Details

Time bar (total: 6.4s)

sample98.0ms

Algorithm
intervals
Results
53.0ms150×body1280valid
21.0ms25×body2560valid
11.0ms57×body640valid
3.0ms18×body320valid
0.0ms4×body160valid
0.0ms2×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize8.0ms

Local error

Found 2 expressions with local error:

0.4b
(- (cos (+ x eps)) (cos x))
2.4b
(cos (+ x eps))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
4×add-log-exp
3×fma-neg
2×pow1 add-exp-log expm1-log1p-u cos-sum add-cbrt-cube log1p-expm1-u
1×associate--l- sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
2 → 40
Calls
2 calls:
7.0ms
(- (cos (+ x eps)) (cos x))
4.0ms
(cos (+ x eps))

series71.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(- (cos (+ x eps)) (cos x))
16.0ms
(cos (+ x eps))

simplify76.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0192385
1523285
22519275
35001220

prune122.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (cos eps))
0.2b
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b
(* (sin x) (sin eps))
1.8b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt
11×prod-diff add-log-exp
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u fma-neg diff-log log1p-expm1-u
3×sub-neg associate--l+ cos-mult sin-mult
2×flip3-- pow-prod-down prod-exp *-commutative flip-- cbrt-unprod unswap-sqr
1×associate--l- frac-sub distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 93
Calls
4 calls:
4.0ms
(* (cos x) (cos eps))
5.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms
(* (sin x) (sin eps))
23.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series301.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (cos x) (cos eps))
82.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
45.0ms
(* (sin x) (sin eps))
130.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify52.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0381988
11342837
25002822

prune300.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.3b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (sin x) (sin eps) (cos x))
1.8b
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite1.0ms

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:
0.0ms
(fma (sin x) (sin eps) (cos x))
0.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series188.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(fma (sin x) (sin eps) (cos x))
139.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify120.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
087209
1240182
2795182
33587180
45001180

prune139.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 11.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.3b
(pow (cos x) 3)
0.5b
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
1.6b
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
145×prod-diff
110×add-sqr-sqrt
98×*-un-lft-identity
93×unpow-prod-down cube-prod
86×add-cube-cbrt
35×sqr-pow
27×cube-mult unpow3
16×difference-of-squares
12×fma-neg
11×add-log-exp
6×pow1 add-exp-log pow-unpow add-cbrt-cube
5×distribute-lft-out--
4×cube-div expm1-log1p-u log1p-expm1-u
3×associate-+l+ fma-def
2×pow-to-exp sub-neg flip3-- pow-pow diff-log pow-exp sum-log cos-mult flip-- sin-mult rem-cube-cbrt
1×difference-cubes +-commutative associate-+l- flip3-+ frac-sub flip-+ distribute-lft-out sub-div
Counts
4 → 268
Calls
4 calls:
15.0ms
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
1.0ms
(pow (cos x) 3)
9.0ms
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
53.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series841.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
28.0ms
(pow (cos x) 3)
107.0ms
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
606.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify166.0ms

Algorithm
egg-herbie
Counts
280 → 280
Iterations

Useful iterations: 2 (121.0ms)

IterNodesCost
08745051
137823725
250013720

prune522.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 11.3b

regimes276.0ms

Accuracy

83.8% (1.7b remaining)

Error of 15.9b against oracle of 14.2b and baseline of 24.5b

bsearch112.0ms

Steps
ItersRangePoint
9
1.6022175866244216e-06
1831.6130620084434
2.811292656550888e-06
7
-5.203951087402867e-31
-1.1349252923434323e-32
-5.119551648445698e-31

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03515
13915
23915

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.5s4507×body1280valid
549.0ms618×body2560valid
384.0ms1835×body640valid
95.0ms646×body320valid
30.0ms305×body160valid
5.0ms89×body80valid