Details

Time bar (total: 6.7s)

sample27.0ms

Algorithm
intervals
Results
7.0ms278×body80nan
7.0ms256×body80valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05122
17122
211122
313122
done13122

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt sqrt-prod
2×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
1×expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-- add-cbrt-cube pow1/2 add-exp-log log1p-expm1-u flip-- add-log-exp difference-of-squares
Counts
1 → 18
Calls
1 calls:
6.0ms
(sqrt (- 1.0 (* x x)))

series59.0ms

Counts
1 → 3
Calls
1 calls:
59.0ms
(sqrt (- 1.0 (* x x)))

simplify2.0s

Counts
21 → 21
Iterations

Useful iterations: 2 (138.0ms)

IterNodesCost
0696613
11625121
25084759
320634759
done50034759

prune95.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (- 1.0 (* x x)))
0.0b
(log1p (expm1 (sqrt (- 1.0 (* x x)))))
1.0b
(expm1 (sqrt (- 1.0 (* x x))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
4×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod log1p-expm1-u
3×expm1-log1p-u add-cbrt-cube add-exp-log add-log-exp
2×sqrt-div
1×rem-sqrt-square log1p-udef expm1-log1p sqrt-pow1 flip3-- pow1/2 log1p-expm1 flip-- expm1-udef difference-of-squares
Counts
3 → 40
Calls
3 calls:
12.0ms
(sqrt (- 1.0 (* x x)))
0.0ms
(log1p (expm1 (sqrt (- 1.0 (* x x)))))
1.0ms
(expm1 (sqrt (- 1.0 (* x x))))

series506.0ms

Counts
3 → 9
Calls
3 calls:
72.0ms
(sqrt (- 1.0 (* x x)))
300.0ms
(log1p (expm1 (sqrt (- 1.0 (* x x)))))
134.0ms
(expm1 (sqrt (- 1.0 (* x x))))

simplify2.5s

Counts
49 → 49
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
010616373
124111284
278110732
3304010666
done501010666

prune197.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(exp (sqrt (- 1.0 (* x x))))
0.0b
(sqrt (- 1.0 (* x x)))
0.0b
(log (exp (sqrt (- 1.0 (* x x)))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
14×exp-prod
13×add-sqr-sqrt
12×sqrt-prod
9×*-un-lft-identity add-cube-cbrt
8×log-pow
5×pow1
4×add-log-exp
3×expm1-log1p-u log-prod add-cbrt-cube add-exp-log log1p-expm1-u difference-of-squares
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 rem-log-exp flip-- rem-exp-log
Counts
3 → 56
Calls
3 calls:
16.0ms
(exp (sqrt (- 1.0 (* x x))))
7.0ms
(sqrt (- 1.0 (* x x)))
10.0ms
(log (exp (sqrt (- 1.0 (* x x)))))

series235.0ms

Counts
3 → 9
Calls
3 calls:
75.0ms
(exp (sqrt (- 1.0 (* x x))))
91.0ms
(sqrt (- 1.0 (* x x)))
68.0ms
(log (exp (sqrt (- 1.0 (* x x)))))

simplify988.0ms

Iterations

Useful iterations: 2 (297.0ms)

IterNodesCost
011921968
125515311
273914612