
Time bar (total: 16.6s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 49.7% | 50.3% | 0% | 0% | 0% | 0 |
| 0% | 0% | 49.7% | 50.3% | 0% | 0% | 0% | 1 |
| 0% | 0% | 49.7% | 50.3% | 0% | 0% | 0% | 2 |
| 25% | 12.4% | 37.3% | 50.3% | 0% | 0% | 0% | 3 |
| 62.5% | 31.1% | 18.6% | 50.3% | 0% | 0% | 0% | 4 |
| 81.3% | 40.4% | 9.3% | 50.3% | 0% | 0% | 0% | 5 |
| 90.6% | 45% | 4.7% | 50.3% | 0% | 0% | 0% | 6 |
| 95.3% | 47.4% | 2.3% | 50.3% | 0% | 0% | 0% | 7 |
| 97.7% | 48.5% | 1.2% | 50.3% | 0% | 0% | 0% | 8 |
| 98.8% | 49.1% | 0.6% | 50.3% | 0% | 0% | 0% | 9 |
| 99.4% | 49.4% | 0.3% | 50.3% | 0% | 0% | 0% | 10 |
| 99.7% | 49.5% | 0.1% | 50.3% | 0% | 0% | 0% | 11 |
| 99.9% | 49.6% | 0.1% | 50.3% | 0% | 0% | 0% | 12 |
Compiled 16 to 12 computations (25% saved)
| 7.4s | 3 852× | 2 | valid |
| 1.8s | 4 309× | 1 | valid |
| 8.0ms | 95× | 0 | valid |
ival-tan: 7.3s (84.3% of total)ival-div: 692.0ms (8% of total)const: 262.0ms (3% of total)adjust: 214.0ms (2.5% of total)ival-sub: 111.0ms (1.3% of total)ival-<: 60.0ms (0.7% of total)ival-and: 12.0ms (0.1% of total)exact: 5.0ms (0.1% of total)ival-assert: 3.0ms (0% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 256 | 0 | - | 0 | - | (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
| 0 | 0 | - | 0 | - | (/.f64 #s(literal 1 binary64) x) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (tan.f64 x) |
| 0 | 0 | - | 0 | - | (/.f64 #s(literal 1 binary64) (tan.f64 x)) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) | cancellation | 256 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 256 | 0 |
| - | 0 | 0 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 256 | 0 | 0 |
| - | 0 | 0 | 0 |
| number | freq |
|---|---|
| 1 | 256 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 597.0ms | 242× | 2 | valid |
| 74.0ms | 266× | 1 | valid |
| 0.0ms | 4× | 0 | valid |
Compiled 71 to 34 computations (52.1% saved)
ival-tan: 567.0ms (87.6% of total)adjust: 48.0ms (7.4% of total)ival-div: 25.0ms (3.9% of total)ival-sub: 6.0ms (0.9% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| 1× | egg-herbie |
| 112× | lower-fma.f64 |
| 112× | lower-fma.f32 |
| 80× | lower-*.f64 |
| 80× | lower-*.f32 |
| 48× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 21 |
| 1 | 21 | 19 |
| 2 | 54 | 16 |
| 3 | 131 | 16 |
| 4 | 204 | 16 |
| 5 | 228 | 16 |
| 6 | 230 | 16 |
| 0 | 6 | 8 |
| 0 | 10 | 8 |
| 1 | 14 | 8 |
| 2 | 22 | 8 |
| 3 | 31 | 8 |
| 4 | 43 | 8 |
| 5 | 63 | 8 |
| 6 | 102 | 8 |
| 7 | 134 | 8 |
| 8 | 192 | 8 |
| 9 | 225 | 8 |
| 10 | 247 | 8 |
| 0 | 247 | 8 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
| Outputs |
|---|
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) |
(negabs x)
Compiled 9 to 6 computations (33.3% saved)
Compiled 1 to 1 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 6.4% | (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
Compiled 9 to 6 computations (33.3% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (tan.f64 x) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (tan.f64 x)) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) x) | |
| cost-diff | 0 | (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
| 112× | lower-fma.f64 |
| 112× | lower-fma.f32 |
| 80× | lower-*.f64 |
| 80× | lower-*.f32 |
| 48× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 19 |
| 0 | 10 | 19 |
| 1 | 14 | 19 |
| 2 | 22 | 19 |
| 3 | 31 | 19 |
| 4 | 43 | 19 |
| 5 | 63 | 19 |
| 6 | 102 | 19 |
| 7 | 134 | 19 |
| 8 | 192 | 19 |
| 9 | 225 | 19 |
| 10 | 247 | 19 |
| 0 | 247 | 19 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
(tan.f64 x) |
| Outputs |
|---|
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
(tan.f64 x) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (/.f64 #s(literal 1 binary64) x) | |
| accuracy | 0 | (tan.f64 x) | |
| accuracy | 0.0078125 | (/.f64 #s(literal 1 binary64) (tan.f64 x)) | |
| accuracy | 59.88441128555766 | (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
| 353.0ms | 121× | 2 | valid |
| 118.0ms | 133× | 1 | valid |
| 0.0ms | 2× | 0 | valid |
Compiled 21 to 8 computations (61.9% saved)
ival-tan: 359.0ms (78.1% of total)ival-div: 91.0ms (19.8% of total)adjust: 6.0ms (1.3% of total)ival-sub: 3.0ms (0.7% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#<alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))> |
#<alt (/.f64 #s(literal 1 binary64) x)> |
#<alt (/.f64 #s(literal 1 binary64) (tan.f64 x))> |
#<alt (tan.f64 x)> |
| Outputs |
|---|
#<alt (* 1/3 x)> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))> |
#<alt (* -1 (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (* -1 (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ (+ 1 (* -1/3 (pow x 2))) x)> |
#<alt (/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)> |
#<alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt x> |
#<alt (* x (+ 1 (* 1/3 (pow x 2))))> |
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))> |
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (- (/ 1 x) (/ 1 (tan x))) |
| 1.0ms | x | @ | inf | (- (/ 1 x) (/ 1 (tan x))) |
| 1.0ms | x | @ | 0 | (- (/ 1 x) (/ 1 (tan x))) |
| 0.0ms | x | @ | -inf | (/ 1 (tan x)) |
| 0.0ms | x | @ | inf | (/ 1 (tan x)) |
| 1× | egg-herbie |
| 18 970× | lower-fma.f64 |
| 18 970× | lower-fma.f32 |
| 3 656× | lower-*.f64 |
| 3 656× | lower-*.f32 |
| 3 436× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 67 | 324 |
| 1 | 179 | 324 |
| 2 | 458 | 318 |
| 3 | 1321 | 318 |
| 4 | 2085 | 318 |
| 5 | 3083 | 318 |
| 6 | 3670 | 318 |
| 7 | 3941 | 318 |
| 8 | 5080 | 318 |
| 9 | 7268 | 318 |
| 0 | 8431 | 300 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/3 x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) |
(* -1 (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(* -1 (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ (+ 1 (* -1/3 (pow x 2))) x) |
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x) |
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
x |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
| Outputs |
|---|
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* -1 (/ (cos x) (sin x))) |
(/.f64 (cos.f64 x) (sin.f64 (neg.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(* -1 (/ (cos x) (sin x))) |
(/.f64 (cos.f64 x) (sin.f64 (neg.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ (+ 1 (* -1/3 (pow x 2))) x) |
(/.f64 (fma.f64 x (*.f64 x #s(literal -1/3 binary64)) #s(literal 1 binary64)) x) |
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x) |
(/.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x) |
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x) |
(/.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x) |
(/ (cos x) (sin x)) |
(/.f64 (cos.f64 x) (sin.f64 x)) |
(/ (cos x) (sin x)) |
(/.f64 (cos.f64 x) (sin.f64 x)) |
(/ (cos x) (sin x)) |
(/.f64 (cos.f64 x) (sin.f64 x)) |
(/ (cos x) (sin x)) |
(/.f64 (cos.f64 x) (sin.f64 x)) |
(/ (cos x) (sin x)) |
(/.f64 (cos.f64 x) (sin.f64 x)) |
(/ (cos x) (sin x)) |
(/.f64 (cos.f64 x) (sin.f64 x)) |
(/ (cos x) (sin x)) |
(/.f64 (cos.f64 x) (sin.f64 x)) |
(/ (cos x) (sin x)) |
(/.f64 (cos.f64 x) (sin.f64 x)) |
x |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(fma.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(fma.f64 x (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64))) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
(fma.f64 x (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) #s(literal 1/3 binary64))) x) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
| 3 072× | lower-fma.f64 |
| 3 072× | lower-fma.f32 |
| 2 002× | lower-*.f64 |
| 2 002× | lower-*.f32 |
| 1 374× | frac-times |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 17 |
| 0 | 10 | 17 |
| 1 | 49 | 17 |
| 2 | 454 | 17 |
| 3 | 5706 | 17 |
| 0 | 9203 | 17 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) x) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
(tan.f64 x) |
| Outputs |
|---|
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))) #s(literal -1 binary64))) |
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) x)) |
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))) (*.f64 x (*.f64 x x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x)))))) |
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 x x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))))) |
(+.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(-.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) x)) |
(-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))) (*.f64 x (*.f64 x x)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))))) |
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(*.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (pow.f64 (tan.f64 x) #s(literal -3 binary64)))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x)))) |
(*.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(*.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (pow.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x)) #s(literal 3 binary64)))) (fma.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x)) (-.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x)) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) |
(*.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x #s(literal 1 binary64)) (*.f64 (tan.f64 x) x)))) |
(*.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (-.f64 (/.f64 (tan.f64 x) x) #s(literal 1 binary64))) (tan.f64 x)) |
(*.f64 (/.f64 (+.f64 (tan.f64 x) x) (*.f64 (sin.f64 x) x)) (cos.f64 x)) |
(exp.f64 (neg.f64 (log.f64 x))) |
(exp.f64 (*.f64 (log.f64 (*.f64 x x)) #s(literal -1/2 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (neg.f64 (log.f64 x)) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)) #s(literal 2 binary64))) |
