Details

Time bar (total: 3.0s)

sample96.0ms

Algorithm
intervals
Results
48.0ms142×body1280valid
25.0ms29×body2560valid
10.0ms47×body640valid
4.0ms27×body320valid
1.0ms8×body160valid
0.0ms3×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 41.2b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.9b
(- (cos (+ x eps)) (cos x))
4.2b
(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))

series71.0ms

Counts
2 → 6
Calls
2 calls:
56.0ms
(- (cos (+ x eps)) (cos x))
15.0ms
(cos (+ x eps))

simplify112.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
0134176
1281167
2840164
32958164
45002164

prune83.0ms

Filtered
30 candidates to 23 candidates (76.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New201030
Fresh000
Picked101
Done000
Total211031

Merged error: 16.7b

Counts
31 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (sin x) (sin eps)) (cos x))
0.1b
(* (cos x) (cos eps))
0.2b
(* (sin x) (sin eps))
2.0b
(- (* (cos x) (cos eps)) (+ (* (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:
5.0ms
(+ (* (sin x) (sin eps)) (cos x))
4.0ms
(* (cos x) (cos eps))
5.0ms
(* (sin x) (sin eps))
9.0ms
(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(+ (* (sin x) (sin eps)) (cos x))
39.0ms
(* (cos x) (cos eps))
48.0ms
(* (sin x) (sin eps))
130.0ms
(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify44.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0332607
11284574
25002565

prune230.0ms

Filtered
77 candidates to 53 candidates (68.8%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New621577
Fresh639
Picked101
Done000
Total691887

Merged error: 16.5b

Counts
87 → 18

localize16.0ms

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))
2.0b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite25.0ms

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:
4.0ms
(* (cos x) (cos eps))
5.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms
(* (sin x) (sin eps))
9.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series298.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (cos x) (cos eps))
82.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
49.0ms
(* (sin x) (sin eps))
128.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify116.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0304632
11061600
24487582
35002582

prune225.0ms

Filtered
82 candidates to 58 candidates (70.7%)
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New78482
Fresh51217
Picked011
Done000
Total8317100

Merged error: 16.5b

Counts
100 → 17

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
0.4b
(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
0.6b
(pow (* (cos x) (cos eps)) 3)
1.9b
(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

rewrite38.0ms

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:
9.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
7.0ms
(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
4.0ms
(pow (* (cos x) (cos eps)) 3)
15.0ms
(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

series585.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
71.0ms
(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
57.0ms
(pow (* (cos x) (cos eps)) 3)
402.0ms
(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

simplify96.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
05381143
126881062
250011058

prune323.0ms

Filtered
121 candidates to 65 candidates (53.7%)
Pruning

23 alts after pruning (22 fresh and 1 done)

PrunedKeptTotal
New10714121
Fresh7815
Picked101
Done011
Total11523138

Merged error: 16.5b

Counts
138 → 23

regimes320.0ms

bsearch3.0ms

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