Details

Time bar (total: 7.8s)

sample119.0ms

Algorithm
intervals
Results
57.0ms128×body1280valid
29.0ms31×body2560valid
17.0ms63×body640valid
4.0ms22×body320valid
1.0ms10×body160valid
0.0ms2×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.8b
(- (cos (+ x eps)) (cos x))
4.6b
(cos (+ x eps))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-exp-log add-cube-cbrt cos-sum add-cbrt-cube
1×associate--l- sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
2 → 24
Calls
2 calls:
6.0ms
(- (cos (+ x eps)) (cos x))
4.0ms
(cos (+ x eps))

series14.0ms

Counts
2 → 6
Calls
2 calls:
9.0ms
(- (cos (+ x eps)) (cos x))
5.0ms
(cos (+ x eps))

simplify108.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
0134176
1281167
2840164
32958164
45002164

prune203.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.7b

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))
2.4b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×add-log-exp
10×*-un-lft-identity
8×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
6×associate-*r* associate-*l*
4×diff-log
3×sub-neg cos-mult sin-mult
2×flip3-- pow-prod-down prod-exp associate--l+ *-commutative flip-- cbrt-unprod unswap-sqr
1×associate--l- frac-sub distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 70
Calls
4 calls:
3.0ms
(* (cos x) (cos eps))
5.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms
(* (sin x) (sin eps))
20.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series58.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (cos x) (cos eps))
19.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
8.0ms
(* (sin x) (sin eps))
22.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify112.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0304632
11061601
24487583
35002583

prune629.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos eps) (cos x))
0.2b
(* (sin x) (sin eps))
0.2b
(+ (* (sin x) (sin eps)) (cos x))
2.3b
(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×add-log-exp
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
3×cos-mult
2×flip3-+ diff-log pow-prod-down prod-exp sum-log *-commutative frac-sub cbrt-unprod flip-+ unswap-sqr
1×+-commutative sub-neg flip3-- flip-- sin-mult associate--r+
Counts
4 → 65
Calls
4 calls:
4.0ms
(* (cos eps) (cos x))
4.0ms
(* (sin x) (sin eps))
4.0ms
(+ (* (sin x) (sin eps)) (cos x))
9.0ms
(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

series51.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (cos eps) (cos x))
9.0ms
(* (sin x) (sin eps))
11.0ms
(+ (* (sin x) (sin eps)) (cos x))
23.0ms
(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

simplify40.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0329606
11247575
25002567

prune655.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (cos eps) (cos x)) (* (cos eps) (cos x)))
0.4b
(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
0.5b
(pow (* (cos eps) (cos x)) 3)
2.2b
(- (pow (* (cos eps) (cos x)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1
20×add-exp-log add-cbrt-cube
18×add-sqr-sqrt pow-prod-down
10×*-un-lft-identity
9×prod-exp cbrt-unprod
8×add-cube-cbrt difference-of-squares sqr-pow
7×cube-div cos-mult
6×unpow-prod-down pow-unpow cube-prod add-log-exp
4×pow-sqr pow-prod-up
3×pow-pow pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp flip3-+ pow-plus unpow3 frac-sub flip-+
1×difference-cubes pow2 frac-times sub-neg flip3-- diff-log associate-*r/ swap-sqr associate-*r* associate-*l* associate-*l/ *-commutative flip-- distribute-lft-out--
Counts
4 → 109
Calls
4 calls:
13.0ms
(* (* (cos eps) (cos x)) (* (cos eps) (cos x)))
6.0ms
(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
3.0ms
(pow (* (cos eps) (cos x)) 3)
24.0ms
(- (pow (* (cos eps) (cos x)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

series175.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(* (* (cos eps) (cos x)) (* (cos eps) (cos x)))
21.0ms
(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
17.0ms
(pow (* (cos eps) (cos x)) 3)
124.0ms
(- (pow (* (cos eps) (cos x)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

simplify94.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
05331122
126691049
250011037

prune998.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 15.3b

regimes788.0ms

Accuracy

84.8% (1.5b remaining)

Error of 16.4b against oracle of 14.9b and baseline of 24.6b

bsearch87.0ms

Steps
ItersRangePoint
10
9.316647860064626e-18
0.006665254470786589
4.819151863418274e-08
6
-1.8496456666423901e-16
-1.9909943074331788e-17
-1.8216181721535518e-16

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04018
14018

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.9s4473×body1280valid
638.0ms667×body2560valid
521.0ms1820×body640valid
127.0ms658×body320valid
41.0ms306×body160valid
5.0ms76×body80valid