(exp.f64 (fma.f64 (log.f64 x) #s(literal -1/2 binary64) (*.f64 (log.f64 x) #s(literal -1/2 binary64)))) |
(exp.f64 (+.f64 (log.f64 (tan.f64 x)) (*.f64 (log.f64 (*.f64 (tan.f64 x) x)) #s(literal -1 binary64)))) |
(exp.f64 (+.f64 (log.f64 (tan.f64 x)) (neg.f64 (log.f64 (*.f64 (tan.f64 x) x))))) |
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x)) |
(neg.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (tan.f64 x) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (tan.f64 x) x) (tan.f64 x))) |
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) |
(/.f64 (tan.f64 x) (*.f64 (tan.f64 x) x)) |
(/.f64 (tan.f64 x) (*.f64 (*.f64 (tan.f64 x) x) #s(literal -1 binary64))) |
(/.f64 (sin.f64 x) (*.f64 (*.f64 (tan.f64 x) x) (cos.f64 x))) |
(/.f64 (sin.f64 x) (*.f64 (*.f64 (tan.f64 x) x) (neg.f64 (cos.f64 x)))) |
(/.f64 #s(literal -1 binary64) x) |
(/.f64 (/.f64 (tan.f64 x) x) (tan.f64 x)) |
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) |
(pow.f64 x #s(literal -1 binary64)) |
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64)) |
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (*.f64 (tan.f64 x) x)) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (*.f64 (tan.f64 x) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (*.f64 (tan.f64 x) x) (tan.f64 x)) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) |
(*.f64 (tan.f64 x) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 (tan.f64 x) x)) |
(*.f64 (sin.f64 x) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (tan.f64 x) x))) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (tan.f64 x) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(*.f64 (/.f64 (sin.f64 x) (tan.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) x)) |
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (tan.f64 x))) |
(*.f64 (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64))) |
(*.f64 (/.f64 (tan.f64 x) (*.f64 (sin.f64 x) x)) (cos.f64 x)) |
(exp.f64 (neg.f64 (log.f64 (tan.f64 x)))) |
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (tan.f64 x))) #s(literal -1/2 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (tan.f64 x))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal -1/2 binary64)) #s(literal 2 binary64))) |
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (*.f64 (tan.f64 x) x)) #s(literal -1 binary64)))) |
(exp.f64 (+.f64 (log.f64 x) (neg.f64 (log.f64 (*.f64 (tan.f64 x) x))))) |
(exp.f64 (fma.f64 (log.f64 (tan.f64 x)) #s(literal -1/2 binary64) (*.f64 (log.f64 (tan.f64 x)) #s(literal -1/2 binary64)))) |
(+.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (tan.f64 x) x) x)) |
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (tan.f64 x) x) (/.f64 #s(literal 1 binary64) x))) |
(/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)) |
(/.f64 (cos.f64 x) (sin.f64 x)) |
(/.f64 #s(literal -1 binary64) (tan.f64 x)) |
(/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))))) |
(/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 x (*.f64 (tan.f64 x) x)) |
(/.f64 x (*.f64 (*.f64 (tan.f64 x) x) #s(literal -1 binary64))) |
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x)) |
(/.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 x))) |
(/.f64 (/.f64 x (tan.f64 x)) x) |
(pow.f64 (tan.f64 x) #s(literal -1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)) |
(pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) |
(pow.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (/.f64 (*.f64 (tan.f64 x) x) x) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (*.f64 (tan.f64 x) x) (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 (tan.f64 x) x)) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (tan.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64)) |
(*.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) (sin.f64 x))) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(*.f64 x (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) x))) |
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)))) |
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 x)))) |
(*.f64 (/.f64 x (tan.f64 x)) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) |
(*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x))) (cos.f64 x)) |
(*.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x))) (cos.f64 x)) |
(*.f64 (/.f64 x (*.f64 (sin.f64 x) x)) (cos.f64 x)) |
(exp.f64 (log.f64 (tan.f64 x))) |
(exp.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64))) |
(+.f64 #s(literal 0 binary64) (tan.f64 x)) |
(-.f64 #s(literal 0 binary64) (tan.f64 x)) |
(tan.f64 x) |
(neg.f64 (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 (tan.f64 x) #s(literal 1 binary64)) |
(/.f64 (tan.f64 x) #s(literal -1 binary64)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/.f64 (sin.f64 x) (neg.f64 (cos.f64 x))) |
(/.f64 (sin.f64 x) (*.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))) |
(/.f64 (sin.f64 x) (*.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 x)))) |
(/.f64 (sin.f64 x) (neg.f64 (neg.f64 (cos.f64 x)))) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (tan.f64 x))))) |
(/.f64 (/.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) |
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x)) |
(/.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) |
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x))) (cos.f64 x)) |
(pow.f64 (tan.f64 x) #s(literal 1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) #s(literal -2 binary64)) |
(pow.f64 (*.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 #s(literal 1 binary64) (tan.f64 x)) |
(*.f64 (tan.f64 x) #s(literal 1 binary64)) |
(*.f64 (tan.f64 x) #s(literal -1 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) |
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))) |
(*.f64 (sin.f64 x) (neg.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)))) |
(*.f64 (sin.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) |
(*.f64 (sin.f64 x) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) |
(*.f64 #s(literal -1 binary64) (tan.f64 x)) |
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) |
Compiled 6 028 to 755 computations (87.5% saved)
3 alts after pruning (3 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 321 | 3 | 324 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 322 | 3 | 325 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.5% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
| ▶ | 99.4% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
| ▶ | 99.1% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) |
Compiled 30 to 18 computations (40% saved)
| 1× | egg-herbie |
Found 10 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) | |
| cost-diff | 0 | (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) | |
| cost-diff | 0 | #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) | |
| cost-diff | 0 | (*.f64 x #s(literal 1/45 binary64)) | |
| cost-diff | 0 | (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) | |
| cost-diff | 0 | (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) | |
| cost-diff | 0 | #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) | |
| cost-diff | 0 | (*.f64 #s(literal 1/3 binary64) x) | |
| cost-diff | 0 | #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) |
| 2 368× | lower-fma.f32 |
| 2 362× | lower-fma.f64 |
| 1 024× | lower-*.f32 |
| 1 012× | lower-*.f64 |
| 646× | associate-*r* |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 116 |
| 0 | 33 | 116 |
| 1 | 68 | 116 |
| 2 | 137 | 116 |
| 3 | 217 | 116 |
| 4 | 244 | 116 |
| 5 | 267 | 116 |
| 6 | 306 | 116 |
| 7 | 339 | 116 |
| 8 | 590 | 116 |
| 9 | 1943 | 116 |
| 10 | 2652 | 116 |
| 11 | 2752 | 116 |
| 12 | 2752 | 116 |
| 13 | 2754 | 116 |
| 14 | 2755 | 116 |
| 0 | 2755 | 116 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) |
(*.f64 #s(literal 1/3 binary64) x) |
#s(literal 1/3 binary64) |
x |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
x |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(*.f64 x #s(literal 1/45 binary64)) |
#s(literal 1/45 binary64) |
#s(literal 1/3 binary64) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
x |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(*.f64 x x) |
(fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) |
(*.f64 x #s(literal 2/945 binary64)) |
#s(literal 2/945 binary64) |
#s(literal 1/45 binary64) |
#s(literal 1/3 binary64) |
| Outputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64))) |
(*.f64 #s(literal 1/3 binary64) x) |
(*.f64 x #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
x |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
x |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(*.f64 x #s(literal 1/45 binary64)) |
#s(literal 1/45 binary64) |
#s(literal 1/3 binary64) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
x |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(*.f64 x x) |
(fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) |
(fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) |
(*.f64 x #s(literal 2/945 binary64)) |
#s(literal 2/945 binary64) |
#s(literal 1/45 binary64) |
#s(literal 1/3 binary64) |
Found 10 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0078125 | (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) | |
| accuracy | 0.0078125 | (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) | |
| accuracy | 0.296875 | (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) | |
| accuracy | 0.43359375 | (*.f64 x #s(literal 2/945 binary64)) | |
| accuracy | 0.0078125 | (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) | |
