal 1/9 binary64) |
(+ 1/9 (* 1/3 x)) |
(fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) |
(+ 1/9 (* x (+ 1/3 x))) |
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64)) |
(+ 1/9 (* x (+ 1/3 x))) |
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64)) |
1/3 |
#s(literal 1/3 binary64) |
(+ 1/3 x) |
(+.f64 #s(literal 1/3 binary64) x) |
(+ 1/3 x) |
(+.f64 #s(literal 1/3 binary64) x) |
(+ 1/3 x) |
(+.f64 #s(literal 1/3 binary64) x) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ (- 1 (* 1/3 (/ 1 x))) x) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 #s(literal 1/3 binary64) x)) |
(/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/9 binary64) x)) x)) |
(/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x) #s(literal -1/3 binary64)) x)) |
(* -9 x) |
(*.f64 #s(literal -9 binary64) x) |
(* x (- (* 3 (/ 1 x)) 9)) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(* x (- (* 3 (/ 1 x)) 9)) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(* x (- (* 3 (/ 1 x)) 9)) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(pow x 3) |
(*.f64 (*.f64 x x) x) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) |
(*.f64 (+.f64 #s(literal 1/3 binary64) x) x) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64)) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64)) |
x |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(+.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(+.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(+.f64 #s(literal 1/3 binary64) x) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x)) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 #s(literal 1/3 binary64) x)) |
(* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x)) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/9 binary64) x)) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x)) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x) #s(literal -1/3 binary64)) x)) |
(* -9 x) |
(*.f64 #s(literal -9 binary64) x) |
(* -1 (* x (- 9 (* 3 (/ 1 x))))) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(* -1 (* x (- 9 (* 3 (/ 1 x))))) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(* -1 (* x (- 9 (* 3 (/ 1 x))))) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(pow x 3) |
(*.f64 (*.f64 x x) x) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) |
(*.f64 (+.f64 #s(literal 1/3 binary64) x) x) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64)) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64)) |
x |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(+.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(+.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(+.f64 #s(literal 1/3 binary64) x) |
| 6 318× | lower-fma.f32 |
| 6 312× | lower-fma.f64 |
| 4 722× | lower-*.f32 |
| 4 720× | lower-*.f64 |
| 3 878× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 67 |
| 0 | 29 | 63 |
| 1 | 131 | 63 |
| 2 | 867 | 63 |
| 0 | 8515 | 63 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) |
#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) |
(fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) |
(-.f64 x #s(literal -1/3 binary64)) |
| Outputs |
|---|
(*.f64 (/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) #s(literal 1/729 binary64))) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 (*.f64 x x) #s(literal -1/9 binary64) #s(literal 1/81 binary64)))) |
(*.f64 (/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64))) (fma.f64 x x #s(literal -1/9 binary64))) |
(*.f64 (/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64)) (-.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) (*.f64 #s(literal 1/9 binary64) (*.f64 x x))))) (-.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) (*.f64 #s(literal 1/9 binary64) (*.f64 x x)))) |
(*.f64 (/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x)) x (*.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64)) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64))) (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64))))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (*.f64 x x) x)) x (*.f64 (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64)) (-.f64 (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64)) (*.f64 (*.f64 (*.f64 x x) x) x))))) |
(*.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64)))) |
(*.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64)))) |
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) |
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) (/.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (fma.f64 x x #s(literal 1/9 binary64)))) |
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1/9 binary64))) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) (/.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64)))) |
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))) |
(*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (fma.f64 x x #s(literal -1/9 binary64))) |
(/.f64 (*.f64 (-.f64 #s(literal 1/81 binary64) (*.f64 (*.f64 (*.f64 x x) x) x)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (-.f64 #s(literal -1/9 binary64) (*.f64 x x))) |
(/.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64))) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (fma.f64 (neg.f64 x) x #s(literal -1/9 binary64))) |
(/.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64))) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64)))) |
(/.f64 (*.f64 #s(literal 1 binary64) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1/9 binary64)))) |
