
Time bar (total: 4.7s)
| 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)
| 451.0ms | 8 256× | 0 | valid |
ival-div: 213.0ms (79.6% of total)ival-add: 39.0ms (14.6% of total)exact: 7.0ms (2.6% of total)ival-true: 6.0ms (2.2% of total)ival-assert: 3.0ms (1.1% 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 #s(literal 1 binary64) #s(literal 3 binary64)) |
| 0 | 0 | - | 0 | - | (+.f64 x (/.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 |
| 38.0ms | 512× | 0 | valid |
Compiled 32 to 19 computations (40.6% saved)
ival-div: 4.0ms (51.7% of total)ival-add: 2.0ms (25.9% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
| 6× | associate--r+ |
| 6× | sub-neg |
| 5× | distribute-lft-neg-in |
| 5× | associate-+l- |
| 5× | distribute-neg-in |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 9 |
| 1 | 20 | 6 |
| 2 | 42 | 6 |
| 3 | 74 | 6 |
| 4 | 96 | 6 |
| 5 | 106 | 6 |
| 0 | 5 | 3 |
| 0 | 8 | 3 |
| 1 | 11 | 3 |
| 0 | 11 | 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 #s(literal 1/3 binary64) x) |
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)) |
| 2× | lower-+.f32 |
| 1× | lift-+.f64 |
| 1× | lift-/.f64 |
| 1× | lower-+.f64 |
| 1× | 1-exp |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 5 | 7 |
| 0 | 8 | 7 |
| 1 | 11 | 7 |
| 0 | 11 | 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 #s(literal 1/3 binary64) x) |
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 | 0.00390625 | (+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) |
| 12.0ms | 256× | 0 | valid |
Compiled 13 to 7 computations (46.2% saved)
ival-div: 2.0ms (54.5% of total)ival-add: 1.0ms (27.3% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (/.f64 #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 (+ 1/3 x) (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 (+ 1/3 x) (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 (+ 1/3 x) (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 (* 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>) () ())) ()) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | inf | (+ x (/ 1 3)) |
| 0.0ms | x | @ | -inf | (+ x (/ 1 3)) |
| 0.0ms | x | @ | 0 | (+ x (/ 1 3)) |
| 1× | egg-herbie |
| 18× | lower-*.f64 |
| 18× | lower-*.f32 |
| 8× | lower-/.f32 |
| 8× | associate-*r* |
| 8× | lower-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 30 |
| 1 | 22 | 30 |
| 2 | 37 | 30 |
| 3 | 77 | 30 |
| 4 | 77 | 30 |
| 5 | 78 | 30 |
| 6 | 80 | 30 |
| 7 | 80 | 30 |
| 0 | 80 | 30 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
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)))) |
| Outputs |
|---|
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)) |
| 4 354× | lower-fma.f64 |
| 4 354× | lower-fma.f32 |
| 2 558× | lower-*.f64 |
| 2 558× | lower-*.f32 |
| 1 934× | lower-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 5 | 4 |
| 0 | 8 | 4 |
| 1 | 25 | 4 |
| 2 | 126 | 4 |
| 3 | 957 | 4 |
| 0 | 8643 | 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 (*.f64 x x) x) x) (*.f64 x x) #s(literal -1/729 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 (*.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) 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 (*.f64 x x) x) x) x) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal 1/19683 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x (-.f64 #s(literal 1/729 binary64) (*.f64 #s(literal 1/27 binary64) (*.f64 (*.f64 x x) x)))))) |
(*.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)))) (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 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal -1/3 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 (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 x x) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))))) (fma.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (fma.f64 #s(literal -1/3 binary64) x (-.f64 #s(literal 1/9 binary64) (*.f64 x x))) (*.f64 (*.f64 (*.f64 x x) 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) (fma.f64 (neg.f64 x) (*.f64 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 (*.f64 (*.f64 (*.f64 x x) 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) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 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))) (-.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal 1/3 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 x #s(literal 1/3 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) (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) 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) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))) (-.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal 1/3 binary64)))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) 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) (fma.f64 x x #s(literal 1/9 binary64)) #s(literal 1/81 binary64))) (-.f64 x #s(literal 1/3 binary64)))) |
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) 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) (fma.f64 x x #s(literal 1/9 binary64)) #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 (*.f64 x x) x) x) (*.f64 x x) #s(literal -1/729 binary64)) (fma.f64 x x #s(literal -1/9 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))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) 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)) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal -1/27 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 (*.f64 x x) x) x) (*.f64 x x) #s(literal -1/729 binary64)) (*.f64 (fma.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)) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal -1/3 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 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (fma.f64 #s(literal -1/3 binary64) x (-.f64 #s(literal 1/9 binary64) (*.f64 x x))) (*.f64 (*.f64 (*.f64 x x) x) x))))) |
(*.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)) (*.f64 (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x (-.f64 #s(literal 1/729 binary64) (*.f64 #s(literal 1/27 binary64) (*.f64 (*.f64 x x) x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal -1/3 binary64))))))) |
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(+.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 x #s(literal 1/3 binary64) #s(literal 1/9 binary64)))) |
(+.f64 (*.f64 (/.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)) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (fma.f64 x x #s(literal -1/9 binary64))) (*.f64 (/.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)) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (*.f64 x #s(literal 1/3 binary64)))) |
(+.f64 (*.f64 (/.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)) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (*.f64 x x)) (*.f64 (/.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)) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (neg.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64))))) |
(+.f64 (*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (*.f64 (fma.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)) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) (*.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (fma.f64 #s(literal -1/3 binary64) x (-.f64 #s(literal 1/9 binary64) (*.f64 x x))))) (*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (*.f64 (fma.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)) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) (*.f64 (*.f64 (*.f64 x x) x) x))) |
(+.f64 (*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (*.f64 (fma.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)) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) (*.f64 (*.f64 (*.f64 x x) x) x)) (*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (*.f64 (fma.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)) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/9 binary64) (*.f64 x (-.f64 x #s(literal -1/3 binary64)))))) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) (*.f64 (fma.f64 #s(literal -1/3 binary64) x #s(literal 1/9 binary64)) (fma.f64 #s(literal -1/3 binary64) x (-.f64 #s(literal 1/9 binary64) (*.f64 x x)))))) |
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x)) #s(literal -1/9 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x)) (*.f64 x x))) |
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x)) (*.f64 x x)) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x)) #s(literal -1/9 binary64))) |
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #s(literal 1/27 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (*.f64 (*.f64 x x) x))) |
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (*.f64 (*.f64 x x) x)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) #s(literal 1/27 binary64))) |
