Details

Time bar (total: 3.2s)

sample284.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
8.0ms257×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0166
1196
2216
3216

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b
(/ (- 1.0 x) (+ 1.0 x))
0.0b
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
45×add-sqr-sqrt
41×times-frac
26×sqrt-prod
24×add-cube-cbrt
11×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
5×add-exp-log add-cbrt-cube associate-/l*
4×pow1 associate-/r* associate-/r/
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num flip--
Counts
3 → 97
Calls
3 calls:
7.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
10.0ms
(/ (- 1.0 x) (+ 1.0 x))
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series161.0ms

Counts
3 → 9
Calls
3 calls:
100.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
53.0ms
(/ (- 1.0 x) (+ 1.0 x))
9.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify43.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0370779
11128734
25001719

prune252.0ms

Filtered
106 candidates to 76 candidates (71.7%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1.0 x) (+ 1.0 x))
0.0b
(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
0.0b
(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
0.0b
(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
151×*-un-lft-identity
100×times-frac
99×add-sqr-sqrt
58×cbrt-prod
57×add-cube-cbrt
52×unpow-prod-down cube-prod
26×distribute-lft-out
21×distribute-lft-out-- difference-of-squares
10×associate-/r/
9×add-exp-log add-cbrt-cube
5×pow1 flip3-+ flip-+ div-inv associate-/l*
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×pow-unpow
2×cbrt-undiv cube-div cube-mult unpow3 div-exp pow-exp associate-/l/ rem-cube-cbrt sqr-pow
1×pow-to-exp cbrt-div flip3-- pow-pow frac-2neg pow1/3 div-sub clear-num flip-- rem-cbrt-cube
Counts
4 → 201
Calls
4 calls:
9.0ms
(/ (- 1.0 x) (+ 1.0 x))
1.0ms
(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
11.0ms
(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
10.0ms
(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

series136.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (- 1.0 x) (+ 1.0 x))
2.0ms
(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
38.0ms
(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
61.0ms
(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

simplify74.0ms

Algorithm
egg-herbie
Counts
213 → 213
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05891594
125241477
250011459

prune384.0ms

Filtered
213 candidates to 103 candidates (48.4%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1.0 x) (+ 1.0 x))
0.0b
(cbrt (exp (log (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
0.0b
(pow (/ (- 1.0 x) (+ 1.0 x)) 3)
4.2b
(log (pow (/ (- 1.0 x) (+ 1.0 x)) 3))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
209×*-un-lft-identity
140×times-frac
137×add-sqr-sqrt
116×log-prod
79×add-cube-cbrt
78×unpow-prod-down cube-prod
61×cbrt-prod
58×exp-sum
36×distribute-lft-out
29×distribute-lft-out-- difference-of-squares
14×associate-/r/
13×add-exp-log
9×add-cbrt-cube
7×flip3-+ flip-+ div-inv
5×pow1 associate-/l*
4×expm1-log1p-u rem-log-exp pow-exp associate-/r* log1p-expm1-u add-log-exp
3×cube-div cube-mult pow-unpow unpow3 div-exp sqr-pow
2×cbrt-undiv pow-to-exp log-div associate-/l/ rem-cube-cbrt
1×cbrt-div flip3-- pow-pow frac-2neg exp-diff pow1/3 div-sub clear-num log-pow flip--
Counts
4 → 267
Calls
4 calls:
9.0ms
(/ (- 1.0 x) (+ 1.0 x))
16.0ms
(cbrt (exp (log (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
10.0ms
(pow (/ (- 1.0 x) (+ 1.0 x)) 3)
12.0ms
(log (pow (/ (- 1.0 x) (+ 1.0 x)) 3))

series321.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (- 1.0 x) (+ 1.0 x))
35.0ms
(cbrt (exp (log (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
65.0ms
(pow (/ (- 1.0 x) (+ 1.0 x)) 3)
186.0ms
(log (pow (/ (- 1.0 x) (+ 1.0 x)) 3))

simplify100.0ms

Algorithm
egg-herbie
Counts
279 → 279
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
07662686
131752153
250022119

prune542.0ms

Filtered
279 candidates to 123 candidates (44.1%)
Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01610
11610

end0.0ms

sample700.0ms

Algorithm
intervals
Results
307.0ms8000×body80valid
207.0ms8059×body80nan