(/.f64 (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (-.f64 #s(literal 1/81 binary64) (*.f64 (*.f64 (*.f64 x x) x) x))) (-.f64 #s(literal -1/9 binary64) (*.f64 x x))) |
(/.f64 (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)))) (fma.f64 (neg.f64 x) x #s(literal -1/9 binary64))) |
(/.f64 (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)))) (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64)))) |
(/.f64 (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1/9 binary64)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (*.f64 (*.f64 x x) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))) (*.f64 (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1/9 binary64)) (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1/9 binary64)))) (-.f64 (*.f64 (*.f64 x x) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1/9 binary64)))) |
(/.f64 (-.f64 (*.f64 (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1/9 binary64)) (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1/9 binary64))) (*.f64 (*.f64 (*.f64 x x) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (*.f64 (*.f64 x x) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))))) (-.f64 (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1/9 binary64)) (*.f64 (*.f64 x x) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 x x) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1/9 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 x x) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (*.f64 (*.f64 x x) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (-.f64 (*.f64 (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1/9 binary64)) (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1/9 binary64))) (*.f64 (*.f64 (*.f64 x x) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1/9 binary64)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1/9 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 x x) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1/9 binary64)) (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1/9 binary64)) (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (*.f64 (*.f64 x x) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))) (*.f64 (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1/9 binary64)) (*.f64 (*.f64 x x) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))) (fma.f64 (neg.f64 x) x #s(literal -1/9 binary64))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))) (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (fma.f64 x x #s(literal 1/9 binary64))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1/9 binary64)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))))) |
(/.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1/9 binary64)))) |
(fma.f64 (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) x) x (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1/9 binary64))) |
(fma.f64 (*.f64 x x) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1/9 binary64))) |
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(fma.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1/9 binary64) (*.f64 (*.f64 x x) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))) |
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(/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) (*.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 x) (-.f64 (neg.f64 x) #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64)))) |
(/.f64 (-.f64 x #s(literal -1/3 binary64)) #s(literal 1 binary64)) |
(/.f64 (-.f64 #s(literal -1/3 binary64) x) #s(literal -1 binary64)) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/3 binary64) x))) |
(neg.f64 (-.f64 #s(literal -1/3 binary64) x)) |
(fma.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))) |
(fma.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64))) (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x))) (fma.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (*.f64 x x)) (*.f64 (*.f64 (*.f64 x x) x) x)) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))) |
(fma.f64 (/.f64 (*.f64 (*.f64 x x) x) (-.f64 #s(literal 1/81 binary64) (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (*.f64 (-.f64 x #s(literal 1/3 binary64)) x)))) (-.f64 #s(literal 1/9 binary64) (*.f64 (-.f64 x #s(literal 1/3 binary64)) x)) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))) |
(fma.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (*.f64 (-.f64 x #s(literal 1/3 binary64)) x)) (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal 1/729 binary64))) (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (-.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal 1/9 binary64)) #s(literal 1/81 binary64)) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))) |
(fma.f64 (/.f64 (*.f64 x x) (fma.f64 (neg.f64 x) x #s(literal 1/9 binary64))) (-.f64 #s(literal -1/3 binary64) x) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))))) |
(fma.f64 (/.f64 (*.f64 x x) (fma.f64 x x #s(literal -1/9 binary64))) (-.f64 x #s(literal -1/3 binary64)) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))))) |
(fma.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (fma.f64 (-.f64 x #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))))) |
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) #s(literal 1/3 binary64)) |
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))) |
(fma.f64 (neg.f64 x) #s(literal -1 binary64) #s(literal 1/3 binary64)) |
(fma.f64 #s(literal 1 binary64) x #s(literal 1/3 binary64)) |
(fma.f64 (*.f64 (*.f64 x x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))) |
