Details

Time bar (total: 4.2s)

sample50.0ms

Algorithm
intervals
Results
24.0ms837×body80nan
9.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0127
1167
2187
3187

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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)

rewrite41.0ms

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:
2.0ms
(- 1.0 (* x x))
3.0ms
(sqrt (- 1.0 (* x x)))
26.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series332.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(- 1.0 (* x x))
61.0ms
(sqrt (- 1.0 (* x x)))
101.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
132.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify50.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0444839
11517802
25002785

prune342.0ms

Filtered
130 candidates to 107 candidates (82.3%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
195×times-frac
119×*-un-lft-identity
115×pow1
111×add-sqr-sqrt add-cube-cbrt
64×sqrt-prod
36×pow-prod-up
32×associate-/l*
23×add-exp-log pow-prod-down add-cbrt-cube
22×pow-sqr
18×pow-plus
16×difference-of-squares
13×pow2 fma-def
9×div-inv
8×prod-exp cbrt-unprod
6×associate-/r* add-log-exp
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u distribute-lft-out
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×+-commutative sqrt-undiv hypot-udef distribute-rgt-out flip3-- flip3-+ swap-sqr associate-*r* associate-*l* frac-add sum-log *-commutative flip-- flip-+ unswap-sqr
Counts
4 → 265
Calls
4 calls:
63.0ms
(+ (/ 1.0 x) (/ (/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (hypot x (sqrt 1.0))) x))
13.0ms
(/ (/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (hypot x (sqrt 1.0))) x)
8.0ms
(/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (hypot x (sqrt 1.0)))
13.0ms
(* (* x x) (* x x))

series922.0ms

Counts
4 → 12
Calls
4 calls:
251.0ms
(+ (/ 1.0 x) (/ (/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (hypot x (sqrt 1.0))) x))
342.0ms
(/ (/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (hypot x (sqrt 1.0))) x)
292.0ms
(/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (hypot x (sqrt 1.0)))
36.0ms
(* (* x x) (* x x))

simplify110.0ms

Algorithm
egg-herbie
Counts
277 → 277
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
09453530
135263344
250013331

prune777.0ms

Filtered
277 candidates to 181 candidates (65.3%)
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
01513
11513

end0.0ms

sample1.4s

Algorithm
intervals
Results
709.0ms24046×body80nan
291.0ms8000×body80valid