| accuracy | 0.0603895303525102 | #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) | |
| accuracy | 0.25 | (*.f64 x #s(literal 1/45 binary64)) | |
| accuracy | 0.30078125 | (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) | |
| accuracy | 0.30078125 | (*.f64 #s(literal 1/3 binary64) x) | |
| accuracy | 0.31022786707002425 | #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) |
| 272.0ms | 121× | 2 | valid |
| 72.0ms | 133× | 1 | valid |
| 0.0ms | 2× | 0 | valid |
Compiled 98 to 23 computations (76.5% saved)
ival-tan: 243.0ms (75.7% of total)ival-mult: 21.0ms (6.5% of total)adjust: 15.0ms (4.7% of total)const: 15.0ms (4.7% of total)ival-add: 12.0ms (3.7% of total)ival-div: 11.0ms (3.4% of total)ival-sub: 4.0ms (1.2% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#<alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))> |
#<alt (*.f64 #s(literal 1/3 binary64) x)> |
#<alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))> |
#<alt (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))> |
#<alt (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))> |
#<alt (*.f64 x #s(literal 1/45 binary64))> |
#<alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))> |
#<alt (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))> |
#<alt (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))> |
#<alt (*.f64 x x)> |
#<alt (*.f64 x #s(literal 2/945 binary64))> |
#<alt (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))> |
| Outputs |
|---|
#<alt (* 1/3 x)> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))> |
#<alt (* -1 (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (* -1 (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))> |
#<alt (* -1 (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (* -1 (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (* 1/3 x)> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* 1/45 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* 1/45 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt 1/3> |
#<alt (+ 1/3 (* 1/45 (pow x 2)))> |
#<alt (+ 1/3 (* 1/45 (pow x 2)))> |
#<alt (+ 1/3 (* 1/45 (pow x 2)))> |
#<alt (* 1/45 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* 1/45 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* 1/45 x)> |
#<alt (* 1/45 x)> |
#<alt (* 1/45 x)> |
#<alt (* 1/45 x)> |
#<alt (* 1/45 x)> |
#<alt (* 1/45 x)> |
#<alt (* 1/45 x)> |
#<alt (* 1/45 x)> |
#<alt (* 1/45 x)> |
#<alt (* 1/45 x)> |
#<alt (* 1/45 x)> |
#<alt (* 1/45 x)> |
#<alt (* 1/3 x)> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))> |
#<alt (* -1 (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (* -1 (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (* 1/3 x)> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))> |
#<alt (* 2/945 (pow x 5))> |
#<alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))> |
#<alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))> |
#<alt (* 2/945 (pow x 5))> |
#<alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))> |
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))> |
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))> |
#<alt 1/3> |
#<alt (+ 1/3 (* 1/45 (pow x 2)))> |
#<alt (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))> |
#<alt (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))> |
#<alt (* 2/945 (pow x 4))> |
#<alt (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))> |
#<alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))> |
#<alt (* 2/945 (pow x 4))> |
#<alt (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))> |
#<alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (* 2/945 x)> |
#<alt (* 2/945 x)> |
#<alt (* 2/945 x)> |
#<alt (* 2/945 x)> |
#<alt (* 2/945 x)> |
#<alt (* 2/945 x)> |
#<alt (* 2/945 x)> |
#<alt (* 2/945 x)> |
#<alt (* 2/945 x)> |
#<alt (* 2/945 x)> |
#<alt (* 2/945 x)> |
#<alt (* 2/945 x)> |
#<alt 1/45> |
#<alt (+ 1/45 (* 2/945 (pow x 2)))> |
#<alt (+ 1/45 (* 2/945 (pow x 2)))> |
#<alt (+ 1/45 (* 2/945 (pow x 2)))> |
#<alt (* 2/945 (pow x 2))> |
#<alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))> |
#<alt (* 2/945 (pow x 2))> |
#<alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))> |
36 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | x | @ | inf | (+ (* x (* x 2/945)) 1/45) |
| 1.0ms | x | @ | 0 | (+ (* (* x x) (+ (* x (* x 2/945)) 1/45)) 1/3) |
| 1.0ms | x | @ | 0 | (* 1/3 x) |
| 0.0ms | x | @ | inf | (* x (+ (* (* x x) (+ (* x (* x 2/945)) 1/45)) 1/3)) |
| 0.0ms | x | @ | 0 | (* x (+ (* x (* x 1/45)) 1/3)) |
| 1× | egg-herbie |
| 15 474× | lower-fma.f64 |
| 15 474× | lower-fma.f32 |
| 3 832× | lower-*.f64 |
| 3 832× | lower-*.f32 |
| 2 178× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 62 | 980 |
| 1 | 189 | 980 |
| 2 | 477 | 980 |
| 3 | 1117 | 980 |
| 4 | 2265 | 980 |
| 5 | 5605 | 980 |
| 0 | 8357 | 905 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/3 x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) |
(* -1 (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(* -1 (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) |
(* -1 (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(* -1 (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(* 1/3 x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* 1/45 (pow x 3)) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* 1/45 (pow x 3)) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
1/3 |
(+ 1/3 (* 1/45 (pow x 2))) |
(+ 1/3 (* 1/45 (pow x 2))) |
(+ 1/3 (* 1/45 (pow x 2))) |
(* 1/45 (pow x 2)) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* 1/45 (pow x 2)) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* 1/45 x) |
(* 1/45 x) |
(* 1/45 x) |
(* 1/45 x) |
(* 1/45 x) |
(* 1/45 x) |
(* 1/45 x) |
(* 1/45 x) |
(* 1/45 x) |
(* 1/45 x) |
(* 1/45 x) |
(* 1/45 x) |
(* 1/3 x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) |
(* -1 (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(* -1 (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(* 1/3 x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(* 2/945 (pow x 5)) |
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) |
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) |
(* 2/945 (pow x 5)) |
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))) |
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))) |
1/3 |
(+ 1/3 (* 1/45 (pow x 2))) |
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))) |
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))) |
(* 2/945 (pow x 4)) |
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) |
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) |
(* 2/945 (pow x 4)) |
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) |
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (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) |
(pow x 2) |
(* 2/945 x) |
(* 2/945 x) |
(* 2/945 x) |
(* 2/945 x) |
(* 2/945 x) |
(* 2/945 x) |
(* 2/945 x) |
(* 2/945 x) |
(* 2/945 x) |
(* 2/945 x) |
(* 2/945 x) |
(* 2/945 x) |
1/45 |
(+ 1/45 (* 2/945 (pow x 2))) |
(+ 1/45 (* 2/945 (pow x 2))) |
(+ 1/45 (* 2/945 (pow x 2))) |
(* 2/945 (pow x 2)) |
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(* 2/945 (pow x 2)) |
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
| Outputs |
|---|
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* -1 (/ (cos x) (sin x))) |
(/.f64 (cos.f64 x) (neg.f64 (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(* -1 (/ (cos x) (sin x))) |
(/.f64 (cos.f64 x) (neg.f64 (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* -1 (/ (cos x) (sin x))) |
(/.f64 (cos.f64 x) (neg.f64 (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(* -1 (/ (cos x) (sin x))) |
(/.f64 (cos.f64 x) (neg.f64 (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* 1/45 (pow x 3)) |
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* 1/45 (pow x 3)) |
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
1/3 |
#s(literal 1/3 binary64) |
(+ 1/3 (* 1/45 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(+ 1/3 (* 1/45 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(+ 1/3 (* 1/45 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(* 1/45 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/45 binary64))) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(* 1/45 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/45 binary64))) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(* 1/45 x) |
(*.f64 x #s(literal 1/45 binary64)) |
(* 1/45 x) |
(*.f64 x #s(literal 1/45 binary64)) |
(* 1/45 x) |
(*.f64 x #s(literal 1/45 binary64)) |
(* 1/45 x) |
(*.f64 x #s(literal 1/45 binary64)) |
(* 1/45 x) |
(*.f64 x #s(literal 1/45 binary64)) |
(* 1/45 x) |
(*.f64 x #s(literal 1/45 binary64)) |
(* 1/45 x) |
(*.f64 x #s(literal 1/45 binary64)) |
(* 1/45 x) |
(*.f64 x #s(literal 1/45 binary64)) |
(* 1/45 x) |
(*.f64 x #s(literal 1/45 binary64)) |
(* 1/45 x) |
(*.f64 x #s(literal 1/45 binary64)) |
(* 1/45 x) |
(*.f64 x #s(literal 1/45 binary64)) |
(* 1/45 x) |
(*.f64 x #s(literal 1/45 binary64)) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* -1 (/ (cos x) (sin x))) |
(/.f64 (cos.f64 x) (neg.f64 (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(* -1 (/ (cos x) (sin x))) |
(/.f64 (cos.f64 x) (neg.f64 (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* 2/945 (pow x 5)) |
(*.f64 x (*.f64 #s(literal 2/945 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) |
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)))) |
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* 2/945 (pow x 5)) |
(*.f64 x (*.f64 #s(literal 2/945 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) |