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))))) |
(fma.f64 #s(literal -1 binary64) (neg.f64 x) #s(literal 1/3 binary64)) |
(fma.f64 x (/.f64 (*.f64 x x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))) |
(fma.f64 x (/.f64 x (-.f64 x #s(literal 1/3 binary64))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))))) |
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1/9 binary64)))) (-.f64 x #s(literal 1/3 binary64))) (/.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 x x #s(literal 1/9 binary64))) (-.f64 x #s(literal 1/3 binary64)))) |
(-.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (neg.f64 x) (-.f64 (neg.f64 x) #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 (neg.f64 x) (-.f64 (neg.f64 x) #s(literal -1/3 binary64)) #s(literal 1/9 binary64)))) |
(-.f64 (/.f64 #s(literal -1/27 binary64) (neg.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))) (/.f64 (*.f64 (*.f64 x x) x) (neg.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))) |
(-.f64 (/.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))) #s(literal -1 binary64)) (/.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1/3 binary64)))) #s(literal -1 binary64))) |
(-.f64 (/.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal -1 binary64)) (/.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal -1 binary64))) |
(-.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 (neg.f64 x) #s(literal 1/3 binary64))) (/.f64 (*.f64 x x) (+.f64 (neg.f64 x) #s(literal 1/3 binary64)))) |
(-.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1/3 binary64)))) (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64)))) |
(-.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))) |
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/3 binary64) x)) |
(-.f64 #s(literal 1/3 binary64) (neg.f64 x)) |
(-.f64 x #s(literal -1/3 binary64)) |
(+.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64)))) (*.f64 x (/.f64 x (-.f64 x #s(literal 1/3 binary64))))) |
(+.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))) |
(+.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) #s(literal 1/3 binary64)) |
(+.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1/3 binary64)))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal 1/3 binary64))))) |
(+.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (neg.f64 (/.f64 #s(literal -1/27 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))) |
(+.f64 #s(literal 0 binary64) (-.f64 x #s(literal -1/3 binary64))) |
(+.f64 #s(literal 1/3 binary64) (*.f64 (neg.f64 x) #s(literal -1 binary64))) |
(+.f64 #s(literal 1/3 binary64) x) |
(+.f64 x #s(literal 1/3 binary64)) |
Compiled 15 692 to 1 732 computations (89% saved)
5 alts after pruning (2 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 586 | 2 | 588 |
| Fresh | 0 | 0 | 0 |
| Picked | 2 | 0 | 2 |
| Done | 0 | 3 | 3 |
| Total | 588 | 5 | 593 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 67.5% | (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) |
| ▶ | 49.8% | (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) |
| ✓ | 100.0% | (-.f64 x #s(literal 1/3 binary64)) |
| ▶ | 99.7% | (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) |
| ✓ | 49.9% | #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) |
Compiled 39 to 26 computations (33.3% saved)
| 1× | egg-herbie |
Found 8 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | #s(approx (- x -1/3) #s(literal 1/3 binary64)) | |
| cost-diff | 0 | (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) | |
| cost-diff | 0 | #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) | |
| cost-diff | 0 | (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) | |
| cost-diff | 0 | (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) | |
| cost-diff | 0 | #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) | |
| cost-diff | 0 | #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) |
| 80× | lower-+.f64 |
| 80× | lower-+.f32 |
| 44× | lower-fma.f32 |
| 40× | lower-fma.f64 |
| 30× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 87 |
| 0 | 30 | 87 |
| 1 | 42 | 83 |
| 2 | 48 | 83 |
| 3 | 52 | 83 |
| 4 | 59 | 83 |
| 5 | 67 | 83 |
| 6 | 83 | 83 |
| 7 | 114 | 83 |
| 8 | 134 | 83 |
| 9 | 144 | 83 |
| 10 | 147 | 83 |
| 11 | 150 | 83 |
| 0 | 150 | 81 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) |
#s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) |
#s(literal -1/9 binary64) |
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
#s(literal -9 binary64) |
x |
#s(literal 3 binary64) |
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) |
#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) |
#s(literal -1/27 binary64) |
(fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) |
x |
#s(approx (- x -1/3) #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
#s(literal 1/9 binary64) |
| Outputs |
|---|
(*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) |
(*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64))) |
#s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) |
#s(literal -1/9 binary64) |
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
#s(literal -9 binary64) |
x |
#s(literal 3 binary64) |
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) |
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) |
#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) |
#s(literal -1/27 binary64) |
(fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) |
(fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) |
x |
