Details

Time bar (total: 5.5s)

sample90.0ms

Algorithm
intervals
Results
44.0ms103×body1280valid
17.0ms68×body640valid
15.0ms17×body2560valid
3.0ms18×body320valid
2.0ms39×body80valid
1.0ms11×body160valid

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 (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 37.9b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.9b
(- (sin (+ x eps)) (sin x))
2.3b
(sin (+ x eps))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
4×sin-sum add-log-exp
3×fma-neg
2×pow1 add-exp-log +-commutative expm1-log1p-u associate--l+ add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- diff-log diff-sin flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 42
Calls
2 calls:
12.0ms
(- (sin (+ x eps)) (sin x))
4.0ms
(sin (+ x eps))

series59.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(- (sin (+ x eps)) (sin x))
19.0ms
(sin (+ x eps))

simplify71.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0193397
1530295
22598285
35002230

prune84.0ms

Filtered
48 candidates to 33 candidates (31.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New45348
Fresh000
Picked101
Done000
Total46349

Merged error: 0.4b

Counts
49 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin x) (- (cos eps) 1))
0.1b
(* (sin eps) (cos x))
0.2b
(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
1.6b
(- (cos eps) 1)

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt *-un-lft-identity
45×prod-diff
42×add-cube-cbrt
22×distribute-rgt-in associate-+r+ distribute-lft-in
13×associate-*r* associate-*l*
12×fma-def
9×add-exp-log
8×pow1 add-cbrt-cube add-log-exp
5×sub-neg
4×expm1-log1p-u associate-*r/ log1p-expm1-u distribute-lft-out difference-of-squares
3×flip3-- fma-neg *-commutative sin-cos-mult flip-- unswap-sqr
2×difference-of-sqr-1 pow-prod-down frac-add prod-exp cbrt-unprod distribute-lft-out--
1×+-commutative expm1-def flip3-+ diff-log sum-log flip-+
Counts
4 → 153
Calls
4 calls:
8.0ms
(* (sin x) (- (cos eps) 1))
4.0ms
(* (sin eps) (cos x))
21.0ms
(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
5.0ms
(- (cos eps) 1)

series230.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sin x) (- (cos eps) 1))
47.0ms
(* (sin eps) (cos x))
118.0ms
(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
19.0ms
(- (cos eps) 1)

simplify66.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05221296
120551023
250011014

prune341.0ms

Filtered
165 candidates to 101 candidates (38.8%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New15312165
Fresh112
Picked101
Done000
Total15513168

Merged error: 0.1b

Counts
168 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* (sin eps) (cos x)) (* (sin x) (cbrt (pow (- (cos eps) 1) 3))))
0.3b
(cbrt (pow (- (cos eps) 1) 3))
0.3b
(pow (- (cos eps) 1) 3)
1.6b
(- (cos eps) 1)

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
32×add-sqr-sqrt
18×add-cube-cbrt
14×unpow-prod-down
12×cbrt-prod fma-def
9×prod-diff
8×add-log-exp
7×associate-*l*
6×add-exp-log difference-of-squares
5×pow1 add-cbrt-cube
4×expm1-log1p-u pow-unpow log1p-expm1-u distribute-lft-out
3×fma-neg difference-of-sqr-1 associate-*r* distribute-lft-out--
2×unpow3 rem-cbrt-cube sqr-pow
1×+-commutative pow-to-exp sub-neg expm1-def flip3-- pow-pow flip3-+ pow1/3 diff-log pow-exp sum-log *-commutative flip-- flip-+ rem-cube-cbrt unswap-sqr
Counts
4 → 109
Calls
4 calls:
25.0ms
(+ (* (sin eps) (cos x)) (* (sin x) (cbrt (pow (- (cos eps) 1) 3))))
4.0ms
(cbrt (pow (- (cos eps) 1) 3))
4.0ms
(pow (- (cos eps) 1) 3)
5.0ms
(- (cos eps) 1)

series213.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(+ (* (sin eps) (cos x)) (* (sin x) (cbrt (pow (- (cos eps) 1) 3))))
19.0ms
(cbrt (pow (- (cos eps) 1) 3))
50.0ms
(pow (- (cos eps) 1) 3)
19.0ms
(- (cos eps) 1)

simplify48.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0392678
11474603
25002592

prune297.0ms

Filtered
121 candidates to 74 candidates (38.8%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1192121
Fresh21012
Picked011
Done000
Total12113134

Merged error: 0.0b

Counts
134 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin eps) (cos x))
0.2b
(+ (* (sin eps) (cos x)) (* (sin x) (log1p (expm1 (- (cos eps) 1)))))
0.2b
(log1p (expm1 (- (cos eps) 1)))
1.6b
(- (cos eps) 1)

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
24×add-sqr-sqrt
16×add-cube-cbrt
12×fma-def
10×associate-*l*
9×prod-diff
8×add-log-exp
7×add-exp-log
6×pow1 associate-*r* add-cbrt-cube
5×expm1-log1p-u
4×log1p-expm1-u distribute-lft-out
3×fma-neg
2×log1p-expm1 *-commutative difference-of-squares unswap-sqr
1×+-commutative sub-neg expm1-def log1p-udef flip3-- flip3-+ diff-log difference-of-sqr-1 pow-prod-down prod-exp sum-log sin-cos-mult flip-- cbrt-unprod flip-+ distribute-lft-out--
Counts
4 → 93
Calls
4 calls:
4.0ms
(* (sin eps) (cos x))
14.0ms
(+ (* (sin eps) (cos x)) (* (sin x) (log1p (expm1 (- (cos eps) 1)))))
1.0ms
(log1p (expm1 (- (cos eps) 1)))
5.0ms
(- (cos eps) 1)

series368.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin eps) (cos x))
146.0ms
(+ (* (sin eps) (cos x)) (* (sin x) (log1p (expm1 (- (cos eps) 1)))))
159.0ms
(log1p (expm1 (- (cos eps) 1)))
19.0ms
(- (cos eps) 1)

simplify48.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0353633
11196518
25001491

prune256.0ms

Filtered
105 candidates to 72 candidates (31.4%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1032105
Fresh2911
Picked101
Done011
Total10612118

Merged error: 0.0b

Counts
118 → 12

regimes121.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01910
11910

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.6s3305×body1280valid
561.0ms610×body2560valid
492.0ms1850×body640valid
125.0ms758×body320valid
57.0ms1102×body80valid
54.0ms375×body160valid