Details

Time bar (total: 3.9s)

sample50.0ms

Algorithm
intervals
Results
24.0ms837×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

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
39×add-sqr-sqrt
36×times-frac
32×add-cube-cbrt
20×sqrt-prod
13×fma-def
8×add-log-exp
7×associate-/l*
6×add-exp-log add-cbrt-cube difference-of-squares
5×pow1
4×expm1-log1p-u sqrt-div log1p-expm1-u div-inv distribute-lft-out
3×flip3-- fma-neg prod-diff associate-/r* flip--
2×associate-/l/
1×cbrt-undiv +-commutative sub-neg rem-sqrt-square distribute-rgt-out frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log div-exp frac-add clear-num sum-log flip-+
Counts
4 → 118
Calls
4 calls:
3.0ms
(- 1.0 (* x x))
6.0ms
(sqrt (- 1.0 (* x x)))
19.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series335.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- 1.0 (* x x))
62.0ms
(sqrt (- 1.0 (* x x)))
103.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
129.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify51.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0444839
11517802
25002785

prune347.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (sqrt 1.0) x))
0.3b
(/ (sqrt (- (sqrt 1.0) x)) (sqrt x))
0.3b
(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
0.5b
(* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
290×sqrt-prod
274×add-sqr-sqrt
232×times-frac
181×*-un-lft-identity
127×add-cube-cbrt
58×associate-*r*
46×associate-*l*
26×difference-of-squares
25×unswap-sqr
20×add-exp-log add-cbrt-cube
16×associate-/l*
14×distribute-lft-out
13×distribute-lft-out--
12×associate-/r*
7×pow1
6×cbrt-undiv sqrt-div div-exp
4×expm1-log1p-u sqrt-undiv prod-exp cbrt-unprod log1p-expm1-u div-inv associate-/l/ add-log-exp
2×frac-2neg flip3-+ clear-num flip-+ hypot-def
1×frac-times rem-sqrt-square flip3-- sqrt-pow1 pow1/2 sqrt-unprod associate-*r/ pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 330
Calls
4 calls:
5.0ms
(sqrt (+ (sqrt 1.0) x))
9.0ms
(/ (sqrt (- (sqrt 1.0) x)) (sqrt x))
8.0ms
(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
59.0ms
(* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))

series493.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(sqrt (+ (sqrt 1.0) x))
127.0ms
(/ (sqrt (- (sqrt 1.0) x)) (sqrt x))
113.0ms
(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
193.0ms
(* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))

simplify130.0ms

Algorithm
egg-herbie
Counts
342 → 342
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
09444325
144464106
250014087

prune907.0ms

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
01714
11714

end0.0ms

sample1.4s

Algorithm
intervals
Results
708.0ms24046×body80nan
287.0ms8000×body80valid