(+.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 1/3 binary64)) |
(+.f64 (/.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 x (/.f64 x (-.f64 x #s(literal 1/3 binary64)))) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/9 binary64) (-.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 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 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1/3 binary64) x) |
Compiled 7 860 to 629 computations (92% saved)
3 alts after pruning (3 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 272 | 3 | 275 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 273 | 3 | 276 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 65.1% | (/.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)) |
| ▶ | 48.7% | #s(approx (+ x (/ 1 3)) #s(literal 1/3 binary64)) |
Compiled 21 to 14 computations (33.3% saved)
| 1× | egg-herbie |
Found 6 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 | #s(approx (+ x (/ 1 3)) #s(literal 1/3 binary64)) |
| 18× | lower-+.f64 |
| 18× | lower-+.f32 |
| 13× | lower-fma.f32 |
| 11× | lower-fma.f64 |
| 8× | +-commutative |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 46 |
| 0 | 24 | 46 |
| 1 | 34 | 44 |
| 2 | 40 | 44 |
| 3 | 49 | 44 |
| 4 | 55 | 44 |
| 0 | 55 | 44 |
| 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 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 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 6 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0078125 | (-.f64 x #s(literal 1/3 binary64)) | |
| accuracy | 0.015625 | (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) | |
| accuracy | 0.0546875 | (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) | |
| accuracy | 21.664116308202175 | (/.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 | 0.00390625 | (-.f64 x #s(literal -1/3 binary64)) | |
| accuracy | 32.8269612340774 | #s(approx (+ x (/ 1 3)) #s(literal 1/3 binary64)) |
| 41.0ms | 256× | 0 | valid |
Compiled 52 to 19 computations (63.5% saved)
const: 14.0ms (44.4% of total)ival-div: 7.0ms (22.2% of total)ival-mult: 5.0ms (15.8% of total)ival-add: 3.0ms (9.5% of total)ival-sub: 2.0ms (6.3% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt #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 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 (+ 1/3 x) (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 x) (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 x) (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 (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>) () ())) ()) |
#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>) () ())) ()) |
#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 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 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 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 (+ 1/3 x) (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 (+ 1/3 x) (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 (+ 1/3 x) (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 (taylor inf 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 (* 1/3 (/ 1 x)))) (taylor inf 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 (* 1/3 (/ 1 x)))) (taylor inf 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 (* 1/3 (/ 1 x)))) (taylor inf 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 (taylor -inf 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 (* 1/3 (/ 1 x)))) (taylor -inf 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 (* 1/3 (/ 1 x)))) (taylor -inf 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 (* 1/3 (/ 1 x)))) (taylor -inf 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 (+ 1/27 (pow x 3)) (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 (+ 1/27 (pow x 3)) (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 (+ 1/27 (pow x 3)) (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) (taylor inf 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 (* 1/27 (/ 1 (pow x 3))))) (taylor inf 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 (* 1/27 (/ 1 (pow x 3))))) (taylor inf 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 (* 1/27 (/ 1 (pow x 3))))) (taylor inf 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) (taylor -inf 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 (* 1/27 (/ 1 (pow x 3))))) (taylor -inf 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 (* 1/27 (/ 1 (pow x 3))))) (taylor -inf 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 (* 1/27 (/ 1 (pow x 3))))) (taylor -inf 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 (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ()) |
#s(alt 1/9 (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 (- x 1/3))) (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 (- x 1/3))) (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 (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 (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 (/ (- 1/3 (* 1/9 (/ 1 x))) 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 (/ (- 1/3 (* 1/9 (/ 1 x))) 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 -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 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 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
21 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | inf | (/ (+ (* (* x x) x) 1/27) (+ (* x (- x 1/3)) 1/9)) |
| 1.0ms | x | @ | 0 | (/ (+ (* (* x x) x) 1/27) (+ (* x (- x 1/3)) 1/9)) |
| 0.0ms | x | @ | -inf | (/ (+ (* (* x x) x) 1/27) (+ (* x (- x 1/3)) 1/9)) |
| 0.0ms | x | @ | inf | (+ (* (* x x) x) 1/27) |
| 0.0ms | x | @ | 0 | (* x x) |
| 1× | egg-herbie |
| 3 889× | lower-fma.f64 |
| 3 889× | lower-fma.f32 |
| 1 652× | lower-*.f64 |
| 1 652× | lower-*.f32 |
| 791× | unsub-neg |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 42 | 280 |
| 1 | 120 | 280 |
| 2 | 294 | 272 |
| 3 | 944 | 272 |
| 4 | 2739 | 272 |
| 5 | 5071 | 272 |
| 6 | 7950 | 272 |
| 0 | 8188 | 265 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
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)))) |
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)))) |
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)))) |
1/27 |
(+ 1/27 (pow x 3)) |
(+ 1/27 (pow x 3)) |
(+ 1/27 (pow x 3)) |
(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 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) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
1/9 |
(+ 1/9 (* -1/3 x)) |
(+ 1/9 (* x (- x 1/3))) |
(+ 1/9 (* x (- x 1/3))) |
(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)))) |
(pow x 2) |
(* (pow x 2) (- 1 (* 1/3 (/ 1 x)))) |
(* (pow x 2) (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x)))) |
(* (pow x 2) (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x)))) |
-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) |
(+ 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)) |
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)) |
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)) |
1/27 |
#s(literal 1/27 binary64) |
(+ 1/27 (pow x 3)) |
(fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) |
(+ 1/27 (pow x 3)) |
(fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) |
(+ 1/27 (pow x 3)) |
(fma.f64 (*.f64 x x) x #s(literal 1/27 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 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) |
(*.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) |
(*.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 (- x 1/3))) |
(fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) |
(+ 1/9 (* x (- x 1/3))) |
(fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) |
(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)) |
(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 (/ (- 1/3 (* 1/9 (/ 1 x))) x)))) |
(fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) |
(* (pow x 2) (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x)))) |
(fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 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)) |
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)) |
| 2 210× | lower-fma.f32 |
| 2 208× | lower-fma.f64 |
| 2 043× | lower-*.f32 |
| 2 042× | lower-*.f64 |
| 1 715× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 39 |
| 0 | 24 | 28 |
| 1 | 91 | 28 |
| 2 | 581 | 28 |
| 3 | 7206 | 28 |
| 0 | 8515 | 28 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (+ x (/ 1 3)) #s(literal 1/3 binary64)) |