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)))) |
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
1/3 |
#s(literal 1/3 binary64) |
(+ 1/3 (* 1/45 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(* 2/945 (pow x 4)) |
(*.f64 #s(literal 2/945 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) |
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)))) |
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(* 2/945 (pow x 4)) |
(*.f64 #s(literal 2/945 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) |
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)))) |
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 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) |
(* 2/945 x) |
(*.f64 x #s(literal 2/945 binary64)) |
(* 2/945 x) |
(*.f64 x #s(literal 2/945 binary64)) |
(* 2/945 x) |
(*.f64 x #s(literal 2/945 binary64)) |
(* 2/945 x) |
(*.f64 x #s(literal 2/945 binary64)) |
(* 2/945 x) |
(*.f64 x #s(literal 2/945 binary64)) |
(* 2/945 x) |
(*.f64 x #s(literal 2/945 binary64)) |
(* 2/945 x) |
(*.f64 x #s(literal 2/945 binary64)) |
(* 2/945 x) |
(*.f64 x #s(literal 2/945 binary64)) |
(* 2/945 x) |
(*.f64 x #s(literal 2/945 binary64)) |
(* 2/945 x) |
(*.f64 x #s(literal 2/945 binary64)) |
(* 2/945 x) |
(*.f64 x #s(literal 2/945 binary64)) |
(* 2/945 x) |
(*.f64 x #s(literal 2/945 binary64)) |
1/45 |
#s(literal 1/45 binary64) |
(+ 1/45 (* 2/945 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) |
(+ 1/45 (* 2/945 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) |
(+ 1/45 (* 2/945 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) |
(* 2/945 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 2/945 binary64)) |
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) |
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) |
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) |
(* 2/945 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 2/945 binary64)) |
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) |
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) |
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) |
(fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) |
| 11 116× | lower-fma.f32 |
| 11 110× | lower-fma.f64 |
| 5 340× | lower-*.f32 |
| 5 328× | lower-*.f64 |
| 2 938× | lower-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 107 |
| 0 | 33 | 107 |
| 1 | 143 | 107 |
| 2 | 1082 | 107 |
| 0 | 8750 | 107 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) |
(*.f64 #s(literal 1/3 binary64) x) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(*.f64 x #s(literal 1/45 binary64)) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(*.f64 x x) |
(*.f64 x #s(literal 2/945 binary64)) |
(fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) |
| Outputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64))) |
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/3 binary64))) |
(*.f64 x #s(literal 1/3 binary64)) |
(*.f64 #s(literal 1/3 binary64) x) |
(*.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal 1 binary64)) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) |
(+.f64 (*.f64 x #s(literal 1/3 binary64)) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))))) |
(+.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))) (*.f64 x #s(literal 1/3 binary64))) |
(-.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/9 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))) |
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/3 binary64)) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))))) |
(fma.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))) (*.f64 x #s(literal 1/3 binary64))) |
(fma.f64 x #s(literal 1/3 binary64) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))))) |
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))) (*.f64 x #s(literal 1/3 binary64))) |
(fma.f64 #s(literal 1/3 binary64) x (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))))) |
(fma.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64))))) |
(fma.f64 #s(literal 1/45 binary64) (*.f64 x (*.f64 x x)) (*.f64 x #s(literal 1/3 binary64))) |
(fma.f64 (*.f64 x #s(literal 1/45 binary64)) (*.f64 x x) (*.f64 x #s(literal 1/3 binary64))) |
(fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/45 binary64)) (*.f64 x #s(literal 1/3 binary64))) |
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(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 4/893025 binary64)))) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64))) (*.f64 (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64)) #s(literal 1/2025 binary64))) (*.f64 (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64)) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64)))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8/843908625 binary64)) #s(literal 1/91125 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 4/893025 binary64))) (+.f64 #s(literal 1/2025 binary64) (*.f64 (*.f64 x x) #s(literal -2/42525 binary64))))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 4/893025 binary64))) #s(literal -1/2025 binary64)))) (neg.f64 (fma.f64 (*.f64 x x) #s(literal -2/945 binary64) #s(literal 1/45 binary64)))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1/2025 binary64) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 4/893025 binary64)))))) (neg.f64 (-.f64 #s(literal 1/45 binary64) (*.f64 x (*.f64 x #s(literal 2/945 binary64)))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 4/893025 binary64)))) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/2025 binary64) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 4/893025 binary64)))) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64))) (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 4/893025 binary64)))) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64))) (fma.f64 (/.f64 #s(literal 1/2025 binary64) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64))) (/.f64 #s(literal 1/2025 binary64) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64))) (*.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 4/893025 binary64)))) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64))) (/.f64 #s(literal 1/2025 binary64) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64))))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 4/893025 binary64)))) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64))) (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 4/893025 binary64)))) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64)))) (*.f64 (/.f64 #s(literal 1/2025 binary64) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64))) (/.f64 #s(literal 1/2025 binary64) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64))))) (+.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 4/893025 binary64)))) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64))) (/.f64 #s(literal 1/2025 binary64) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64))))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8/843908625 binary64)) #s(literal 1/91125 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 4/893025 binary64))) (+.f64 #s(literal 1/2025 binary64) (*.f64 (*.f64 x x) #s(literal -2/42525 binary64)))))) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8/843908625 binary64)) #s(literal 1/91125 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2025 binary64) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 4/893025 binary64)) #s(literal 2/42525 binary64)))))) |
(*.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 4/893025 binary64))) #s(literal -1/2025 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal -1/45 binary64)))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8/843908625 binary64)) #s(literal 1/91125 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 4/893025 binary64))) (+.f64 #s(literal 1/2025 binary64) (*.f64 (*.f64 x x) #s(literal -2/42525 binary64))))))) |
(*.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 4/893025 binary64))) #s(literal -1/2025 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -2/945 binary64) #s(literal 1/45 binary64)))) |
(*.f64 (-.f64 #s(literal 1/2025 binary64) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 4/893025 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/45 binary64) (*.f64 x (*.f64 x #s(literal 2/945 binary64)))))) |
Compiled 11 554 to 926 computations (92% saved)
5 alts after pruning (2 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 459 | 2 | 461 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 3 | 3 |
| Done | 0 | 0 | 0 |
| Total | 459 | 5 | 464 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.9% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))) |
| ▶ | 98.9% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))) |
| ✓ | 99.5% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
| ✓ | 99.4% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
| ✓ | 99.1% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) |
Compiled 49 to 31 computations (36.7% saved)
| 1× | egg-herbie |
Found 7 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) | |
| cost-diff | 0 | #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))) | |
| cost-diff | 1088 | (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) x) | |
| cost-diff | 0 | #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))) | |
| cost-diff | 1088 | (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) |
| 552× | lower-fma.f32 |
| 550× | lower-fma.f64 |
| 376× | lower-*.f32 |
| 374× | lower-*.f64 |
| 168× | associate-*r* |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 75 |
| 0 | 23 | 71 |
| 1 | 35 | 67 |
| 2 | 59 | 67 |
| 3 | 87 | 67 |