#s(approx (- x -1/3) #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
#s(literal 1/9 binary64) |
Found 8 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0234375 | (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) | |
| accuracy | 20.3105395498375 | (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) | |
| accuracy | 31.82102830291946 | #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) | |
| accuracy | 32.03160924390678 | #s(approx (- x -1/3) #s(literal 1/3 binary64)) | |
| accuracy | 0 | (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) | |
| accuracy | 14.698514384628556 | (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) | |
| accuracy | 32.12210910256336 | #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) | |
| accuracy | 32.348081041745836 | #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) |
| 78.0ms | 248× | 0 | valid |
| 1.0ms | 5× | 1 | valid |
| 1.0ms | 3× | 2 | valid |
Compiled 68 to 24 computations (64.7% saved)
ival-mult: 43.0ms (60.8% of total)const: 14.0ms (19.8% of total)ival-div: 5.0ms (7.1% of total)ival-add: 5.0ms (7.1% of total)ival-sub: 2.0ms (2.8% of total)adjust: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) (patch #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (- x -1/3) #s(literal 1/3 binary64)) (patch #s(approx (- x -1/3) #s(literal 1/3 binary64)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt -1/3 (taylor 0 x) (#s(alt (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- x 1/3) (taylor 0 x) (#s(alt (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) (patch (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt -1/9 (taylor 0 x) (#s(alt #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) (patch #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
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#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) (patch #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) (patch #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 x) (taylor -inf x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (- (* 1/3 (/ 1 x)) 1) x)) (taylor -inf x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x)) (taylor -inf x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x)) (taylor -inf x) (#s(alt #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) (patch #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -9 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- 9 (* 3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- 9 (* 3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- 9 (* 3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (patch (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (pow x 3) (taylor -inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (patch #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (patch (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt #s(approx (- x -1/3) #s(literal 1/3 binary64)) (patch #s(approx (- x -1/3) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- x -1/3) #s(literal 1/3 binary64)) (patch #s(approx (- x -1/3) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- x -1/3) #s(literal 1/3 binary64)) (patch #s(approx (- x -1/3) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/3 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (- x -1/3) #s(literal 1/3 binary64)) (patch #s(approx (- x -1/3) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | ((* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (+ (* -9 x) 3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9) (- x -1/3)) |
| 1.0ms | x | @ | inf | ((* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (+ (* -9 x) 3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9) (- x -1/3)) |
| 1.0ms | x | @ | 0 | ((* (+ (* x x) -1/9) (/ -1 (- -1/3 x))) (+ (* x x) -1/9) (/ -1 (- -1/3 x)) (+ (* -9 x) 3) (/ (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9)) (+ (* (* x x) x) -1/27) (+ (* x (- x -1/3)) 1/9) (- x -1/3)) |
| 1× | egg-herbie |
| 7 720× | lower-fma.f64 |
| 7 720× | lower-fma.f32 |
| 3 206× | lower-*.f64 |
| 3 206× | lower-*.f32 |
| 1 476× | div-sub |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 94 | 430 |
| 1 | 270 | 422 |
| 2 | 659 | 414 |
| 3 | 1994 | 410 |
| 4 | 4709 | 410 |
| 0 | 8237 | 379 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
-1/3 |
(- x 1/3) |
(- x 1/3) |
(- x 1/3) |
-1/9 |
(- (pow x 2) 1/9) |
(- (pow x 2) 1/9) |
(- (pow x 2) 1/9) |
3 |
(+ 3 (* -9 x)) |
(+ 3 (* x (- (* 27 x) 9))) |
(+ 3 (* x (- (* x (+ 27 (* -81 x))) 9))) |
3 |
(+ 3 (* -9 x)) |
(+ 3 (* -9 x)) |
(+ 3 (* -9 x)) |
-1/3 |
(- x 1/3) |
(- x 1/3) |
(- x 1/3) |
-1/27 |
(- (pow x 3) 1/27) |
(- (pow x 3) 1/27) |
(- (pow x 3) 1/27) |
1/9 |
(+ 1/9 (* 1/3 x)) |
(+ 1/9 (* x (+ 1/3 x))) |
(+ 1/9 (* x (+ 1/3 x))) |
1/3 |
(+ 1/3 x) |
(+ 1/3 x) |
(+ 1/3 x) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(pow x 2) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(/ 1 x) |
(/ (- 1 (* 1/3 (/ 1 x))) x) |
(/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x) |
(/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x) |
(* -9 x) |
(* x (- (* 3 (/ 1 x)) 9)) |
(* x (- (* 3 (/ 1 x)) 9)) |
(* x (- (* 3 (/ 1 x)) 9)) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(pow x 3) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
x |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(pow x 2) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(/ 1 x) |
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x)) |
(* -9 x) |
(* -1 (* x (- 9 (* 3 (/ 1 x))))) |
(* -1 (* x (- 9 (* 3 (/ 1 x))))) |
