Details

Time bar (total: 6.5s)

sample111.0ms

Algorithm
intervals
Results
58.0ms145×body1280valid
22.0ms22×body2560valid
16.0ms61×body640valid
3.0ms16×body320valid
1.0ms11×body160valid
0.0ms1×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b
(- (cos (+ x eps)) (cos x))
3.5b
(cos (+ x eps))

rewrite11.0ms

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:
6.0ms
(- (cos (+ x eps)) (cos x))
4.0ms
(cos (+ x eps))

series67.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(- (cos (+ x eps)) (cos x))
14.0ms
(cos (+ x eps))

simplify71.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0192385
1523285
22519275
35001220

prune117.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (cos eps))
0.1b
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b
(* (sin x) (sin eps))
1.2b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite25.0ms

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))
9.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series294.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (cos x) (cos eps))
81.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
43.0ms
(* (sin x) (sin eps))
126.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify48.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0381988
11342837
25002822

prune306.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (sin x) (sin eps) (cos x))
1.2b
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos 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 (sin x) (sin eps) (cos x))
1.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series184.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(fma (sin x) (sin eps) (cos x))
134.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify115.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
087209
1240182
2795182
33587180
45001180

prune126.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
0.4b
(pow (cos x) 3)
0.5b
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
1.0b
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
144×prod-diff
113×add-sqr-sqrt
99×*-un-lft-identity
93×unpow-prod-down cube-prod
87×add-cube-cbrt
35×sqr-pow
27×cube-mult unpow3
16×difference-of-squares
12×fma-neg
8×pow1 add-exp-log frac-times cos-mult add-cbrt-cube sin-mult
6×pow-unpow add-log-exp
5×flip3-- flip3-+ flip-- flip-+ distribute-lft-out--
4×cube-div expm1-log1p-u associate-*r* associate-*l/ frac-sub log1p-expm1-u sub-div
3×associate-*l*
2×pow-to-exp pow-pow associate-*r/ pow-exp rem-cube-cbrt
1×difference-cubes distribute-rgt-in sub-neg distribute-lft-in diff-log pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
4 → 283
Calls
4 calls:
14.0ms
(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
2.0ms
(pow (cos x) 3)
6.0ms
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
22.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series944.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
27.0ms
(pow (cos x) 3)
107.0ms
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
607.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify73.0ms

Algorithm
egg-herbie
Counts
295 → 295
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
010835870
150014483

prune646.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.9b

regimes251.0ms

Accuracy

86.5% (1.4b remaining)

Error of 15.8b against oracle of 14.5b and baseline of 24.7b

bsearch176.0ms

Steps
ItersRangePoint
10
8.960609758249674e-23
4.5131138850246713e-07
1.2305748660245976e-07
11
-1.5073415317839904e-10
-5.397704668065765e-30
-1.4155618696900624e-10

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06569
16769
26769

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.5s4460×body1280valid
566.0ms663×body2560valid
391.0ms1836×body640valid
100.0ms675×body320valid
27.0ms287×body160valid
4.0ms79×body80valid