| 4 | 109 | 67 |
| 5 | 134 | 67 |
| 6 | 169 | 67 |
| 7 | 201 | 67 |
| 8 | 375 | 67 |
| 9 | 846 | 67 |
| 10 | 1104 | 67 |
| 11 | 1132 | 67 |
| 12 | 1134 | 67 |
| 13 | 1137 | 67 |
| 14 | 1138 | 67 |
| 0 | 1138 | 67 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))) |
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) |
#s(literal 1/3 binary64) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))) |
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) |
x |
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
#s(literal 1 binary64) |
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) |
#s(literal 1/45 binary64) |
(*.f64 x x) |
#s(literal 1/3 binary64) |
| Outputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64))) |
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 x #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
x |
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
#s(literal 1 binary64) |
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
#s(literal 1/45 binary64) |
(*.f64 x x) |
#s(literal 1/3 binary64) |
Found 7 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (*.f64 x x) | |
| accuracy | 0.0078125 | (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) | |
| accuracy | 0.0078125 | (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) | |
| accuracy | 0.0603895303525102 | #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))) | |
| accuracy | 0 | (/.f64 #s(literal 1 binary64) x) | |
| accuracy | 0.31022786707002425 | #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))) | |
| accuracy | 0.37109375 | (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) |
| 220.0ms | 121× | 2 | valid |
| 56.0ms | 133× | 1 | valid |
| 0.0ms | 2× | 0 | valid |
Compiled 63 to 16 computations (74.6% saved)
ival-tan: 209.0ms (81% of total)ival-div: 19.0ms (7.4% of total)const: 10.0ms (3.9% of total)adjust: 9.0ms (3.5% of total)ival-sub: 6.0ms (2.3% of total)ival-mult: 3.0ms (1.2% of total)ival-add: 2.0ms (0.8% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#<alt (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))> |
#<alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))> |
#<alt (/.f64 #s(literal 1 binary64) x)> |
#<alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))> |
#<alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))> |
#<alt (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))> |
#<alt (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))> |
#<alt (*.f64 x x)> |
| Outputs |
|---|
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))> |
#<alt (* -1 (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (* -1 (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (* 1/3 x)> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* 1/45 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* 1/45 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* 1/3 x)> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))> |
#<alt (* -1 (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (* -1 (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt 3> |
#<alt (+ 3 (* -1/5 (pow x 2)))> |
#<alt (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))> |
#<alt (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))> |
#<alt (/ 45 (pow x 2))> |
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))> |
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))> |
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))> |
#<alt (/ 45 (pow x 2))> |
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))> |
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))> |
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))> |
#<alt 1/3> |
#<alt (+ 1/3 (* 1/45 (pow x 2)))> |
#<alt (+ 1/3 (* 1/45 (pow x 2)))> |
#<alt (+ 1/3 (* 1/45 (pow x 2)))> |
#<alt (* 1/45 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* 1/45 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
24 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | inf | (/ 1 (+ (* 1/45 (* x x)) 1/3)) |
| 0.0ms | x | @ | 0 | (/ 1 (+ (* 1/45 (* x x)) 1/3)) |
| 0.0ms | x | @ | -inf | (/ 1 (+ (* 1/45 (* x x)) 1/3)) |
| 0.0ms | x | @ | 0 | (/ 1/3 (/ 1 x)) |
| 0.0ms | x | @ | -inf | (+ (* 1/45 (* x x)) 1/3) |
| 1× | egg-herbie |
| 10 150× | lower-fma.f64 |
| 10 150× | lower-fma.f32 |
| 3 108× | lower-*.f64 |
| 3 108× | lower-*.f32 |
| 2 516× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 76 | 656 |
| 1 | 196 | 656 |
| 2 | 494 | 656 |
| 3 | 1172 | 656 |
| 4 | 2414 | 656 |
| 5 | 5304 | 656 |
| 0 | 8343 | 620 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) |
(* -1 (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(* -1 (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(* 1/3 x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* 1/45 (pow x 3)) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* 1/45 (pow x 3)) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* 1/3 x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) |
(* -1 (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(* -1 (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
3 |
(+ 3 (* -1/5 (pow x 2))) |
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) |
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) |
(/ 45 (pow x 2)) |
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) |
(/ 45 (pow x 2)) |
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) |
1/3 |
(+ 1/3 (* 1/45 (pow x 2))) |
(+ 1/3 (* 1/45 (pow x 2))) |
(+ 1/3 (* 1/45 (pow x 2))) |
(* 1/45 (pow x 2)) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* 1/45 (pow x 2)) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (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) |
(pow x 2) |
| Outputs |
|---|
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) |
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 1/4725 binary64) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))) #s(literal 1/3 binary64))) |
(* -1 (/ (cos x) (sin x))) |
(neg.f64 (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(* -1 (/ (cos x) (sin x))) |
(neg.f64 (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* 1/45 (pow x 3)) |
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* 1/45 (pow x 3)) |
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/45 binary64)))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) |
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 1/4725 binary64) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))) #s(literal 1/3 binary64))) |
(* -1 (/ (cos x) (sin x))) |
(neg.f64 (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(* -1 (/ (cos x) (sin x))) |
(neg.f64 (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
3 |
#s(literal 3 binary64) |
(+ 3 (* -1/5 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/75 binary64) #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/1125 binary64)) #s(literal 1/75 binary64)) #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(/ 45 (pow x 2)) |
(/.f64 #s(literal 45 binary64) (*.f64 x x)) |
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 x x)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -675 binary64) (*.f64 x x)))) (*.f64 x x)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) |
(/.f64 (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -151875 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))))) (*.f64 x x)) |
(/ 45 (pow x 2)) |
(/.f64 #s(literal 45 binary64) (*.f64 x x)) |
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 x x)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -675 binary64) (*.f64 x x)))) (*.f64 x x)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) |
(/.f64 (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -151875 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))))) (*.f64 x x)) |
1/3 |
#s(literal 1/3 binary64) |
(+ 1/3 (* 1/45 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(+ 1/3 (* 1/45 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(+ 1/3 (* 1/45 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(* 1/45 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/45 binary64))) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(* 1/45 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/45 binary64))) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) |
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 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) |
| 5 146× | lower-fma.f32 |
| 5 144× | lower-fma.f64 |
| 3 734× | lower-*.f32 |
| 3 732× | lower-*.f64 |
| 2 930× | lower-/.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 68 |
| 0 | 23 | 64 |
| 1 | 105 | 60 |
| 2 | 753 | 60 |
| 3 | 7018 | 60 |
| 0 | 8473 | 60 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))) |
(/.f64 #s(literal 1 binary64) x) |
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))) |
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) |
(*.f64 x x) |
| Outputs |
|---|
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 (*.f64 #s(literal 1/3 binary64) x))) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/3 binary64) x)) |
(neg.f64 (*.f64 #s(literal -1/3 binary64) x)) |
(neg.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) x))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 3 binary64) x))) |
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) x)) |
(/.f64 x #s(literal 3 binary64)) |
(/.f64 (*.f64 #s(literal 1/3 binary64) x) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 3 binary64) x))) |
(/.f64 #s(literal -1/3 binary64) (/.f64 #s(literal -1 binary64) x)) |
(/.f64 (*.f64 #s(literal -1/3 binary64) x) #s(literal -1 binary64)) |
(/.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64))) |
