Details

Time bar (total: 2.5s)

sample153.0ms

Algorithm
intervals
Results
80.0ms54×body2560valid
43.0ms97×body1280valid
11.0ms49×body640valid
5.0ms30×body320valid
3.0ms1×body5120valid
2.0ms17×body160valid
1.0ms8×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

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: 30.9b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) (sin x))
2.3b
(- 1.0 (cos x))

rewrite12.0ms

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:
7.0ms
(/ (- 1.0 (cos x)) (sin x))
4.0ms
(- 1.0 (cos x))

series61.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(/ (- 1.0 (cos x)) (sin x))
19.0ms
(- 1.0 (cos x))

simplify85.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0233396
1673373
22640373
35002373

prune155.0ms

Filtered
58 candidates to 42 candidates (72.4%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New431558
Fresh000
Picked101
Done000
Total441559

Merged error: 0.1b

Counts
59 → 15

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) (sin x))
0.3b
(exp (/ (- 1.0 (cos x)) (sin x)))
1.4b
(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.3b
(- 1.0 (cos x))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt *-un-lft-identity
45×times-frac
38×exp-prod
33×add-cube-cbrt
20×log-pow
11×distribute-lft-out-- difference-of-squares
7×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
3×log-prod div-sub associate-/r* div-inv
2×flip3-- exp-diff flip-- associate-/l/
1×cbrt-undiv sub-neg log-div frac-2neg diff-log div-exp rem-log-exp clear-num rem-exp-log
Counts
4 → 112
Calls
4 calls:
10.0ms
(/ (- 1.0 (cos x)) (sin x))
6.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
8.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms
(- 1.0 (cos x))

series138.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (- 1.0 (cos x)) (sin x))
48.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
36.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms
(- 1.0 (cos x))

simplify95.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0303818
1799768
22970766
35001766

prune286.0ms

Filtered
124 candidates to 89 candidates (71.8%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New1195124
Fresh31114
Picked101
Done000
Total12316139

Merged error: 0.1b

Counts
139 → 16

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
0.4b
(pow (cos x) 3)
0.5b
(+ (cos x) 1.0)
2.0b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
157×add-sqr-sqrt
89×*-un-lft-identity
80×difference-of-squares
75×times-frac
63×unpow-prod-down cube-prod
41×sqr-pow
37×add-cube-cbrt
25×associate-/l* distribute-lft-out--
8×add-log-exp
7×add-exp-log add-cbrt-cube
5×pow1 difference-cubes
3×pow-unpow associate-/r*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative cube-mult pow-to-exp sub-neg pow-pow frac-2neg diff-log unpow3 div-sub div-exp pow-exp clear-num sum-log div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 189
Calls
4 calls:
24.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
2.0ms
(pow (cos x) 3)
4.0ms
(+ (cos x) 1.0)
16.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series226.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
28.0ms
(pow (cos x) 3)
10.0ms
(+ (cos x) 1.0)
53.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify102.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
06172953
126992889
250022810

prune411.0ms

Filtered
201 candidates to 105 candidates (52.2%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1956201
Fresh8715
Picked101
Done000
Total20413217

Merged error: 0.1b

Counts
217 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.5b
(+ (cos x) 1.0)
0.8b
(log (exp (pow (cos x) 3)))
2.0b
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
17×*-un-lft-identity
14×log-pow
12×add-cube-cbrt exp-prod
7×pow1 unpow-prod-down cube-prod add-log-exp
6×log-prod
5×add-exp-log add-cbrt-cube
4×difference-of-squares
3×pow-unpow associate--r+ sqr-pow
2×cube-mult unpow3 distribute-lft-out--
1×+-commutative pow-to-exp sub-neg flip3-- pow-pow flip3-+ diff-log rem-log-exp pow-exp sum-log flip-- flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 80
Calls
4 calls:
3.0ms
(pow (cos x) 3)
4.0ms
(+ (cos x) 1.0)
4.0ms
(log (exp (pow (cos x) 3)))
16.0ms
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

series127.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(pow (cos x) 3)
11.0ms
(+ (cos x) 1.0)
28.0ms
(log (exp (pow (cos x) 3)))
52.0ms
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

simplify44.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0296446
11109381
25001373

prune225.0ms

Filtered
92 candidates to 60 candidates (65.2%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New90292
Fresh01212
Picked101
Done000
Total9114105

Merged error: 0.1b

Counts
105 → 14

regimes147.0ms

bsearch2.0ms

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