Details

Time bar (total: 1.6s)

sample37.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
11.0ms250×body80nan

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0127
1167
2167

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
28×add-sqr-sqrt
27×times-frac
22×add-cube-cbrt
20×sqrt-prod
7×associate-/l*
5×add-exp-log add-cbrt-cube add-log-exp difference-of-squares
4×pow1 sqrt-div distribute-lft-out
3×associate-/r* div-inv
2×flip3-- flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square distribute-rgt-out frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp frac-add clear-num sum-log flip-+
Counts
3 → 78
Calls
3 calls:
3.0ms
(sqrt (- 1.0 (* x x)))
21.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
5.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series17.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(sqrt (- 1.0 (* x x)))
6.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
7.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify42.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0394713
11362690
25001672

prune149.0ms

Filtered
87 candidates to 70 candidates (19.5%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New86187
Fresh000
Picked101
Done000
Total87188

Merged error: 0b

Counts
88 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (- 1.0 (* x x)))
0.0b
(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))
0.0b
(+ 1.0 (sqrt (- 1.0 (* x x))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
17×*-un-lft-identity
13×associate-*l*
12×add-exp-log add-cube-cbrt
11×times-frac
8×add-cbrt-cube
6×pow1
5×add-log-exp
4×associate-*r* prod-exp sqrt-prod
3×flip3-+ flip-+ unswap-sqr
2×frac-times sqrt-div associate-*r/ div-exp cbrt-unprod distribute-lft-out
1×cbrt-undiv +-commutative distribute-rgt-in rem-sqrt-square rec-exp flip3-- distribute-lft-in sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*l/ sum-log *-commutative flip-- div-inv difference-of-squares
Counts
3 → 70
Calls
3 calls:
2.0ms
(sqrt (- 1.0 (* x x)))
10.0ms
(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))
5.0ms
(+ 1.0 (sqrt (- 1.0 (* x x))))

series13.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(sqrt (- 1.0 (* x x)))
5.0ms
(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))
4.0ms
(+ 1.0 (sqrt (- 1.0 (* x x))))

simplify54.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0507625
12275562
25003552

prune126.0ms

Filtered
79 candidates to 63 candidates (20.3%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New79079
Fresh000
Picked011
Done000
Total79180

Merged error: 0b

Counts
80 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0147
1147

end0.0ms

sample1.1s

Algorithm
intervals
Results
403.0ms8000×body80valid
370.0ms8124×body80nan

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