(* -1 (* x (- 9 (* 3 (/ 1 x))))) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(pow x 3) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
x |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
| Outputs |
|---|
-1/3 |
#s(literal -1/3 binary64) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
-1/9 |
#s(literal -1/9 binary64) |
(- (pow x 2) 1/9) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(- (pow x 2) 1/9) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(- (pow x 2) 1/9) |
(fma.f64 x x #s(literal -1/9 binary64)) |
3 |
#s(literal 3 binary64) |
(+ 3 (* -9 x)) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(+ 3 (* x (- (* 27 x) 9))) |
(fma.f64 (fma.f64 #s(literal 27 binary64) x #s(literal -9 binary64)) x #s(literal 3 binary64)) |
(+ 3 (* x (- (* x (+ 27 (* -81 x))) 9))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -81 binary64) x #s(literal 27 binary64)) x #s(literal -9 binary64)) x #s(literal 3 binary64)) |
3 |
#s(literal 3 binary64) |
(+ 3 (* -9 x)) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(+ 3 (* -9 x)) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(+ 3 (* -9 x)) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
-1/3 |
#s(literal -1/3 binary64) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
(- x 1/3) |
(-.f64 x #s(literal 1/3 binary64)) |
-1/27 |
#s(literal -1/27 binary64) |
(- (pow x 3) 1/27) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(- (pow x 3) 1/27) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(- (pow x 3) 1/27) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
1/9 |
#s(literal 1/9 binary64) |
(+ 1/9 (* 1/3 x)) |
(fma.f64 #s(literal 1/3 binary64) x #s(literal 1/9 binary64)) |
(+ 1/9 (* x (+ 1/3 x))) |
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64)) |
(+ 1/9 (* x (+ 1/3 x))) |
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64)) |
1/3 |
#s(literal 1/3 binary64) |
(+ 1/3 x) |
(+.f64 #s(literal 1/3 binary64) x) |
(+ 1/3 x) |
(+.f64 #s(literal 1/3 binary64) x) |
(+ 1/3 x) |
(+.f64 #s(literal 1/3 binary64) x) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ (- 1 (* 1/3 (/ 1 x))) x) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 #s(literal 1/3 binary64) x)) |
(/ (- (+ 1 (/ 1/9 (pow x 2))) (* 1/3 (/ 1 x))) x) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/9 binary64) x)) x)) |
(/ (- (+ 1 (/ 1/9 (pow x 2))) (+ (* 1/3 (/ 1 x)) (* 1/27 (/ 1 (pow x 3))))) x) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x) #s(literal -1/3 binary64)) x)) |
(* -9 x) |
(*.f64 #s(literal -9 binary64) x) |
(* x (- (* 3 (/ 1 x)) 9)) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(* x (- (* 3 (/ 1 x)) 9)) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(* x (- (* 3 (/ 1 x)) 9)) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
x |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* x (- 1 (* 1/3 (/ 1 x)))) |
(-.f64 x #s(literal 1/3 binary64)) |
(pow x 3) |
(*.f64 (*.f64 x x) x) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(* (pow x 3) (- 1 (* 1/27 (/ 1 (pow x 3))))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) |
(*.f64 (+.f64 #s(literal 1/3 binary64) x) x) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64)) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64)) |
x |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(+.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(+.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(+.f64 #s(literal 1/3 binary64) x) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(* (pow x 2) (- 1 (* 1/9 (/ 1 (pow x 2))))) |
(fma.f64 x x #s(literal -1/9 binary64)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(* -1 (/ (- (* 1/3 (/ 1 x)) 1) x)) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 #s(literal 1/3 binary64) x)) |
(* -1 (/ (- (* -1 (/ (- (* 1/9 (/ 1 x)) 1/3) x)) 1) x)) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/9 binary64) x)) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/27 (/ 1 x)) 1/9) x)) 1/3) x)) 1) x)) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/27 binary64) x) #s(literal 1/9 binary64)) x) #s(literal -1/3 binary64)) x)) |
(* -9 x) |
(*.f64 #s(literal -9 binary64) x) |
(* -1 (* x (- 9 (* 3 (/ 1 x))))) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(* -1 (* x (- 9 (* 3 (/ 1 x))))) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(* -1 (* x (- 9 (* 3 (/ 1 x))))) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
x |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(* -1 (* x (- (* 1/3 (/ 1 x)) 1))) |
(-.f64 x #s(literal 1/3 binary64)) |
(pow x 3) |
(*.f64 (*.f64 x x) x) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(* -1 (* (pow x 3) (- (* 1/27 (/ 1 (pow x 3))) 1))) |
(fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 1/3 (/ 1 x)))) |
(*.f64 (+.f64 #s(literal 1/3 binary64) x) x) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64)) |
(* (pow x 2) (+ 1 (+ (/ 1/9 (pow x 2)) (* 1/3 (/ 1 x))))) |
(fma.f64 (+.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64)) |
x |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(+.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(+.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1 (* 1/3 (/ 1 x)))) |
(+.f64 #s(literal 1/3 binary64) x) |
| 5 924× | lower-fma.f32 |
| 5 920× | lower-fma.f64 |
| 4 190× | lower-*.f32 |
| 4 188× | lower-*.f64 |
| 3 446× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 79 |
| 0 | 30 | 75 |
| 1 | 131 | 75 |
| 2 | 832 | 75 |
| 3 | 7469 | 75 |
| 0 | 8391 | 73 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) |