(-.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)) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (neg.f64 (fma.f64 x x #s(literal -1/9 binary64)))) (neg.f64 (-.f64 x #s(literal -1/3 binary64)))) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (neg.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (neg.f64 (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (*.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) (-.f64 (fma.f64 x x #s(literal -1/9 binary64)) (*.f64 #s(literal -1/3 binary64) x)))) (-.f64 (fma.f64 x x #s(literal -1/9 binary64)) (*.f64 #s(literal -1/3 binary64) x))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x (*.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))))) (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))) |
(*.f64 (/.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 binary64)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -1/19683 binary64))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x (fma.f64 (*.f64 #s(literal 1/27 binary64) x) (*.f64 x x) #s(literal 1/729 binary64)))) |
(*.f64 (/.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 binary64)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 binary64))) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))) |
(*.f64 (/.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)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #s(literal 1/729 binary64)) (-.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 binary64)) (*.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 x x) x))))) (-.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 binary64)) (*.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 x x) x)))) |
(*.f64 (/.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)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (fma.f64 (*.f64 (fma.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 x x) x) #s(literal 1/729 binary64)) (fma.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 x x) x) #s(literal 1/729 binary64))) (fma.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 x x) x) #s(literal 1/729 binary64)) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) (*.f64 (*.f64 (*.f64 x x) x) x)) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) (*.f64 (*.f64 (*.f64 x x) x) x))))) (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 (fma.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 x x) x) #s(literal 1/729 binary64)) (-.f64 (fma.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 x x) x) #s(literal 1/729 binary64)) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (-.f64 #s(literal 1/81 binary64) (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x))) (-.f64 #s(literal 1/9 binary64) (*.f64 (-.f64 x #s(literal 1/3 binary64)) x))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (neg.f64 (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x #s(literal -1/81 binary64)))) (fma.f64 (-.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (neg.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/729 binary64)))) (neg.f64 (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x))) |
(*.f64 (/.f64 (-.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x #s(literal -1/81 binary64))) (fma.f64 (-.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))) |
(*.f64 (/.f64 (-.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/729 binary64))) (neg.f64 (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 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)))) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) |
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x #s(literal -1/81 binary64)))) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/729 binary64)))) (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/27 binary64) (*.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)))) |
(*.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) x #s(literal 1/27 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 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)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #s(literal 1/729 binary64)))) |
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 binary64)) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x #s(literal -1/81 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 (-.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/729 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 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 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)) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x #s(literal -1/81 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #s(literal 1/729 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 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)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/729 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #s(literal 1/729 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))))) |
(*.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1/9 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) (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 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #s(literal 1/729 binary64)))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x #s(literal -1/81 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1/3 binary64) x) x #s(literal 1/9 binary64))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x #s(literal -1/81 binary64))) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/729 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/729 binary64))) (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))) |
(*.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 (fma.f64 x x #s(literal 1/9 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x #s(literal -1/81 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 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/729 binary64))) (*.f64 (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))) |
(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 binary64)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) |
(*.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) x))) |
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (-.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 x x) x))) |
(*.f64 (/.f64 #s(literal 1 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 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x)) (fma.f64 x x #s(literal -1/9 binary64))) |
(*.f64 (neg.f64 (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 binary64) (neg.f64 (-.f64 x #s(literal -1/3 binary64)))) |
(*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 binary64)) (/.f64 (/.f64 #s(literal 1 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 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 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 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 binary64)) (/.f64 #s(literal 1 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))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (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)))) |
(*.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x #s(literal -1/81 binary64)))) |
(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x))) |
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(/.f64 (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(literal 1 binary64)) (-.f64 x #s(literal -1/3 binary64))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x #s(literal -1/9 binary64)))) (neg.f64 (-.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)))) (neg.f64 (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 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 #s(literal 1 binary64) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #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 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (*.f64 (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))) #s(literal 1/27 binary64))) (*.f64 (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))) (fma.f64 #s(literal 1/3 binary64) x (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 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1/81 binary64)) (*.f64 (-.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))) |
(/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) |
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -1/19683 binary64)) (*.f64 (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x (fma.f64 (*.f64 #s(literal 1/27 binary64) x) (*.f64 x x) #s(literal 1/729 binary64))))) |
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1/9 binary64))) (neg.f64 (-.f64 x #s(literal -1/3 binary64)))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (neg.f64 (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/3 binary64) x)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 binary64)) (*.f64 (-.f64 x #s(literal -1/3 binary64)) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64))))) |
