Details

Time bar (total: 4.5s)

sample47.0ms

Algorithm
intervals
Results
22.0ms781×body80nan
9.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0127
1167
2167

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
29×*-un-lft-identity
27×times-frac
25×add-sqr-sqrt
21×add-cube-cbrt
16×sqrt-prod
8×log-prod
7×associate-/l*
5×add-exp-log
4×add-cbrt-cube distribute-lft-out difference-of-squares
3×pow1 log-div associate-/r* div-inv
2×sqrt-div associate-/l/ add-log-exp
1×cbrt-undiv distribute-rgt-out flip3-- frac-2neg flip3-+ div-exp rem-log-exp frac-add clear-num log-pow flip-- flip-+
Counts
2 → 65
Calls
2 calls:
25.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series432.0ms

Counts
2 → 6
Calls
2 calls:
301.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
130.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify43.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0421699
11454665
25002654

prune179.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite504.0ms

Algorithm
rewrite-expression-head
Rules
814×sqrt-prod
722×times-frac
432×add-sqr-sqrt
364×*-un-lft-identity
358×add-cube-cbrt
74×difference-of-squares
52×sqrt-div
46×associate-/r*
25×associate-/r/
13×flip3-- flip-- div-inv associate-/l*
11×add-exp-log
10×add-cbrt-cube
5×log-prod
4×pow1 cbrt-undiv div-exp
3×log-div add-log-exp
2×frac-2neg clear-num associate-/l/ distribute-lft-out
1×flip3-+ rem-log-exp frac-add log-pow flip-+
Counts
3 → 497
Calls
3 calls:
22.0ms
(/ (sqrt (sqrt (- 1.0 (* x x)))) (/ x (sqrt (sqrt (- 1.0 (* x x))))))
429.0ms
(log (+ (/ 1.0 x) (/ (sqrt (sqrt (- 1.0 (* x x)))) (/ x (sqrt (sqrt (- 1.0 (* x x))))))))
10.0ms
(/ x (sqrt (sqrt (- 1.0 (* x x)))))

series720.0ms

Counts
3 → 9
Calls
3 calls:
137.0ms
(/ (sqrt (sqrt (- 1.0 (* x x)))) (/ x (sqrt (sqrt (- 1.0 (* x x))))))
298.0ms
(log (+ (/ 1.0 x) (/ (sqrt (sqrt (- 1.0 (* x x)))) (/ x (sqrt (sqrt (- 1.0 (* x x))))))))
286.0ms
(/ x (sqrt (sqrt (- 1.0 (* x x)))))

simplify115.0ms

Algorithm
egg-herbie
Counts
506 → 506
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0149310457
150029360

prune1.0s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01213
11213

end0.0ms

sample1.4s

Algorithm
intervals
Results
698.0ms23922×body80nan
286.0ms8000×body80valid