#s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) |
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) |
#s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) |
(fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) |
#s(approx (- x -1/3) #s(literal 1/3 binary64)) |
| Outputs |
|---|
(*.f64 #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64))) |
(*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) |
#s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) |
#s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) |
(*.f64 (/.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64)) (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal -27 binary64))) (fma.f64 #s(literal 81 binary64) (*.f64 x x) (fma.f64 #s(literal -27 binary64) x #s(literal 9 binary64)))) |
(*.f64 (/.f64 (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal 27 binary64)) (*.f64 (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64)) (-.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64)) (*.f64 x #s(literal 27 binary64))))) (-.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64)) (*.f64 x #s(literal 27 binary64)))) |
(*.f64 (/.f64 (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal 27 binary64)) (fma.f64 #s(literal 531441 binary64) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x) (*.f64 (*.f64 (fma.f64 x #s(literal 27 binary64) #s(literal 9 binary64)) (fma.f64 x #s(literal 27 binary64) #s(literal 9 binary64))) (fma.f64 x #s(literal 27 binary64) #s(literal 9 binary64))))) (fma.f64 #s(literal 6561 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (fma.f64 x #s(literal 27 binary64) #s(literal 9 binary64)) (-.f64 (fma.f64 x #s(literal 27 binary64) #s(literal 9 binary64)) (*.f64 #s(literal 81 binary64) (*.f64 x x)))))) |
(*.f64 (/.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64)) (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64))) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) |
(*.f64 (-.f64 #s(literal 9 binary64) (*.f64 #s(literal 81 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 3 binary64) (*.f64 #s(literal -9 binary64) x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))) (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64))) (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal 27 binary64))) |
(*.f64 (neg.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 9 binary64) x #s(literal 3 binary64)))) |
(*.f64 (neg.f64 (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal 27 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64))))) |
(*.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64)))) |
(*.f64 (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal 27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64)))) |
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal -1 binary64)) |
(/.f64 (*.f64 (fma.f64 #s(literal 6561 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -81 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64)))) (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal 9 binary64))) |
(/.f64 (*.f64 (fma.f64 #s(literal 531441 binary64) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x) #s(literal -729 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64)))) (fma.f64 #s(literal 6561 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (fma.f64 (*.f64 x x) #s(literal 729 binary64) #s(literal 81 binary64)))) |
(/.f64 (*.f64 (fma.f64 #s(literal 531441 binary64) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x) #s(literal -729 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64)))) (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal -27 binary64))) |
(/.f64 (*.f64 (fma.f64 #s(literal -387420489 binary64) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) (*.f64 (*.f64 (*.f64 x x) x) x)) #s(literal 19683 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64)))) (fma.f64 #s(literal 531441 binary64) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x) (-.f64 #s(literal 729 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal -19683 binary64))))) |
(/.f64 (*.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))) |
(/.f64 (*.f64 (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal 27 binary64)) #s(literal 1 binary64)) (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 #s(literal 81 binary64) x) (/.f64 x (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64)))) (*.f64 (*.f64 #s(literal 81 binary64) x) (/.f64 x (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))))) (*.f64 (/.f64 #s(literal 9 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))) (/.f64 #s(literal 9 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))))) (fma.f64 (*.f64 #s(literal 81 binary64) x) (/.f64 x (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))) (/.f64 #s(literal 9 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal 81 binary64) x) (/.f64 x (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 9 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 #s(literal 81 binary64) x) (/.f64 x (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64)))) (*.f64 (*.f64 #s(literal 81 binary64) x) (/.f64 x (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64)))) (fma.f64 (/.f64 #s(literal 9 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))) (/.f64 #s(literal 9 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 81 binary64) x) (/.f64 x (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64)))) (/.f64 #s(literal 9 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 9 binary64) (*.f64 #s(literal 81 binary64) (*.f64 x x)))) (neg.f64 (-.f64 #s(literal 3 binary64) (*.f64 #s(literal -9 binary64) x)))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64)))) (neg.f64 (fma.f64 #s(literal 9 binary64) x #s(literal 3 binary64)))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal 27 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64))))) |