(pow.f64 (/.f64 #s(literal 3 binary64) x) #s(literal -1 binary64)) |
(*.f64 #s(literal 1/3 binary64) x) |
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x)) |
(*.f64 x #s(literal 1/3 binary64)) |
(*.f64 (*.f64 #s(literal 1/3 binary64) x) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (*.f64 #s(literal -1/3 binary64) x)) |
(*.f64 #s(literal -1/3 binary64) (neg.f64 x)) |
(*.f64 (neg.f64 x) #s(literal -1/3 binary64)) |
(*.f64 (pow.f64 (/.f64 #s(literal 3 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 3 binary64) x) #s(literal -1/2 binary64))) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) |
(exp.f64 (neg.f64 (log.f64 x))) |
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) x)) |
(neg.f64 (/.f64 #s(literal -1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (neg.f64 x)) |
(/.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) |
(pow.f64 x #s(literal -1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) |
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64)) |
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) |
(*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64))) |
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))) #s(literal -1 binary64))) |
(+.f64 (*.f64 #s(literal 1/3 binary64) x) (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x)))) |
(+.f64 (*.f64 #s(literal 1/3 binary64) x) (*.f64 (neg.f64 x) (*.f64 (*.f64 x x) #s(literal -1/45 binary64)))) |
(+.f64 (*.f64 #s(literal 1/3 binary64) x) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) (neg.f64 x))) |
(+.f64 (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))) (*.f64 #s(literal 1/3 binary64) x)) |
(+.f64 (*.f64 (neg.f64 x) (*.f64 (*.f64 x x) #s(literal -1/45 binary64))) (*.f64 #s(literal 1/3 binary64) x)) |
(+.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) (neg.f64 x)) (*.f64 #s(literal 1/3 binary64) x)) |
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)))) |
(-.f64 (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))) (*.f64 #s(literal -1/3 binary64) x)) |
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)))) |
(fma.f64 #s(literal 1/3 binary64) x (*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x)))) |
(fma.f64 #s(literal 1/3 binary64) x (*.f64 (neg.f64 x) (*.f64 (*.f64 x x) #s(literal -1/45 binary64)))) |
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(*.f64 (pow.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 1/91125 binary64) (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x)) #s(literal 1/27 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))) |
(*.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64))) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(*.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/91125 binary64) (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x)) #s(literal 1/27 binary64)) (fma.f64 #s(literal 1/8303765625 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)))))) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (-.f64 (fma.f64 (*.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))))) (*.f64 #s(literal 1/4100625 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/91125 binary64) (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x)) #s(literal 1/27 binary64)) (*.f64 (fma.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)) (+.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) (*.f64 (*.f64 x x) #s(literal 1/135 binary64))))) (+.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) (*.f64 (*.f64 x x) #s(literal 1/135 binary64)))) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) (fma.f64 (*.f64 #s(literal 1/91125 binary64) (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x)) #s(literal -1/27 binary64))) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2025 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/135 binary64) #s(literal 1/9 binary64)))) |
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x))) |
(neg.f64 (*.f64 x (neg.f64 x))) |
(/.f64 x (/.f64 #s(literal 1 binary64) x)) |
(/.f64 (*.f64 x x) #s(literal 1 binary64)) |
(/.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) x)) |
(/.f64 (*.f64 x (neg.f64 x)) #s(literal -1 binary64)) |
(pow.f64 x #s(literal 2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 1 binary64)) |
(pow.f64 (neg.f64 x) #s(literal 2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 x x)) |
(*.f64 x x) |
(*.f64 (*.f64 x x) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (*.f64 x (neg.f64 x))) |
(*.f64 (neg.f64 x) (neg.f64 x)) |
Compiled 9 393 to 1 070 computations (88.6% saved)
5 alts after pruning (2 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 441 | 2 | 443 |
| Fresh | 0 | 0 | 0 |
| Picked | 2 | 0 | 2 |
| Done | 0 | 3 | 3 |
| Total | 443 | 5 | 448 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.9% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))) |
| ▶ | 99.5% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) |
| ✓ | 99.5% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
| ✓ | 99.4% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
| ✓ | 99.1% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) |
Compiled 47 to 27 computations (42.6% saved)
| 1× | egg-herbie |
Found 7 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) | |
| cost-diff | 0 | #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) | |
| cost-diff | 0 | (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))) | |
| cost-diff | 0 | #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))) | |
| cost-diff | 0 | #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) | |
| cost-diff | 0 | (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) | |
| cost-diff | 0 | #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) |
| 568× | lower-fma.f32 |
| 566× | lower-fma.f64 |
| 440× | lower-*.f32 |
| 438× | lower-*.f64 |
| 176× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 22 | 121 |
| 0 | 27 | 121 |
| 1 | 39 | 121 |
| 2 | 51 | 121 |
| 3 | 60 | 121 |
| 4 | 73 | 121 |
| 5 | 93 | 121 |
| 6 | 132 | 121 |
| 7 | 164 | 121 |
| 8 | 280 | 121 |
| 9 | 577 | 121 |
| 10 | 795 | 121 |
| 11 | 995 | 121 |
| 12 | 1205 | 121 |
| 13 | 1269 | 121 |
| 14 | 1321 | 121 |
| 15 | 1345 | 121 |
| 16 | 1350 | 121 |
| 17 | 1351 | 121 |
| 0 | 1351 | 115 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) |
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) |
x |
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) |
#s(literal 3 binary64) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))) |
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))) |
x |
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) |
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(*.f64 x #s(literal -1/5 binary64)) |
#s(literal -1/5 binary64) |
#s(literal 3 binary64) |
| Outputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) |
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) |
x |
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) |
#s(literal 3 binary64) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))) |
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))) |
x |
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) |
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(*.f64 x #s(literal -1/5 binary64)) |
#s(literal -1/5 binary64) |
#s(literal 3 binary64) |
Found 7 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))) | |
| accuracy | 0.06033714035566541 | #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) | |
| accuracy | 0.0603895303525102 | #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))) | |
| accuracy | 0.29296875 | (*.f64 x #s(literal -1/5 binary64)) | |
| accuracy | 0 | (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) | |
| accuracy | 0.0603895303525102 | #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) | |
| accuracy | 0.31629075529423506 | #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) |
| 227.0ms | 121× | 2 | valid |
| 58.0ms | 133× | 1 | valid |
| 0.0ms | 2× | 0 | valid |
Compiled 73 to 20 computations (72.6% saved)
ival-tan: 210.0ms (78.2% of total)ival-div: 18.0ms (6.7% of total)adjust: 12.0ms (4.5% of total)const: 12.0ms (4.5% of total)ival-mult: 6.0ms (2.2% of total)ival-add: 5.0ms (1.9% of total)ival-sub: 4.0ms (1.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#<alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))> |
#<alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))> |
#<alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))> |
#<alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))> |
#<alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))> |
#<alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))> |
#<alt (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))> |
#<alt (*.f64 x #s(literal -1/5 binary64))> |
| Outputs |
|---|
#<alt (* 1/3 x)> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))> |
#<alt (* -1 (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (* -1 (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (* 1/3 x)> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* 1/45 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* 1/45 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt 3> |
#<alt (+ 3 (* -1/5 (pow x 2)))> |
#<alt (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))> |
#<alt (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))> |
#<alt (/ 45 (pow x 2))> |
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))> |
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))> |
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))> |
#<alt (/ 45 (pow x 2))> |
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))> |
