Details

Time bar (total: 1.4s)

analyze5.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%50%50%3
12.5%25%62.5%4
18.7%12.5%68.8%5
21.9%6.2%71.9%6
23.4%3.1%73.5%7
24.2%1.6%74.2%8
24.6%0.8%74.6%9
24.8%0.4%74.8%10
24.9%0.2%74.9%11
24.9%0.1%75%12
25%0%75%13
25%0%75%14

sample19.0ms

Algorithm
intervals
Results
13.0ms256×body80valid

simplify126.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (124.0ms)

IterNodesCost
0489211
1489211

prune6.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 0.3b

Counts
2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- 1.0 (* x x)))
0.0b
(+ 1.0 (sqrt (- 1.0 (* x x))))
0.0b
(/ (+ 1.0 (sqrt (- 1.0 (* x x)))) x)
0.2b
(log (/ (+ 1.0 (sqrt (- 1.0 (* x x)))) x))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
24×add-sqr-sqrt times-frac
22×add-cube-cbrt
16×log-prod
9×add-exp-log
8×distribute-lft-out
6×pow1 add-cbrt-cube add-log-exp
4×sqrt-prod associate-/l*
3×associate-/r*
2×flip3-+ sqrt-div div-exp rem-log-exp flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square log-div flip3-- frac-2neg sqrt-pow1 pow1/2 clear-num sum-log log-pow flip-- difference-of-squares
Counts
4 → 88
Calls
4 calls:
3.0ms
(sqrt (- 1.0 (* x x)))
5.0ms
(+ 1.0 (sqrt (- 1.0 (* x x))))
7.0ms
(/ (+ 1.0 (sqrt (- 1.0 (* x x)))) x)
6.0ms
(log (/ (+ 1.0 (sqrt (- 1.0 (* x x)))) x))

series27.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(sqrt (- 1.0 (* x x)))
4.0ms
(+ 1.0 (sqrt (- 1.0 (* x x))))
9.0ms
(/ (+ 1.0 (sqrt (- 1.0 (* x x)))) x)
11.0ms
(log (/ (+ 1.0 (sqrt (- 1.0 (* x x)))) x))

simplify28.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
049951479
149951479

prune164.0ms

Filtered
77 candidates to 100 candidates (-29.9%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New991100
Fresh000
Picked101
Done000
Total1001101

Merged error: 0b

Counts
101 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 (sqrt (- 1.0 (* x x)))))
0.0b
(sqrt (+ 1.0 (sqrt (- 1.0 (* x x)))))
0.4b
(/ (sqrt (+ 1.0 (sqrt (- 1.0 (* x x))))) (sqrt x))
0.4b
(/ (sqrt (+ 1.0 (sqrt (- 1.0 (* x x))))) (sqrt x))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
112×sqrt-prod
98×*-un-lft-identity
84×times-frac
68×add-sqr-sqrt
66×add-cube-cbrt
16×distribute-lft-out
14×associate-/l*
12×associate-/r*
8×add-exp-log sqrt-div add-cbrt-cube
6×pow1
4×flip3-+ flip-+ associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 172
Calls
4 calls:
5.0ms
(sqrt (+ 1.0 (sqrt (- 1.0 (* x x)))))
5.0ms
(sqrt (+ 1.0 (sqrt (- 1.0 (* x x)))))
9.0ms
(/ (sqrt (+ 1.0 (sqrt (- 1.0 (* x x))))) (sqrt x))
9.0ms
(/ (sqrt (+ 1.0 (sqrt (- 1.0 (* x x))))) (sqrt x))

series45.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(sqrt (+ 1.0 (sqrt (- 1.0 (* x x)))))
8.0ms
(sqrt (+ 1.0 (sqrt (- 1.0 (* x x)))))
13.0ms
(/ (sqrt (+ 1.0 (sqrt (- 1.0 (* x x))))) (sqrt x))
16.0ms
(/ (sqrt (+ 1.0 (sqrt (- 1.0 (* x x))))) (sqrt x))

simplify44.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
052173822

prune381.0ms

Filtered
106 candidates to 184 candidates (-73.6%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New1840184
Fresh000
Picked011
Done000
Total1841185

Merged error: 0b

Counts
185 → 1

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03027
13027

end0.0ms

sample506.0ms

Algorithm
intervals
Results
416.0ms8000×body80valid
0.0ms6×body80nan

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