(/.f64 (*.f64 (fma.f64 #s(literal 6561 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -81 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal 9 binary64)) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64)))) |
(/.f64 (*.f64 (fma.f64 #s(literal 531441 binary64) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x) #s(literal -729 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 6561 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (fma.f64 (*.f64 x x) #s(literal 729 binary64) #s(literal 81 binary64))) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64)))) |
(/.f64 (*.f64 (fma.f64 #s(literal 531441 binary64) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x) #s(literal -729 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal -27 binary64)) (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64)))) |
(/.f64 (*.f64 (fma.f64 #s(literal -387420489 binary64) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) (*.f64 (*.f64 (*.f64 x x) x) x)) #s(literal 19683 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 531441 binary64) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x) (-.f64 #s(literal 729 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal -19683 binary64)))) (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64)))) |
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 81 binary64) (*.f64 x x)) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))) (*.f64 (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64)) #s(literal 9 binary64))) (*.f64 (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64)) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64)))) |
(/.f64 (fma.f64 #s(literal 6561 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -81 binary64)) (*.f64 (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64)) (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal 9 binary64)))) |
(/.f64 (-.f64 #s(literal 9 binary64) (*.f64 #s(literal 81 binary64) (*.f64 x x))) (-.f64 #s(literal 3 binary64) (*.f64 #s(literal -9 binary64) x))) |
(/.f64 (fma.f64 #s(literal 531441 binary64) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x) #s(literal -729 binary64)) (*.f64 (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64)) (fma.f64 #s(literal 6561 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (fma.f64 (*.f64 x x) #s(literal 729 binary64) #s(literal 81 binary64))))) |
(/.f64 (fma.f64 #s(literal 531441 binary64) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x) #s(literal -729 binary64)) (*.f64 (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64)) (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal -27 binary64)))) |
(/.f64 (fma.f64 #s(literal -387420489 binary64) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) (*.f64 (*.f64 (*.f64 x x) x) x)) #s(literal 19683 binary64)) (*.f64 (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64)) (fma.f64 #s(literal 531441 binary64) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x) (-.f64 #s(literal 729 binary64) (*.f64 (*.f64 (*.f64 x x) x) #s(literal -19683 binary64)))))) |
(/.f64 (neg.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64))) (fma.f64 #s(literal 9 binary64) x #s(literal 3 binary64))) |
(/.f64 (neg.f64 (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal 27 binary64))) (neg.f64 (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64)))) |
(/.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64)) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))) |
(/.f64 (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal 27 binary64)) (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 3 binary64) (*.f64 #s(literal -9 binary64) x)) (-.f64 #s(literal 9 binary64) (*.f64 #s(literal 81 binary64) (*.f64 x x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64))))) |
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64))) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64)))) |
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal 27 binary64))) (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64)))) |
(neg.f64 (/.f64 (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64)) (fma.f64 #s(literal 9 binary64) x #s(literal 3 binary64)))) |
(neg.f64 (/.f64 (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal 27 binary64)) (neg.f64 (fma.f64 x (-.f64 (*.f64 #s(literal 81 binary64) x) #s(literal -27 binary64)) #s(literal 9 binary64))))) |
(fma.f64 (/.f64 (*.f64 #s(literal 81 binary64) (*.f64 x x)) (fma.f64 #s(literal -729 binary64) (*.f64 (*.f64 x x) x) #s(literal -27 binary64))) (fma.f64 #s(literal 81 binary64) (*.f64 x x) (fma.f64 #s(literal -27 binary64) x #s(literal 9 binary64))) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))))) |
(fma.f64 (/.f64 (*.f64 #s(literal 81 binary64) (*.f64 x x)) (fma.f64 #s(literal 81 binary64) (*.f64 x x) #s(literal -9 binary64))) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))))) |
(fma.f64 (*.f64 (*.f64 #s(literal -9 binary64) x) x) (/.f64 #s(literal -9 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))))) |
(fma.f64 (*.f64 #s(literal 81 binary64) x) (/.f64 x (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))))) |
(fma.f64 #s(literal 81 binary64) (/.f64 (*.f64 x x) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))))) |