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 binary64)) (*.f64 (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 binary64)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64))) (-.f64 x #s(literal -1/3 binary64)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 binary64)) (*.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 #s(literal 1/3 binary64) x (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 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (+.f64 #s(literal 1/9 binary64) (-.f64 (*.f64 x x) (*.f64 #s(literal -1/3 binary64) x)))) |
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 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 (/.f64 (*.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 x x))) (-.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 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x #s(literal -1/729 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))) (neg.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))) |
(fma.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal 1/19683 binary64))) (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #s(literal 1/729 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 (/.f64 (*.f64 x x) (-.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 x x) x))) (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 (*.f64 x x) (neg.f64 (fma.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 (*.f64 x x) x) (*.f64 (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x 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 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))))) |
(fma.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x (*.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))))) (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 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))))) |
(fma.f64 (/.f64 (*.f64 x x) #s(literal 1 binary64)) (/.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 (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 #s(literal 1/3 binary64) x (fma.f64 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 (*.f64 x x) x #s(literal 1/27 binary64))) (/.f64 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 1/9 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 (*.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 (/.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 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x 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 (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 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))))) |
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #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) x #s(literal -1/3 binary64)) |
(fma.f64 x (/.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x 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))))) |
(fma.f64 x #s(literal 1 binary64) #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 x x) (/.f64 x (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))))) (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (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)) (/.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 (/.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 #s(literal 1 binary64) x) #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 x x) (/.f64 x (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))))) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #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 28 461 to 1 729 computations (93.9% saved)
3 alts after pruning (1 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 902 | 1 | 903 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 2 | 3 |
| Done | 0 | 0 | 0 |
| Total | 903 | 3 | 906 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 48.8% | (/.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)) |
| ✓ | 48.7% | #s(approx (+ x (/ 1 3)) #s(literal 1/3 binary64)) |
Compiled 17 to 12 computations (29.4% saved)
| 1× | egg-herbie |
Found 4 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))) |
| 16× | lower-+.f64 |
| 16× | lower-+.f32 |
| 13× | lower-fma.f32 |
| 12× | lower-fma.f64 |
| 7× | lower-*.f64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 11 | 38 |
| 0 | 15 | 38 |
| 1 | 22 | 34 |
| 2 | 29 | 34 |
| 3 | 38 | 34 |
| 4 | 44 | 34 |
| 0 | 44 | 34 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(/.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 #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 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0078125 | (-.f64 x #s(literal 1/3 binary64)) | |
| accuracy | 0.015625 | (fma.f64 x (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) | |
| accuracy | 21.664116308202175 | (/.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 | 32.81555264287227 | #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) |
| 30.0ms | 256× | 0 | valid |
Compiled 38 to 13 computations (65.8% saved)
ival-mult: 9.0ms (39.7% of total)const: 8.0ms (35.3% of total)ival-div: 2.0ms (8.8% of total)ival-add: 2.0ms (8.8% of total)ival-sub: 1.0ms (4.4% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#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 #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 (+ 1/3 x) (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 (+ 1/3 x) (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 (+ 1/3 x) (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 (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 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 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 (+ 1/27 (pow x 3)) (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 (+ 1/27 (pow x 3)) (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 (+ 1/27 (pow x 3)) (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) (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 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 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 (- x 1/3))) (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 (- x 1/3))) (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 (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 (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 (/ (- 1/3 (* 1/9 (/ 1 x))) 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 (/ (- 1/3 (* 1/9 (/ 1 x))) 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 -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 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 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/3 binary64)) (patch (-.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | 0 | (/ (+ (* (* x x) x) 1/27) (+ (* x (- x 1/3)) 1/9)) |
| 0.0ms | x | @ | -inf | (/ (+ (* (* x x) x) 1/27) (+ (* x (- x 1/3)) 1/9)) |
| 0.0ms | x | @ | inf | (/ (+ (* (* x x) x) 1/27) (+ (* x (- x 1/3)) 1/9)) |
| 0.0ms | x | @ | -inf | (- x 1/3) |
| 0.0ms | x | @ | -inf | (+ (* (* x x) x) 1/27) |
| 1× | egg-herbie |
| 3 889× | lower-fma.f64 |
| 3 889× | lower-fma.f32 |
| 1 652× | lower-*.f64 |
| 1 652× | lower-*.f32 |
| 791× | unsub-neg |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 42 | 184 |
| 1 | 120 | 184 |
| 2 | 293 | 176 |
| 3 | 949 | 176 |
| 4 | 2721 | 176 |
| 5 | 5050 | 176 |
| 6 | 7925 | 176 |
| 0 | 8170 | 169 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
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)))) |
1/27 |
(+ 1/27 (pow x 3)) |
(+ 1/27 (pow x 3)) |
(+ 1/27 (pow x 3)) |
(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 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))))) |
1/9 |
(+ 1/9 (* -1/3 x)) |
(+ 1/9 (* x (- x 1/3))) |
(+ 1/9 (* x (- x 1/3))) |
(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)))) |
(pow x 2) |
(* (pow x 2) (- 1 (* 1/3 (/ 1 x)))) |
(* (pow x 2) (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x)))) |
(* (pow x 2) (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x)))) |
-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) |
(+ 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)) |
1/27 |
#s(literal 1/27 binary64) |
(+ 1/27 (pow x 3)) |
(fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) |
(+ 1/27 (pow x 3)) |
(fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) |
(+ 1/27 (pow x 3)) |
(fma.f64 (*.f64 x x) x #s(literal 1/27 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 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)) |
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 (- x 1/3))) |
(fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) |
(+ 1/9 (* x (- x 1/3))) |
(fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) |