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))> |
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))> |
#<alt (* 1/3 x)> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))> |
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))> |
#<alt (* -1 (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (* -1 (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (- (/ 1 x) (/ (cos x) (sin x)))> |
#<alt (* 1/3 x)> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))> |
#<alt (* 1/45 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* 1/45 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt 3> |
#<alt (+ 3 (* -1/5 (pow x 2)))> |
#<alt (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))> |
#<alt (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))> |
#<alt (/ 45 (pow x 2))> |
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))> |
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))> |
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))> |
#<alt (/ 45 (pow x 2))> |
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))> |
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))> |
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))> |
#<alt 3> |
#<alt (+ 3 (* -1/5 (pow x 2)))> |
#<alt (+ 3 (* -1/5 (pow x 2)))> |
#<alt (+ 3 (* -1/5 (pow x 2)))> |
#<alt (* -1/5 (pow x 2))> |
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))> |
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))> |
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))> |
#<alt (* -1/5 (pow x 2))> |
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))> |
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))> |
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))> |
#<alt (* -1/5 x)> |
#<alt (* -1/5 x)> |
#<alt (* -1/5 x)> |
#<alt (* -1/5 x)> |
#<alt (* -1/5 x)> |
#<alt (* -1/5 x)> |
#<alt (* -1/5 x)> |
#<alt (* -1/5 x)> |
#<alt (* -1/5 x)> |
#<alt (* -1/5 x)> |
#<alt (* -1/5 x)> |
#<alt (* -1/5 x)> |
24 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | -inf | (* x -1/5) |
| 0.0ms | x | @ | inf | (* x -1/5) |
| 0.0ms | x | @ | 0 | (* x -1/5) |
| 0.0ms | x | @ | inf | (+ (* x (* x -1/5)) 3) |
| 0.0ms | x | @ | 0 | (+ (* x (* x -1/5)) 3) |
| 1× | egg-herbie |
| 12 352× | lower-fma.f64 |
| 12 352× | lower-fma.f32 |
| 3 826× | lower-*.f64 |
| 3 826× | lower-*.f32 |
| 2 020× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 79 | 830 |
| 1 | 199 | 830 |
| 2 | 495 | 830 |
| 3 | 1160 | 830 |
| 4 | 2270 | 830 |
| 5 | 3887 | 830 |
| 6 | 6469 | 830 |
| 0 | 8104 | 779 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/3 x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) |
(* -1 (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(* -1 (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(* 1/3 x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* 1/45 (pow x 3)) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* 1/45 (pow x 3)) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
3 |
(+ 3 (* -1/5 (pow x 2))) |
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) |
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) |
(/ 45 (pow x 2)) |
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) |
(/ 45 (pow x 2)) |
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) |
(* 1/3 x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) |
(* -1 (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(* -1 (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(* 1/3 x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(* 1/45 (pow x 3)) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* 1/45 (pow x 3)) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
3 |
(+ 3 (* -1/5 (pow x 2))) |
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) |
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) |
(/ 45 (pow x 2)) |
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) |
(/ 45 (pow x 2)) |
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) |
3 |
(+ 3 (* -1/5 (pow x 2))) |
(+ 3 (* -1/5 (pow x 2))) |
(+ 3 (* -1/5 (pow x 2))) |
(* -1/5 (pow x 2)) |
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) |
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) |
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) |
(* -1/5 (pow x 2)) |
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) |
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) |
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) |
(* -1/5 x) |
(* -1/5 x) |
(* -1/5 x) |
(* -1/5 x) |
(* -1/5 x) |
(* -1/5 x) |
(* -1/5 x) |
(* -1/5 x) |
(* -1/5 x) |
(* -1/5 x) |
(* -1/5 x) |
(* -1/5 x) |
| Outputs |
|---|
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* -1 (/ (cos x) (sin x))) |
(neg.f64 (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(* -1 (/ (cos x) (sin x))) |
(neg.f64 (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* 1/45 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* 1/45 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
3 |
#s(literal 3 binary64) |
(+ 3 (* -1/5 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/75 binary64)) #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/1125 binary64) #s(literal 1/75 binary64)) #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(/ 45 (pow x 2)) |
(/.f64 #s(literal 45 binary64) (*.f64 x x)) |
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 x x)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/.f64 (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 x x)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) |
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (/.f64 #s(literal -151875 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))))) (*.f64 x x)) |
(/ 45 (pow x 2)) |
(/.f64 #s(literal 45 binary64) (*.f64 x x)) |
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 x x)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/.f64 (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 x x)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) |
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (/.f64 #s(literal -151875 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))))) (*.f64 x x)) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) |
(* -1 (/ (cos x) (sin x))) |
(neg.f64 (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(* -1 (/ (cos x) (sin x))) |
(neg.f64 (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(- (/ 1 x) (/ (cos x) (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x))) |
(* 1/3 x) |
(*.f64 #s(literal 1/3 binary64) x) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* x (+ 1/3 (* 1/45 (pow x 2)))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* 1/45 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* 1/45 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/45 binary64) (*.f64 x x))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) |
3 |
#s(literal 3 binary64) |
(+ 3 (* -1/5 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/75 binary64)) #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/1125 binary64) #s(literal 1/75 binary64)) #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(/ 45 (pow x 2)) |
(/.f64 #s(literal 45 binary64) (*.f64 x x)) |
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 x x)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/.f64 (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 x x)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) |
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (/.f64 #s(literal -151875 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))))) (*.f64 x x)) |
(/ 45 (pow x 2)) |
(/.f64 #s(literal 45 binary64) (*.f64 x x)) |
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 x x)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) |
(/.f64 (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (*.f64 x x)) |
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) |
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -675 binary64) (*.f64 x x))) (/.f64 #s(literal -151875 binary64) (*.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))))))) (*.f64 x x)) |
3 |
#s(literal 3 binary64) |
(+ 3 (* -1/5 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(+ 3 (* -1/5 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(+ 3 (* -1/5 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(* -1/5 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/5 binary64))) |
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) |
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) |
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) |
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(* -1/5 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/5 binary64))) |
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) |
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) |
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) |
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(* -1/5 x) |
(*.f64 x #s(literal -1/5 binary64)) |
(* -1/5 x) |
(*.f64 x #s(literal -1/5 binary64)) |
(* -1/5 x) |
(*.f64 x #s(literal -1/5 binary64)) |
(* -1/5 x) |
(*.f64 x #s(literal -1/5 binary64)) |
(* -1/5 x) |
(*.f64 x #s(literal -1/5 binary64)) |
(* -1/5 x) |
(*.f64 x #s(literal -1/5 binary64)) |
(* -1/5 x) |
(*.f64 x #s(literal -1/5 binary64)) |
(* -1/5 x) |
(*.f64 x #s(literal -1/5 binary64)) |
(* -1/5 x) |
(*.f64 x #s(literal -1/5 binary64)) |
(* -1/5 x) |
(*.f64 x #s(literal -1/5 binary64)) |
(* -1/5 x) |
(*.f64 x #s(literal -1/5 binary64)) |
(* -1/5 x) |
(*.f64 x #s(literal -1/5 binary64)) |
| 6 144× | lower-fma.f32 |
| 6 142× | lower-fma.f64 |
| 4 394× | lower-*.f32 |
| 4 392× | lower-*.f64 |
