Details

Time bar (total: 2.6s)

sample43.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 50.024414%

Guaranteed chance to sample good point: 99.987787%

Results
13.0ms256×body80valid

simplify568.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0166
1196
2216
3216

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite33.0ms

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×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 → 91
Calls
3 calls:
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
7.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
20.0ms
(/ (- 1.0 x) (+ 1.0 x))

series18.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
5.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
10.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify39.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0354753
11071709
25001688

prune158.0ms

Filtered
70 candidates to 100 candidates (-42.9%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New991100
Fresh000
Picked101
Done000
Total1001101

Merged error: 0b

Counts
101 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
1144×times-frac
1018×*-un-lft-identity
958×sqrt-prod
706×add-sqr-sqrt
462×add-cube-cbrt
165×distribute-lft-out
113×distribute-lft-out-- difference-of-squares
46×associate-/l*
39×sqrt-div
36×associate-/r/
19×flip3-+ flip-+
18×div-inv
14×associate-/r*
11×add-exp-log add-cbrt-cube
8×rem-sqrt-square
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×div-sub associate-/l/
2×frac-2neg sqrt-pow1 pow1/2 clear-num
1×flip3-- flip--
Counts
4 → 743
Calls
4 calls:
3.0ms
(sqrt (+ 1.0 x))
39.0ms
(sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x))))
8.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))
20.0ms
(/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))

series19.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(sqrt (+ 1.0 x))
5.0ms
(sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x))))
7.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))
4.0ms
(/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))

simplify183.0ms

Algorithm
egg-herbie
Counts
755 → 755
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
0127712222
1433610997
2500310843

prune885.0ms

Filtered
234 candidates to 755 candidates (-222.6%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New7550755
Fresh000
Picked011
Done000
Total7551756

Merged error: 0b

Counts
756 → 1

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01310
11310

end0.0ms

sample527.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 50.024414%

Guaranteed chance to sample good point: 99.987787%

Results
381.0ms8000×body80valid

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