Details

Time bar (total: 5.3s)

sample89.0ms

Algorithm
intervals
Results
53.0ms803×body80nan
18.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0127
1167
2187
3187

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
49×*-un-lft-identity
42×times-frac
39×add-sqr-sqrt
33×add-cube-cbrt
20×sqrt-prod
13×fma-def
8×log-prod distribute-lft-out
7×add-exp-log associate-/l*
6×pow1 add-cbrt-cube div-inv add-log-exp
5×difference-of-squares
4×expm1-log1p-u sqrt-div log1p-expm1-u
3×log-div associate-/r*
2×distribute-rgt-out flip3-- flip3-+ frac-add flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp clear-num sum-log log-pow
Counts
4 → 119
Calls
4 calls:
23.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)
3.0ms
(sqrt (- 1.0 (* x x)))
28.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series592.0ms

Counts
4 → 12
Calls
4 calls:
296.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
132.0ms
(/ (sqrt (- 1.0 (* x x))) x)
60.0ms
(sqrt (- 1.0 (* x x)))
104.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify54.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05371057
119231003
25001992

prune362.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 x) (* (sqrt (/ (sqrt (- 1.0 (* x x))) x)) (sqrt (/ (sqrt (- 1.0 (* x x))) x))))
0.1b
(sqrt (/ (sqrt (- 1.0 (* x x))) x))
0.1b
(sqrt (/ (sqrt (- 1.0 (* x x))) x))
0.5b
(* (sqrt (/ (sqrt (- 1.0 (* x x))) x)) (sqrt (/ (sqrt (- 1.0 (* x x))) x)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
276×sqrt-prod
195×add-sqr-sqrt
167×times-frac
103×add-cube-cbrt *-un-lft-identity
36×swap-sqr
28×associate-*r* associate-*l*
21×pow1
18×difference-of-squares
16×unswap-sqr
13×fma-def
10×sqrt-pow1 pow1/2 sqrt-div
7×div-inv
6×add-exp-log rem-sqrt-square add-cbrt-cube add-log-exp
5×pow-prod-up
4×expm1-log1p-u log1p-expm1-u
3×pow-prod-down frac-add pow-sqr
2×frac-times associate-*r/ associate-*l/
1×+-commutative pow2 flip3-+ pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod flip-+
Counts
4 → 247
Calls
4 calls:
13.0ms
(+ (/ 1.0 x) (* (sqrt (/ (sqrt (- 1.0 (* x x))) x)) (sqrt (/ (sqrt (- 1.0 (* x x))) x))))
6.0ms
(sqrt (/ (sqrt (- 1.0 (* x x))) x))
6.0ms
(sqrt (/ (sqrt (- 1.0 (* x x))) x))
43.0ms
(* (sqrt (/ (sqrt (- 1.0 (* x x))) x)) (sqrt (/ (sqrt (- 1.0 (* x x))) x)))

series802.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(+ (/ 1.0 x) (* (sqrt (/ (sqrt (- 1.0 (* x x))) x)) (sqrt (/ (sqrt (- 1.0 (* x x))) x))))
207.0ms
(sqrt (/ (sqrt (- 1.0 (* x x))) x))
199.0ms
(sqrt (/ (sqrt (- 1.0 (* x x))) x))
252.0ms
(* (sqrt (/ (sqrt (- 1.0 (* x x))) x)) (sqrt (/ (sqrt (- 1.0 (* x x))) x)))

simplify117.0ms

Algorithm
egg-herbie
Counts
259 → 259
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
07002882
134272670
250022609

prune666.0ms

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
01214
11214

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.5s23724×body80nan
582.0ms8000×body80valid