| 3 460× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 22 | 116 |
| 0 | 27 | 116 |
| 1 | 121 | 116 |
| 2 | 862 | 116 |
| 0 | 8645 | 110 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) |
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) |
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))) |
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))) |
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) |
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)) |
(*.f64 x #s(literal -1/5 binary64)) |
| Outputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) x)) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))) |
(neg.f64 (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))) |
(neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) x))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) x)) |
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) |
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) |
(/.f64 x (*.f64 (neg.f64 #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #s(literal -1 binary64))) |
(/.f64 (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #s(literal 1 binary64)) |
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(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/625 binary64) #s(literal -81 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64))) #s(literal 9 binary64)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64)))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/125 binary64)) #s(literal 27 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64))) (-.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) #s(literal -3/5 binary64))))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64))) #s(literal -9 binary64)))) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/5 binary64) #s(literal 3 binary64)))) |
(/.f64 (neg.f64 (-.f64 #s(literal 9 binary64) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64)))))) (neg.f64 (-.f64 #s(literal 3 binary64) (*.f64 (*.f64 x x) #s(literal -1/5 binary64))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64)))) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 9 binary64) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64)))) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64))) (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64)))) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64))) (fma.f64 (/.f64 #s(literal 9 binary64) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 9 binary64) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64))) (*.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64)))) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 9 binary64) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64))))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64)))) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64))) (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64)))) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64)))) (*.f64 (/.f64 #s(literal 9 binary64) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 9 binary64) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64))))) (+.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64)))) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 9 binary64) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64))))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/125 binary64)) #s(literal 27 binary64)) #s(literal 1 binary64)) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64))) (-.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) #s(literal -3/5 binary64))))) |
(/.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64))) #s(literal -9 binary64)) #s(literal 1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/125 binary64))) (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/15625 binary64)) #s(literal 19683 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64))) (-.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) #s(literal -3/5 binary64)))))) (-.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/15625 binary64) #s(literal 729 binary64)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -27/125 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/15625 binary64) #s(literal -729 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64))) (-.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) #s(literal -3/5 binary64)))))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/125 binary64)) #s(literal -27 binary64))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/15625 binary64) #s(literal -729 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64)))) (fma.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/625 binary64) (+.f64 #s(literal 81 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 9/25 binary64))))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/625 binary64) #s(literal -81 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64)))) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64))) #s(literal 9 binary64))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/125 binary64)) #s(literal 27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64))) (-.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) #s(literal -3/5 binary64)))))) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/125 binary64)) #s(literal 27 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))))) |
(*.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64))) #s(literal -9 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64)))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/125 binary64)) #s(literal 27 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64))) (-.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) #s(literal -3/5 binary64))))))) |
(*.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64))) #s(literal -9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/5 binary64) #s(literal 3 binary64)))) |
(*.f64 (-.f64 #s(literal 9 binary64) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/25 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 3 binary64) (*.f64 (*.f64 x x) #s(literal -1/5 binary64))))) |
(/.f64 #s(literal -1/5 binary64) (/.f64 #s(literal 1 binary64) x)) |
(/.f64 (*.f64 x #s(literal -1/5 binary64)) #s(literal 1 binary64)) |
(/.f64 (*.f64 #s(literal -1/5 binary64) (neg.f64 x)) #s(literal -1 binary64)) |
(/.f64 (*.f64 (neg.f64 x) #s(literal -1/5 binary64)) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/5 binary64))) |
(*.f64 x #s(literal -1/5 binary64)) |
(*.f64 #s(literal -1/5 binary64) x) |
(*.f64 (*.f64 x #s(literal -1/5 binary64)) #s(literal 1 binary64)) |
Compiled 3 905 to 432 computations (88.9% saved)
5 alts after pruning (0 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 236 | 0 | 236 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 2 | 2 |
| Done | 0 | 3 | 3 |
| Total | 236 | 5 | 241 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.9% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))) |
| ✓ | 99.5% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) |
| ✓ | 99.5% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
| ✓ | 99.4% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
| ✓ | 99.1% | #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) |
Compiled 115 to 55 computations (52.2% saved)
| Inputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))) |
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
| Outputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))) |
2 calls:
| 3.0ms | x |
| 2.0ms | (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | x |
| 99.9% | 1 | (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
Compiled 11 to 7 computations (36.4% saved)
| Inputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))) |
| Outputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) |
2 calls:
| 2.0ms | x |
| 2.0ms | (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | x |
| 99.5% | 1 | (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
Compiled 11 to 7 computations (36.4% saved)
Total -0.0b remaining (-0%)
Threshold costs -0b (-0%)
| Inputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) |
| Outputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) |
2 calls:
| 1.0ms | x |
| 1.0ms | (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.1% | 1 | x |
| 99.1% | 1 | (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
Compiled 11 to 7 computations (36.4% saved)
| 1× | egg-herbie |
| 4× | *-commutative_binary64 |
| 2× | 1-exp_binary64 |
| 2× | 1-exp_binary32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 61 |
| 1 | 29 | 61 |
| 1× | saturated |
| Inputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) |
| Outputs |
|---|
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) |
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64))) |
| 18 970× | lower-fma.f64 |
| 18 970× | lower-fma.f32 |
| 11 116× | lower-fma.f32 |
| 11 110× | lower-fma.f64 |
| 10 150× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 107 |
| 0 | 33 | 107 |
| 1 | 143 | 107 |
| 2 | 1082 | 107 |
| 0 | 8750 | 107 |
| 0 | 67 | 324 |
| 1 | 179 | 324 |
| 2 | 458 | 318 |
| 3 | 1321 | 318 |
| 4 | 2085 | 318 |
| 5 | 3083 | 318 |
| 6 | 3670 | 318 |
| 7 | 3941 | 318 |
| 8 | 5080 | 318 |
| 9 | 7268 | 318 |
| 0 | 8431 | 300 |
| 0 | 76 | 656 |
| 1 | 196 | 656 |
| 2 | 494 | 656 |
| 3 | 1172 | 656 |
| 4 | 2414 | 656 |
| 5 | 5304 | 656 |
| 0 | 8343 | 620 |
| 1× | done |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 68 to 40 computations (41.2% saved)
(negabs x)
Compiled 152 to 88 computations (42.1% saved)
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