Details

Time bar (total: 3.2s)

analyze231.0ms (7.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
75%25%0%5
75%25%0%6
78.1%21.9%0%7
78.1%21.9%0%8
78.1%21.9%0%9
78.1%21.9%0%10
78.1%21.9%0%11
78.1%21.9%0%12
78.1%21.9%0%13
78.1%21.8%0%14

sample67.0ms (2.1%)

Algorithm
1×intervals
Results
36.0ms71×body2560valid
9.0ms34×body1280valid
7.0ms45×body640valid
4.0ms29×body320valid
2.0ms67×body80valid
1.0ms10×body160valid

simplify23.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
05008
15008

prune5.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.8b

Counts
2 → 1

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

1.6b
(- 1.0 (cos x))
19.9b
(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-cube-cbrt add-log-exp
3×distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 41
Calls

2 calls:

7.0ms
(/ (- 1.0 (cos x)) (* x x))
3.0ms
(- 1.0 (cos x))

series9.0ms (0.3%)

Counts
2 → 6
Calls

2 calls:

6.0ms
(/ (- 1.0 (cos x)) (* x x))
3.0ms
(- 1.0 (cos x))

simplify55.0ms (1.7%)

Algorithm
1×egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
04894437
14894437

prune103.0ms (3.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New371047
Fresh000
Picked101
Done000
Total381048

Merged error: 0.0b

Counts
48 → 10

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.1b
(* (pow x 4) 1/720)
0.2b
(* (* x x) 1/24)
13.0b
(+ (* (pow x 4) 1/720) (- 1/2 (* (* x x) 1/24)))

rewrite18.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
13×add-exp-log add-sqr-sqrt
10×add-cbrt-cube
8×pow1 associate-*l* add-log-exp
7×add-cube-cbrt *-un-lft-identity
6×associate-*r* prod-exp
4×unpow-prod-down cbrt-unprod unswap-sqr
3×pow-prod-down
2×sum-log *-commutative sqr-pow
1×+-commutative pow-to-exp associate-+r- sub-neg associate-+r+ flip3-+ diff-log pow-exp flip-+
Counts
3 → 58
Calls

3 calls:

6.0ms
(+ (* (pow x 4) 1/720) (- 1/2 (* (* x x) 1/24)))
5.0ms
(* (* x x) 1/24)
5.0ms
(* (pow x 4) 1/720)

series11.0ms (0.3%)

Counts
3 → 9
Calls

3 calls:

5.0ms
(+ (* (pow x 4) 1/720) (- 1/2 (* (* x x) 1/24)))
4.0ms
(* (pow x 4) 1/720)
3.0ms
(* (* x x) 1/24)

simplify28.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
05259575

prune130.0ms (4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New67067
Fresh099
Picked011
Done000
Total671077

Merged error: 0.0b

Counts
77 → 10

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b
(/ (- 1.0 (cos x)) x)
1.6b
(- 1.0 (cos x))

rewrite29.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
62×add-sqr-sqrt
47×*-un-lft-identity
46×times-frac
29×add-cube-cbrt
27×add-exp-log
19×associate-*r*
17×add-cbrt-cube
13×associate-*l*
9×div-exp
8×prod-exp distribute-lft-out-- difference-of-squares
6×unswap-sqr
5×pow1 cbrt-undiv associate-/l* add-log-exp
4×cbrt-unprod
3×associate-/r* div-inv
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×frac-times sub-neg frac-2neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 113
Calls

3 calls:

13.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
6.0ms
(/ (- 1.0 (cos x)) x)
5.0ms
(- 1.0 (cos x))

series14.0ms (0.4%)

Counts
3 → 9
Calls

3 calls:

5.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
5.0ms
(/ (- 1.0 (cos x)) x)
3.0ms
(- 1.0 (cos x))

simplify44.0ms (1.4%)

Algorithm
1×egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
056581207

prune175.0ms (5.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1193122
Fresh448
Picked011
Done011
Total1239132

Merged error: 0.0b

Counts
132 → 9

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- 1.0 (cos x))) x)
0.1b
(/ (sqrt (- 1.0 (cos x))) x)
1.6b
(- 1.0 (cos x))
1.6b
(- 1.0 (cos x))

rewrite27.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
58×add-sqr-sqrt *-un-lft-identity
48×times-frac
40×sqrt-prod
38×add-cube-cbrt
16×associate-/l*
10×distribute-lft-out-- difference-of-squares
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r*
4×pow1 flip3-- sqrt-div flip-- associate-/l/
2×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 124
Calls

4 calls:

6.0ms
(/ (sqrt (- 1.0 (cos x))) x)
6.0ms
(/ (sqrt (- 1.0 (cos x))) x)
5.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series23.0ms (0.7%)

Counts
4 → 12
Calls

4 calls:

8.0ms
(/ (sqrt (- 1.0 (cos x))) x)
8.0ms
(/ (sqrt (- 1.0 (cos x))) x)
3.0ms
(- 1.0 (cos x))
3.0ms
(- 1.0 (cos x))

simplify47.0ms (1.5%)

Algorithm
1×egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
049801524
149801524

prune246.0ms (7.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1342136
Fresh156
Picked011
Done022
Total13510145

Merged error: 0.0b

Counts
145 → 10

regimes65.0ms (2%)

Accuracy

Total 0.1b remaining (55.4%)

Threshold costs 0.1b (55.4%)

bsearch34.0ms (1%)

Steps
ItersRangePoint
9
3.2576454935691815e-07
0.029958914207946503
0.029706365761949148
10
-0.35037948264050944
-3.301560155890433e-12
-0.032035318607155715

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07346
17346

end0.0ms (0%)

sample1.8s (55.4%)

Algorithm
1×intervals
Results
836.0ms1624×body2560valid
330.0ms1224×body1280valid
239.0ms1443×body640valid
115.0ms955×body320valid
89.0ms2293×body80valid
38.0ms461×body160valid

Profiling

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