Details

Time bar (total: 6.6s)

sample141.0ms

Algorithm
intervals
Results
77.0ms59×body2560valid
37.0ms91×body1280valid
15.0ms67×body640valid
3.0ms18×body320valid
2.0ms12×body160valid
1.0ms9×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.3b
(- 1.0 (cos x))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
15×times-frac
9×prod-diff
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×fma-neg associate-/r*
2×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 68
Calls
2 calls:
7.0ms
(/ (- 1.0 (cos x)) (sin x))
4.0ms
(- 1.0 (cos x))

series61.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(/ (- 1.0 (cos x)) (sin x))
18.0ms
(- 1.0 (cos x))

simplify35.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0292569
1965460
25002460

prune184.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
0.0b
(fma 1/240 (pow x 5) (* 1/2 x))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
1.0ms
(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
1.0ms
(fma 1/240 (pow x 5) (* 1/2 x))

series180.0ms

Counts
2 → 6
Calls
2 calls:
57.0ms
(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
123.0ms
(fma 1/240 (pow x 5) (* 1/2 x))

simplify34.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
061148
1188130
21009130
35002130

prune95.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
0.3b
(exp (/ (- 1.0 (cos x)) (sin x)))
0.8b
(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.3b
(- 1.0 (cos x))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt *-un-lft-identity
45×times-frac
40×add-cube-cbrt
38×exp-prod
20×log-pow
11×distribute-lft-out-- difference-of-squares
9×prod-diff
7×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×log-prod fma-neg div-sub associate-/r* div-inv
2×flip3-- exp-diff flip-- associate-/l/
1×cbrt-undiv sub-neg log-div frac-2neg diff-log div-exp rem-log-exp clear-num rem-exp-log
Counts
4 → 132
Calls
4 calls:
7.0ms
(/ (- 1.0 (cos x)) (sin x))
10.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms
(- 1.0 (cos x))

series132.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (- 1.0 (cos x)) (sin x))
46.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
34.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms
(- 1.0 (cos x))

simplify40.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03681009
11099873
25002871

prune350.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x)))
0.3b
(pow (cos x) 3)
0.4b
(fma (cos x) (cos x) (* 1.0 (cos x)))
1.1b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
156×add-sqr-sqrt
144×prod-diff
114×unpow-prod-down *-un-lft-identity cube-prod
84×add-cube-cbrt
50×sqr-pow
48×difference-of-squares
26×cube-mult unpow3
25×times-frac associate-/l*
15×distribute-lft-out--
12×fma-neg
10×add-exp-log add-cbrt-cube
6×add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×difference-cubes pow-unpow
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub pow-exp prod-exp clear-num associate-/r* cbrt-unprod fma-udef div-inv rem-cube-cbrt
Counts
4 → 297
Calls
4 calls:
29.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x)))
2.0ms
(pow (cos x) 3)
1.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
15.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series317.0ms

Counts
4 → 12
Calls
4 calls:
191.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x)))
28.0ms
(pow (cos x) 3)
45.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
53.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify124.0ms

Algorithm
egg-herbie
Counts
309 → 309
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
07683882
129222862
250022805

prune398.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

regimes152.0ms

Accuracy

98.9% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 32.1b

bsearch79.0ms

Steps
ItersRangePoint
10
4.9177062248324165e-05
42925490.781275615
0.02286088640089938
8
-1.0806682141483241
-0.0004106978961831668
-0.022628612332283863

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03935
13935

end0.0ms

sample4.1s

Algorithm
intervals
Results
2.1s1578×body2560valid
1.2s2765×body1280valid
444.0ms1928×body640valid
134.0ms902×body320valid
49.0ms459×body160valid
29.0ms6×body5120valid
22.0ms362×body80valid