Details

Time bar (total: 3.6s)

sample49.0ms

Algorithm
intervals
Results
24.0ms844×body80nan
9.0ms256×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0127
1167
2187
3187

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
47×*-un-lft-identity
42×times-frac
35×add-sqr-sqrt
31×add-cube-cbrt
16×sqrt-prod
13×fma-def
8×log-prod distribute-lft-out
7×associate-/l*
6×add-exp-log div-inv
5×add-cbrt-cube add-log-exp
4×pow1 difference-of-squares
3×expm1-log1p-u log-div associate-/r* log1p-expm1-u
2×distribute-rgt-out flip3-+ sqrt-div frac-add flip-+ associate-/l/
1×cbrt-undiv +-commutative flip3-- frac-2neg div-exp rem-log-exp clear-num sum-log log-pow flip--
Counts
3 → 101
Calls
3 calls:
18.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
19.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
9.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series522.0ms

Counts
3 → 9
Calls
3 calls:
293.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
99.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
130.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify47.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0479926
11679875
25001867

prune282.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt (- 1.0 (* x x))) x)
0.0b
(/ (sqrt (- 1.0 (* x x))) x)
0.1b
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.1b
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
68×times-frac
58×*-un-lft-identity
52×sqrt-prod
42×add-cube-cbrt
14×associate-/l*
12×hypot-def
10×sqrt-div
8×add-exp-log add-cbrt-cube distribute-lft-out difference-of-squares
6×pow1 associate-/r* div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square distribute-rgt-out flip3-- frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp frac-add clear-num flip-- flip-+
Counts
4 → 152
Calls
4 calls:
8.0ms
(/ (sqrt (- 1.0 (* x x))) x)
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)
20.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
20.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series664.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(/ (sqrt (- 1.0 (* x x))) x)
127.0ms
(/ (sqrt (- 1.0 (* x x))) x)
204.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
198.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify55.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
05151466
117181416
250021378

prune562.0ms

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
01217
11217

end0.0ms

sample1.3s

Algorithm
intervals
Results
683.0ms23786×body80nan
285.0ms8000×body80valid