(fma.f64 (*.f64 #s(literal 81 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))))) |
(fma.f64 (*.f64 #s(literal -9 binary64) x) (/.f64 (*.f64 #s(literal -9 binary64) x) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))))) |
(fma.f64 #s(literal -9 binary64) (/.f64 (*.f64 (*.f64 #s(literal -9 binary64) x) x) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))))) |
(fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal 81 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 #s(literal -9 binary64) x #s(literal -3 binary64))))) |
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(fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) (/.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))))) |
(fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) |
(fma.f64 (*.f64 x x) (/.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))))) |
(fma.f64 x (/.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(approx (- x -1/3) #s(literal 1/3 binary64))) x) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))))) |
(fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) |
(-.f64 (/.f64 #s(literal 1/81 binary64) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x))) (/.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x)))) |
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) #s(literal 1 binary64))) |
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)))) |
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/9 binary64) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x))) |
(+.f64 (neg.f64 (*.f64 (neg.f64 x) #s(approx (- x -1/3) #s(literal 1/3 binary64)))) #s(literal 1/9 binary64)) |
(+.f64 (/.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) x) #s(approx (- x -1/3) #s(literal 1/3 binary64))) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) (neg.f64 (/.f64 #s(literal 1/81 binary64) (fma.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))))) |
(+.f64 (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x) #s(literal 1/9 binary64)) |
(+.f64 #s(literal 1/9 binary64) (neg.f64 (*.f64 (neg.f64 x) #s(approx (- x -1/3) #s(literal 1/3 binary64))))) |
(+.f64 #s(literal 1/9 binary64) (*.f64 #s(approx (- x -1/3) #s(literal 1/3 binary64)) x)) |
#s(approx (- x -1/3) #s(literal 1/3 binary64)) |
Compiled 7 112 to 719 computations (89.9% saved)
5 alts after pruning (0 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 308 | 0 | 308 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 2 | 2 |
| Done | 0 | 3 | 3 |
| Total | 308 | 5 | 313 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 67.5% | (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) |
| ✓ | 49.8% | (/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) |
| ✓ | 100.0% | (-.f64 x #s(literal 1/3 binary64)) |
| ✓ | 99.7% | (*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) |
| ✓ | 49.9% | #s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) |
Compiled 108 to 54 computations (50% saved)
| Inputs |
|---|
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) |
(-.f64 x #s(literal 1/3 binary64)) |
(*.f64 #s(approx (+ (* x x) -1/9) #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) |
(-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) |
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(approx (/ -1 (- -1/3 x)) (fma.f64 #s(literal -9 binary64) x #s(literal 3 binary64)))) |
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x #s(approx (- x -1/3) #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) |
(/.f64 #s(approx (+ (* (* x x) x) -1/27) #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) |
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/3 binary64) x))) |
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x (-.f64 x #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) |
| Outputs |
|---|
(-.f64 x #s(literal 1/3 binary64)) |
2 calls:
| 7.0ms | (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) |
Compiled 8 to 6 computations (25% saved)
Total -0.0b remaining (-0%)
Threshold costs -0b (-0%)
| Inputs |
|---|
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) |
| Outputs |
|---|
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) |
2 calls:
| 1.0ms | x |
| 1.0ms | (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 49.9% | 1 | x |
| 49.9% | 1 | (-.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) |
Compiled 8 to 6 computations (25% saved)
| 1× | egg-herbie |
| 4× | +-commutative_binary64 |
| 4× | sub-neg_binary64 |
| 2× | *-commutative_binary64 |
| 2× | 1-exp_binary64 |
| 2× | neg-sub0_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 8 |
| 1 | 14 | 8 |
| 2 | 18 | 8 |
| 3 | 20 | 8 |
| 4 | 21 | 8 |
| 1× | saturated |
| Inputs |
|---|
(-.f64 x #s(literal 1/3 binary64)) |
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) |
| Outputs |
|---|
(-.f64 x #s(literal 1/3 binary64)) |
#s(approx (- x (/ 1 3)) #s(literal -1/3 binary64)) |
| 6 912× | lower-fma.f64 |
| 6 912× | lower-fma.f32 |
| 4 474× | lower-*.f64 |
| 4 474× | lower-*.f32 |
| 3 944× | lower-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 30 |
| 1 | 32 | 30 |
| 2 | 75 | 30 |
| 3 | 158 | 30 |
| 4 | 412 | 30 |
| 5 | 523 | 30 |
| 6 | 576 | 30 |
| 7 | 599 | 30 |
| 8 | 601 | 30 |
| 0 | 601 | 30 |
| 0 | 5 | 4 |
| 0 | 8 | 4 |
| 1 | 27 | 4 |
| 2 | 129 | 4 |
| 3 | 979 | 4 |
| 0 | 8557 | 4 |
| 1× | done |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | saturated |
Compiled 17 to 13 computations (23.5% saved)
Compiled 24 to 18 computations (25% saved)
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