Details

Time bar (total: 6.3s)

sample124.0ms

Algorithm
intervals
Results
59.0ms47×body2560valid
34.0ms86×body1280valid
16.0ms74×body640valid
3.0ms21×body320valid
1.0ms13×body160valid
1.0ms15×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.8b
(- 1.0 (cos x))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
15×times-frac
12×add-cube-cbrt
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r*
2×pow1 flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 52
Calls
2 calls:
22.0ms
(/ (- 1.0 (cos x)) (sin x))
6.0ms
(- 1.0 (cos x))

series55.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(/ (- 1.0 (cos x)) (sin x))
19.0ms
(- 1.0 (cos x))

simplify80.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0233396
1673373
22654373
35001373

prune156.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos x) (+ (cos x) 1.0))
0.4b
(+ (cos x) 1.0)
0.4b
(pow (cos x) 3)
1.6b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
23×*-un-lft-identity
16×difference-of-squares
15×unpow-prod-down cube-prod
9×add-cube-cbrt sqr-pow
8×add-log-exp
7×pow1 add-exp-log add-cbrt-cube
5×distribute-lft-out--
4×associate-*r*
3×pow-unpow associate-*l*
2×flip3-+ associate-*r/ flip-+ distribute-lft-out
1×difference-cubes +-commutative distribute-rgt-in cube-mult pow-to-exp sub-neg flip3-- pow-pow distribute-lft-in diff-log unpow3 pow-prod-down pow-exp prod-exp sum-log *-commutative flip-- cbrt-unprod rem-cube-cbrt unswap-sqr
Counts
4 → 92
Calls
4 calls:
22.0ms
(* (cos x) (+ (cos x) 1.0))
7.0ms
(+ (cos x) 1.0)
5.0ms
(pow (cos x) 3)
23.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series115.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (cos x) (+ (cos x) 1.0))
10.0ms
(+ (cos x) 1.0)
28.0ms
(pow (cos x) 3)
50.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify66.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
0353593
11734555
25001535

prune257.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b
(/ (sin x) (- 1.0 (cos x)))
1.8b
(- 1.0 (cos x))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
105×add-sqr-sqrt *-un-lft-identity
71×add-cube-cbrt
26×associate-/r*
17×distribute-lft-out-- difference-of-squares
16×add-exp-log
11×associate-/r/
10×add-cbrt-cube
8×div-exp
6×flip3-- flip-- div-inv associate-/l*
5×add-log-exp
4×pow1 cbrt-undiv
2×rec-exp frac-2neg 1-exp clear-num
1×sub-neg pow-flip diff-log inv-pow
Counts
3 → 159
Calls
3 calls:
18.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
15.0ms
(/ (sin x) (- 1.0 (cos x)))
6.0ms
(- 1.0 (cos x))

series94.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
37.0ms
(/ (sin x) (- 1.0 (cos x)))
22.0ms
(- 1.0 (cos x))

simplify63.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05101595
123961452
250021339

prune257.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (cos x) 1.0)
0.4b
(pow (cos x) 3)
0.4b
(log (exp (+ (cos x) 1.0)))
1.6b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
23×*-un-lft-identity
16×difference-of-squares
15×unpow-prod-down cube-prod
9×add-cube-cbrt sqr-pow
8×add-log-exp
6×pow1
5×add-exp-log log-pow add-cbrt-cube distribute-lft-out--
4×log-prod exp-prod
3×pow-unpow
2×distribute-lft-out
1×difference-cubes +-commutative cube-mult pow-to-exp sub-neg flip3-- pow-pow flip3-+ diff-log unpow3 rem-log-exp exp-sum pow-exp sum-log flip-- flip-+ rem-cube-cbrt
Counts
4 → 86
Calls
4 calls:
6.0ms
(+ (cos x) 1.0)
3.0ms
(pow (cos x) 3)
20.0ms
(log (exp (+ (cos x) 1.0)))
23.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series98.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(+ (cos x) 1.0)
27.0ms
(pow (cos x) 3)
13.0ms
(log (exp (+ (cos x) 1.0)))
47.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify45.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0306525
11147494
25001474

prune248.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.1b

regimes146.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.3b

bsearch69.0ms

Steps
ItersRangePoint
8
0.002806896206153352
41.96612619086958
0.021731898587967143
7
-0.5149414008252181
-0.002950799818357885
-0.01849382956573876

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04426
14426

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.2s1642×body2560valid
1.2s2775×body1280valid
413.0ms1830×body640valid
143.0ms914×body320valid
59.0ms481×body160valid
22.0ms355×body80valid
13.0ms3×body5120valid