(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)) |
(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 (/ (- 1/3 (* 1/9 (/ 1 x))) x)))) |
(fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) |
(* (pow x 2) (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x)))) |
(fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 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)) |
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)) |
| 2 295× | lower-fma.f32 |
| 2 294× | lower-fma.f64 |
| 2 017× | lower-*.f64 |
| 2 017× | lower-*.f32 |
| 1 577× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 11 | 34 |
| 0 | 15 | 30 |
| 1 | 70 | 30 |
| 2 | 447 | 30 |
| 3 | 4506 | 30 |
| 0 | 8708 | 30 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.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 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (-.f64 #s(literal 1/81 binary64) (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))))) (-.f64 #s(literal 1/9 binary64) (*.f64 (-.f64 x #s(literal 1/3 binary64)) x))) |
(*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (neg.f64 (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/81 binary64)))) (fma.f64 (neg.f64 x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) |
(*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (neg.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/729 binary64)))) (neg.f64 (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))) |
(*.f64 (/.f64 (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/81 binary64))) (fma.f64 (neg.f64 x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) |
(*.f64 (/.f64 (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/729 binary64))) (neg.f64 (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)))) |
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/81 binary64)))) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/729 binary64)))) (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))) |
(*.f64 (pow.f64 (/.f64 (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 -1/2 binary64)) (pow.f64 (/.f64 (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 -1/2 binary64))) |
(*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))) |
(*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/81 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))))) |
(*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/81 binary64))) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64))) |
(*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/729 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))))) |
(*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/729 binary64))) (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/81 binary64))) (*.f64 (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)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/729 binary64))) (*.f64 (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)))) |
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))))) |
(*.f64 (/.f64 #s(literal 1 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))) |
(*.f64 #s(literal -1 binary64) (/.f64 (neg.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)))) |
(*.f64 (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/81 binary64)))) |
(*.f64 #s(literal 1 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)))) |
(*.f64 (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)) (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/729 binary64)))) |
(*.f64 (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))) |
(*.f64 (/.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(literal 1 binary64)) |
(*.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)))) |
(pow.f64 (exp.f64 (log.f64 (/.f64 (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 binary64)) |
(pow.f64 (*.f64 (/.f64 (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))) (/.f64 (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 -1/2 binary64)) |
(pow.f64 (pow.f64 (/.f64 (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 -1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (/.f64 (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 binary64)) |
(pow.f64 (/.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(literal 1 binary64)) |
(/.f64 (/.f64 (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) #s(literal -1 binary64)) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) |
(/.f64 (*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/81 binary64))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/729 binary64))) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x (fma.f64 (*.f64 #s(literal 1/9 binary64) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/81 binary64)))) |
(/.f64 (*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/81 binary64))) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/81 binary64))) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64))) |
(/.f64 (*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/729 binary64))) (*.f64 (fma.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal -1/9 binary64)) #s(literal 1/81 binary64)) (-.f64 (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/81 binary64)) (*.f64 #s(literal -1/9 binary64) (*.f64 (-.f64 x #s(literal 1/3 binary64)) x))))) (-.f64 (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/81 binary64)) (*.f64 #s(literal -1/9 binary64) (*.f64 (-.f64 x #s(literal 1/3 binary64)) x)))) |
(/.f64 (*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/729 binary64))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) (-.f64 x #s(literal 1/3 binary64))) (*.f64 x x)) x)) (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) (*.f64 (*.f64 (fma.f64 #s(literal -1/9 binary64) (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal 1/81 binary64)) (fma.f64 #s(literal -1/9 binary64) (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal 1/81 binary64))) (fma.f64 #s(literal -1/9 binary64) (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal 1/81 binary64))))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x)) x (*.f64 (fma.f64 #s(literal -1/9 binary64) (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal 1/81 binary64)) (-.f64 (fma.f64 #s(literal -1/9 binary64) (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) #s(literal 1/81 binary64)) (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))))))) |
(/.f64 (*.f64 (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) #s(literal 1 binary64)) (fma.f64 (neg.f64 x) (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64))) |
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)))) (fma.f64 (neg.f64 x) (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/9 binary64))) |
(/.f64 (*.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64))) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/729 binary64))) (*.f64 (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) x) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal -1/81 binary64)) (fma.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/3 binary64)) (-.f64 x #s(literal 1/3 binary64))) x) x (fma.f64 (*.f64 #s(literal 1/9 binary64) x) (-.f64 x #s(literal 1/3 binary64)) #s(literal 1/81 binary64))))) |
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(*.f64 (fma.f64 x x #s(literal -1/9 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64)))) |
(*.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))) |
(*.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal -1/3 binary64) x))))) |
(*.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))))) |
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal -1/3 binary64) x))) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))) #s(literal -1 binary64)) |
(/.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1/81 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 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)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1/3 binary64)))) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (*.f64 x x) x)) (*.f64 x x) #s(literal -1/19683 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x (fma.f64 (*.f64 #s(literal 1/27 binary64) x) (*.f64 x x) #s(literal 1/729 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))))) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))) (*.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64))))) (*.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal -1/3 binary64))))) (fma.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 (*.f64 (*.f64 x x) x) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))))) (*.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))))) (fma.f64 x (/.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))))) |
