Details

Time bar (total: 3.6s)

sample51.0ms

Algorithm
intervals
Results
25.0ms844×body80nan
9.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0127
1167
2167

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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)

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
33×times-frac
28×add-sqr-sqrt
24×add-cube-cbrt
16×sqrt-prod
8×log-prod distribute-lft-out
7×associate-/l*
6×add-exp-log
5×add-cbrt-cube div-inv add-log-exp
4×pow1 difference-of-squares
3×log-div associate-/r*
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 → 82
Calls
3 calls:
20.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
20.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series528.0ms

Counts
3 → 9
Calls
3 calls:
295.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
101.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
133.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify46.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0460892
11594844
25002822

prune229.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize14.0ms

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)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
54×times-frac
52×add-sqr-sqrt
48×sqrt-prod
42×add-cube-cbrt
14×associate-/l*
10×sqrt-div
8×add-exp-log add-cbrt-cube distribute-lft-out difference-of-squares
6×pow1 associate-/r* div-inv
4×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 → 132
Calls
4 calls:
6.0ms
(/ (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)))
21.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series674.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ (sqrt (- 1.0 (* x x))) x)
136.0ms
(/ (sqrt (- 1.0 (* x x))) x)
199.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
203.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify51.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04891422
116331374
250011336

prune502.0ms

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

sample1.4s

Algorithm
intervals
Results
704.0ms23786×body80nan
297.0ms8000×body80valid