Details

Time bar (total: 7.1s)

analyze513.0ms (7.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%100%0%3
37.5%62.5%0%4
43.7%56.2%0%5
46.9%53.1%0%6
48.4%51.5%0%7
49.2%50.8%0%8
49.6%50.4%0%9
49.8%50.2%0%10
49.9%50.1%0%11
49.9%50%0%12
50%50%0%13
50%49.9%0%14

sample152.0ms (2.1%)

Algorithm
1×intervals
Results
78.0ms54×body2560valid
41.0ms87×body1280valid
17.0ms67×body640valid
6.0ms33×body320valid
1.0ms10×body160valid
0.0ms5×body80valid

simplify12.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (10.0ms)

IterNodesCost
02297
12297

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.8b

Counts
2 → 1

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
0.9b
(- 1.0 (cos x))

rewrite11.0ms (0.2%)

Algorithm
1×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 → 51
Calls

2 calls:

6.0ms
(/ (- 1.0 (cos x)) (sin x))
4.0ms
(- 1.0 (cos x))

series12.0ms (0.2%)

Counts
2 → 6
Calls

2 calls:

8.0ms
(/ (- 1.0 (cos x)) (sin x))
4.0ms
(- 1.0 (cos x))

simplify41.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
05058605

prune140.0ms (2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New421557
Fresh000
Picked101
Done000
Total431558

Merged error: 0.2b

Counts
58 → 15

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(* 1/240 (pow x 5))
0.1b
(* 1/24 (pow x 3))

rewrite12.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
21×add-sqr-sqrt
19×associate-*r*
12×add-exp-log
9×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down
7×unswap-sqr
6×associate-*l* prod-exp add-cbrt-cube
4×cube-prod sqr-pow
2×pow1 pow-to-exp pow-exp *-commutative cbrt-unprod add-log-exp
1×cube-mult unpow3
Counts
2 → 56
Calls

2 calls:

6.0ms
(* 1/24 (pow x 3))
5.0ms
(* 1/240 (pow x 5))

series8.0ms (0.1%)

Counts
2 → 6
Calls

2 calls:

4.0ms
(* 1/240 (pow x 5))
4.0ms
(* 1/24 (pow x 3))

simplify42.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
05108391

prune155.0ms (2.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New62062
Fresh01414
Picked011
Done000
Total621577

Merged error: 0.2b

Counts
77 → 15

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
0.3b
(exp (/ (- 1.0 (cos x)) (sin x)))
0.7b
(log (exp (/ (- 1.0 (cos x)) (sin x))))
0.9b
(- 1.0 (cos x))

rewrite26.0ms (0.4%)

Algorithm
1×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 → 111
Calls

4 calls:

7.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
6.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
6.0ms
(/ (- 1.0 (cos x)) (sin x))
4.0ms
(- 1.0 (cos x))

series32.0ms (0.5%)

Counts
4 → 12
Calls

4 calls:

14.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
8.0ms
(/ (- 1.0 (cos x)) (sin x))
7.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms
(- 1.0 (cos x))

simplify48.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
055251215

prune232.0ms (3.3%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New1185123
Fresh31013
Picked101
Done011
Total12216138

Merged error: 0.1b

Counts
138 → 16

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x)))))
0.3b
(pow (cos x) 3)
0.4b
(+ 1.0 (cos x))
0.7b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite46.0ms (0.6%)

Algorithm
1×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 → 188
Calls

4 calls:

18.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x)))))
11.0ms
(- (pow 1.0 3) (pow (cos x) 3))
4.0ms
(+ 1.0 (cos x))
2.0ms
(pow (cos x) 3)

series38.0ms (0.5%)

Counts
4 → 12
Calls

4 calls:

24.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x)))))
7.0ms
(- (pow 1.0 3) (pow (cos x) 3))
5.0ms
(pow (cos x) 3)
2.0ms
(+ 1.0 (cos x))

simplify50.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
052004897

prune569.0ms (8%)

Pruning

19 alts after pruning (18 fresh and 1 done)

PrunedKeptTotal
New1928200
Fresh41014
Picked101
Done011
Total19719216

Merged error: 0.1b

Counts
216 → 19

regimes262.0ms (3.7%)

Accuracy

Total 0.6b remaining (77.2%)

Threshold costs 0.6b (77.2%)

bsearch1.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06369
16369

end0.0ms (0%)

sample4.7s (65.7%)

Algorithm
1×intervals
Results
2.3s1611×body2560valid
1.4s2796×body1280valid
482.0ms1853×body640valid
177.0ms936×body320valid
58.0ms469×body160valid
30.0ms330×body80valid
30.0ms5×body5120valid

Profiling

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