(/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 x x)) (-.f64 #s(literal -1/3 binary64) x)) |
(/.f64 (-.f64 (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x)) (*.f64 (*.f64 (-.f64 x #s(literal -1/3 binary64)) (-.f64 x #s(literal -1/3 binary64))) (-.f64 x #s(literal -1/3 binary64)))) (/.f64 #s(literal 1/729 binary64) (*.f64 (*.f64 (-.f64 x #s(literal -1/3 binary64)) (-.f64 x #s(literal -1/3 binary64))) (-.f64 x #s(literal -1/3 binary64))))) (fma.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))) (*.f64 x (/.f64 x (-.f64 x #s(literal -1/3 binary64)))) (fma.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 x #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (-.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 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x)) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))))) (/.f64 #s(literal 1/19683 binary64) (*.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (fma.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (*.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x x #s(literal -1/9 binary64)))) (neg.f64 (neg.f64 (-.f64 x #s(literal -1/3 binary64))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))))) |
(/.f64 (*.f64 (fma.f64 x x #s(literal -1/9 binary64)) #s(literal 1 binary64)) (-.f64 x #s(literal -1/3 binary64))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1/81 binary64)) #s(literal 1 binary64)) (*.f64 (fma.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) (*.f64 (*.f64 x x) x)) (*.f64 x x) #s(literal -1/19683 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x (fma.f64 (*.f64 #s(literal 1/27 binary64) x) (*.f64 x x) #s(literal 1/729 binary64))) (fma.f64 #s(literal 1/3 binary64) x (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(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64))) (-.f64 x #s(literal -1/3 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #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 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (*.f64 (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))) #s(literal 1/27 binary64))) (*.f64 (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))))) |
(/.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1/81 binary64)) (*.f64 (-.f64 x #s(literal -1/3 binary64)) (fma.f64 x x #s(literal 1/9 binary64)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (*.f64 x x) x)) (*.f64 x x) #s(literal -1/19683 binary64)) (*.f64 (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal -1/3 binary64) x))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x (fma.f64 (*.f64 #s(literal 1/27 binary64) x) (*.f64 x x) #s(literal 1/729 binary64))))) |
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (*.f64 x x) x)) (*.f64 x x) #s(literal -1/19683 binary64)) (*.f64 (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))) (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) x (fma.f64 (*.f64 #s(literal 1/27 binary64) x) (*.f64 x x) #s(literal 1/729 binary64))))) |
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1/9 binary64))) (neg.f64 (-.f64 x #s(literal -1/3 binary64)))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal -1/3 binary64) x))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (neg.f64 (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 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) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) (*.f64 (-.f64 x #s(literal -1/3 binary64)) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 #s(literal 1/9 binary64) (*.f64 x x) #s(literal 1/81 binary64))))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) (*.f64 (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal -1/3 binary64) x))) (fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal -1/729 binary64)) (*.f64 (fma.f64 #s(literal 1/3 binary64) x (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) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal -1/3 binary64) x))) (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64)))) |
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (+.f64 #s(literal 1/9 binary64) (-.f64 (*.f64 x x) (*.f64 #s(literal -1/3 binary64) x)))) |
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal -1/3 binary64) x)))) |
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) |
(neg.f64 (/.f64 (neg.f64 (fma.f64 x x #s(literal -1/9 binary64))) (-.f64 x #s(literal -1/3 binary64)))) |
(neg.f64 (/.f64 (neg.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64))) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))))) |
(neg.f64 (/.f64 (fma.f64 x x #s(literal -1/9 binary64)) (neg.f64 (-.f64 x #s(literal -1/3 binary64))))) |
(neg.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/27 binary64)) (neg.f64 (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))))) |
(fma.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))) (-.f64 (fma.f64 x x #s(literal -1/9 binary64)) (*.f64 #s(literal 1/3 binary64) x)))) (-.f64 (fma.f64 x x #s(literal -1/9 binary64)) (*.f64 #s(literal 1/3 binary64) x)) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x 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 x x) x) x) (*.f64 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 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 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))) (-.f64 (fma.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 (sqrt.f64 x) (sqrt.f64 x) #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 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))))) |
(fma.f64 (*.f64 (*.f64 x x) x) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))))) |
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x 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 x (/.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x 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 x x) x) (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal -1/3 binary64) x)))) (/.f64 #s(literal 1/27 binary64) (fma.f64 x x (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal -1/3 binary64) x))))) |
(-.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 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64))))) |
(-.f64 x #s(literal 1/3 binary64)) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/3 binary64)))) #s(literal -1 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 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))) (neg.f64 (/.f64 #s(literal 1/27 binary64) (fma.f64 #s(literal 1/3 binary64) x (fma.f64 x x #s(literal 1/9 binary64)))))) |
(+.f64 #s(literal -1/3 binary64) x) |
(+.f64 x #s(literal -1/3 binary64)) |
Compiled 8 293 to 862 computations (89.6% saved)
3 alts after pruning (1 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 293 | 1 | 294 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 2 | 2 |
| Total | 294 | 3 | 297 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 48.1% | (/.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)) |
| ✓ | 48.7% | #s(approx (+ x (/ 1 3)) #s(literal 1/3 binary64)) |
Compiled 16 to 11 computations (31.3% saved)
| 1× | egg-herbie |
Found 4 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))) |
| 6× | lower-+.f64 |
| 6× | lower-+.f32 |
| 5× | lower-*.f64 |
| 5× | lower-*.f32 |
| 4× | lower-fma.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 44 |
| 0 | 16 | 44 |
| 1 | 22 | 40 |
| 2 | 25 | 40 |
| 0 | 25 | 40 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(/.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) 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 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.015625 | (fma.f64 x #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(literal 1/9 binary64)) | |
| accuracy | 21.664116308202175 | (/.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 | 32.81555264287227 | #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) | |
| accuracy | 32.90052258737504 | #s(approx (- x 1/3) #s(literal -1/3 binary64)) |
| 30.0ms | 256× | 0 | valid |
Compiled 38 to 14 computations (63.2% saved)
const: 11.0ms (47.3% of total)ival-mult: 7.0ms (30.1% of total)ival-div: 2.0ms (8.6% of total)ival-add: 2.0ms (8.6% of total)ival-sub: 1.0ms (4.3% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#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) 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 (+ 1/3 x) (taylor 0 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 (+ 1/3 x) (taylor 0 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 (+ 1/3 x) (taylor 0 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 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 (* 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 #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 (* 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 #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 (* 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 #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 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 (* 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 #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 (* 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 #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 (* 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 #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 1/27 (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 (+ 1/27 (pow x 3)) (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 (+ 1/27 (pow x 3)) (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 (+ 1/27 (pow x 3)) (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) (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 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 1/9 (taylor 0 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 (+ 1/9 (* -1/3 x)) (taylor 0 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 (+ 1/9 (* x (- x 1/3))) (taylor 0 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 (+ 1/9 (* x (- x 1/3))) (taylor 0 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) (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 (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 (/ (- 1/3 (* 1/9 (/ 1 x))) 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 (/ (- 1/3 (* 1/9 (/ 1 x))) 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 -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 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>) () ())) ()) |
#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 (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (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 (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (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 (* -1 (* x (- (* 1/3 (/ 1 x)) 1))) (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>) () ())) ()) |
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | 0 | (/ (+ (* (* x x) x) 1/27) (+ (* x (- x 1/3)) 1/9)) |
| 0.0ms | x | @ | -inf | (/ (+ (* (* x x) x) 1/27) (+ (* x (- x 1/3)) 1/9)) |
| 0.0ms | x | @ | inf | (/ (+ (* (* x x) x) 1/27) (+ (* x (- x 1/3)) 1/9)) |
| 0.0ms | x | @ | -inf | (- x 1/3) |
| 0.0ms | x | @ | inf | (+ (* (* x x) x) 1/27) |
| 1× | egg-herbie |
| 3 889× | lower-fma.f64 |
| 3 889× | lower-fma.f32 |
| 1 652× | lower-*.f64 |
| 1 652× | lower-*.f32 |
| 791× | unsub-neg |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 42 | 184 |
| 1 | 120 | 184 |
| 2 | 293 | 176 |
| 3 | 949 | 176 |
| 4 | 2721 | 176 |
| 5 | 5050 | 176 |
| 6 | 7925 | 176 |
| 0 | 8170 | 169 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
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)))) |
1/27 |
(+ 1/27 (pow x 3)) |
(+ 1/27 (pow x 3)) |
(+ 1/27 (pow x 3)) |
(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 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))))) |
1/9 |
(+ 1/9 (* -1/3 x)) |
(+ 1/9 (* x (- x 1/3))) |
(+ 1/9 (* x (- x 1/3))) |
(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)))) |
(pow x 2) |
(* (pow x 2) (- 1 (* 1/3 (/ 1 x)))) |
(* (pow x 2) (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x)))) |
(* (pow x 2) (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x)))) |
-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) |
(+ 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)) |
1/27 |
#s(literal 1/27 binary64) |
(+ 1/27 (pow x 3)) |
(fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) |
(+ 1/27 (pow x 3)) |
(fma.f64 (*.f64 x x) x #s(literal 1/27 binary64)) |
(+ 1/27 (pow x 3)) |
(fma.f64 (*.f64 x x) x #s(literal 1/27 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 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)) |
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 (- x 1/3))) |
(fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) |
(+ 1/9 (* x (- x 1/3))) |
(fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) |
(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)) |
(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 (/ (- 1/3 (* 1/9 (/ 1 x))) x)))) |
(fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 binary64)) |
(* (pow x 2) (+ 1 (* -1 (/ (- 1/3 (* 1/9 (/ 1 x))) x)))) |
(fma.f64 (-.f64 x #s(literal 1/3 binary64)) x #s(literal 1/9 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)) |
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)) |
| 2 512× | lower-fma.f32 |
| 2 511× | lower-fma.f64 |
| 2 390× | lower-*.f64 |
| 2 390× | lower-*.f32 |
| 1 366× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 40 |
| 0 | 16 | 36 |
| 1 | 70 | 36 |
| 2 | 436 | 36 |
| 3 | 3798 | 36 |
| 0 | 8521 | 36 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.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 (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) |
(*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (-.f64 #s(literal 1/81 binary64) (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)))) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x))) |
(*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (neg.f64 (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64)))) (neg.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))) |
(*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (neg.f64 x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)) #s(literal -1/729 binary64))) (neg.f64 (fma.f64 (*.f64 #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)) #s(literal 1/81 binary64)))) |
(*.f64 (/.f64 (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64))) (neg.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))) |
(*.f64 (/.f64 (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) (fma.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64)))) (*.f64 x x) #s(literal 1/729 binary64))) (neg.f64 (fma.f64 (*.f64 #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)) #s(literal 1/81 binary64)))) |
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #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(literal 1 binary64) (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64)))) (*.f64 x x) #s(literal 1/729 binary64)))) (fma.f64 (*.f64 #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)) #s(literal 1/81 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) |
(*.f64 (pow.f64 (/.f64 (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 -1/2 binary64)) (pow.f64 (/.f64 (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 -1/2 binary64))) |
(*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64))) (pow.f64 (/.f64 (/.f64 #s(literal 1 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 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (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 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64))) (*.f64 (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)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64)))) (*.f64 x x) #s(literal 1/729 binary64))) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #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)) #s(literal 1/81 binary64))) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64)))) (*.f64 x x) #s(literal 1/729 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (*.f64 #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)) #s(literal 1/81 binary64)) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)))) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64)))) (*.f64 x x) #s(literal 1/729 binary64))) (*.f64 (fma.f64 (*.f64 #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)) #s(literal 1/81 binary64)) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)))) |
(*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))))) |
(*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #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 x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64)))) (*.f64 x x) #s(literal 1/729 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #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)) #s(literal 1/81 binary64))))) |
(*.f64 (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64)))) (*.f64 x x) #s(literal 1/729 binary64))) (fma.f64 (*.f64 #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)) #s(literal 1/81 binary64))) |
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)))) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))))) |
(*.f64 (/.f64 #s(literal 1 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))) |
(*.f64 #s(literal -1 binary64) (/.f64 (neg.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)))) |
(*.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)) (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64)))) |
(*.f64 #s(literal 1 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)))) |
(*.f64 (fma.f64 (*.f64 #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)) #s(literal 1/81 binary64)) (/.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (fma.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64)))) (*.f64 x x) #s(literal 1/729 binary64)))) |
(*.f64 (neg.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) |
(*.f64 (/.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(literal 1 binary64)) |
(*.f64 #s(approx (+ (* (* x x) x) 1/27) #s(literal 1/27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) |
(pow.f64 (exp.f64 (log.f64 (/.f64 (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 binary64)) |
(pow.f64 (*.f64 (/.f64 (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))) (/.f64 (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 -1/2 binary64)) |
(pow.f64 (pow.f64 (/.f64 (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 -1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (/.f64 (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 binary64)) |
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(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64))) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64))) #s(approx (- x 1/3) #s(literal -1/3 binary64)))) (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64))) #s(approx (- x 1/3) #s(literal -1/3 binary64)))) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) x) (*.f64 (*.f64 (*.f64 x x) x) x)) #s(literal 1/387420489 binary64)) (*.f64 (fma.f64 (*.f64 #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)) #s(literal 1/81 binary64)) (fma.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)) (*.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64)))) (*.f64 x x))) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (-.f64 #s(literal 1/531441 binary64) (*.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)) (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal 1/729 binary64))))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64))) (*.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64))) (neg.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))) |
(/.f64 (fma.f64 (*.f64 (neg.f64 x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)) #s(literal -1/729 binary64)) (*.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 #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)) #s(literal 1/81 binary64))))) |
(/.f64 (fma.f64 (*.f64 (neg.f64 x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)) #s(literal -1/729 binary64)) (neg.f64 (fma.f64 (*.f64 #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)) #s(literal 1/81 binary64)))) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) |
(/.f64 (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64)) (*.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64)))) |
(/.f64 (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 binary64)) (neg.f64 (neg.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal -1/9 binary64))))) |
(/.f64 (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #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 1 binary64) (/.f64 (-.f64 #s(literal 1/9 binary64) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)) (-.f64 #s(literal 1/81 binary64) (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64)))) (*.f64 x x) #s(literal 1/729 binary64)) (*.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #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)) #s(literal 1/81 binary64)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64)))) (*.f64 x x) #s(literal 1/729 binary64)) (neg.f64 (neg.f64 (fma.f64 (*.f64 #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)) #s(literal 1/81 binary64))))) |
(/.f64 (fma.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64)))) (*.f64 x x) #s(literal 1/729 binary64)) (fma.f64 (*.f64 #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)) #s(literal 1/81 binary64))) |
(/.f64 (-.f64 #s(literal -1/9 binary64) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)) #s(literal -1 binary64)) |
(/.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)) #s(literal 1 binary64)) |
(neg.f64 (-.f64 #s(literal -1/9 binary64) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x))) |
(fma.f64 (exp.f64 (log.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)))) x #s(literal 1/9 binary64)) |
(fma.f64 (pow.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x #s(literal 1/9 binary64)) |
(fma.f64 (/.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)) (fma.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64)))) (*.f64 x x) #s(literal -1/729 binary64))) (fma.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 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal 1/9 binary64) #s(literal 1/81 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 (/.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)) (fma.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(literal -1/81 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 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) x) (/.f64 #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 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (/.f64 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 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (/.f64 (*.f64 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 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)) (/.f64 #s(literal 1 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 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (/.f64 (*.f64 #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 #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 (exp.f64 (log.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)))) #s(literal 1/9 binary64)) |
(fma.f64 x (pow.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) #s(literal 1 binary64)) #s(literal 1/9 binary64)) |
(fma.f64 x (/.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) 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))))) |
(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 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x)))) |
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (/.f64 x (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 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (/.f64 x (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))) |
(exp.f64 (neg.f64 (*.f64 (log.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal -1 binary64)))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x #s(literal 1/9 binary64)))) #s(literal -1 binary64))) |
(+.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 #s(approx (- x 1/3) #s(literal -1/3 binary64)) x) #s(approx (- x 1/3) #s(literal -1/3 binary64))) (/.f64 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))))) |
(+.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 6 787 to 651 computations (90.4% saved)
3 alts after pruning (0 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 250 | 0 | 250 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 2 | 2 |
| Total | 250 | 3 | 253 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 48.1% | (/.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)) |
| ✓ | 48.7% | #s(approx (+ x (/ 1 3)) #s(literal 1/3 binary64)) |
Compiled 57 to 29 computations (49.1% saved)
| Inputs |
|---|
#s(approx (+ x (/ 1 3)) #s(literal 1/3 binary64)) |
(-.f64 x #s(literal -1/3 binary64)) |
(+.f64 x (/.f64 #s(literal 1 binary64) #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 (*.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:
| 2.0ms | x |
| 2.0ms | (+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) |
| 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 |
|---|---|---|
| 48.7% | 1 | x |
| 48.7% | 1 | (+.f64 x (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) |
Compiled 8 to 6 computations (25% saved)
| 1× | egg-herbie |
| 2× | +-commutative_binary64 |
| 2× | sub-neg_binary64 |
| 1× | *-commutative_binary64 |
| 1× | 1-exp_binary64 |
| 1× | 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)) |
| 4 354× | lower-fma.f64 |
| 4 354× | lower-fma.f32 |
| 2 558× | lower-*.f64 |
| 2 558× | lower-*.f32 |
| 1 934× | lower-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 30 |
| 1 | 22 | 30 |
| 2 | 37 | 30 |
| 3 | 77 | 30 |
| 4 | 77 | 30 |
| 5 | 78 | 30 |
| 6 | 80 | 30 |
| 7 | 80 | 30 |
| 0 | 80 | 30 |
| 0 | 5 | 4 |
| 0 | 8 | 4 |
| 1 | 25 | 4 |
| 2 | 126 | 4 |
| 3 | 957 | 4 |
| 0 | 8643 | 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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