Details

Time bar (total: 3.1s)

sample48.0ms

Algorithm
intervals
Results
20.0ms739×body80nan
12.0ms256×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
(sqrt (- 1.0 (* x x)))
0.0b
(/ (sqrt (- 1.0 (* x x))) x)
0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
36×times-frac
35×add-sqr-sqrt
29×add-cube-cbrt
20×sqrt-prod
13×fma-def
7×associate-/l*
5×add-exp-log add-cbrt-cube add-log-exp difference-of-squares
4×pow1 sqrt-div div-inv distribute-lft-out
3×expm1-log1p-u associate-/r* log1p-expm1-u
2×flip3-- flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square distribute-rgt-out frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp frac-add clear-num sum-log flip-+
Counts
3 → 97
Calls
3 calls:
3.0ms
(sqrt (- 1.0 (* x x)))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)
26.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series305.0ms

Counts
3 → 9
Calls
3 calls:
65.0ms
(sqrt (- 1.0 (* x x)))
134.0ms
(/ (sqrt (- 1.0 (* x x))) x)
106.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify43.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0415739
11440714
25002698

prune289.0ms

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 1.0) (* (* x x) (* x x)))) (* x (sqrt (+ 1.0 (* x x)))))
0.0b
(sqrt (- (* 1.0 1.0) (* (* x x) (* x x))))
0.0b
(+ (/ 1.0 x) (/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (* x (sqrt (+ 1.0 (* x x))))))
0.2b
(* (* x x) (* x x))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
116×pow1
36×pow-prod-up
23×pow-prod-down
22×pow-sqr
21×add-exp-log add-cbrt-cube
18×*-un-lft-identity pow-plus
17×add-sqr-sqrt
16×add-cube-cbrt times-frac
13×pow2 fma-def
12×sqrt-prod
9×prod-exp cbrt-unprod
7×associate-/l*
6×sqrt-div add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×difference-of-squares
2×cbrt-undiv flip3-- flip3-+ associate-*r/ div-exp associate-/r/ flip-- flip-+ div-inv associate-/l/
1×+-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 swap-sqr associate-*r* associate-*l* frac-add clear-num associate-/r* sum-log *-commutative distribute-lft-out unswap-sqr
Counts
4 → 146
Calls
4 calls:
11.0ms
(/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (* x (sqrt (+ 1.0 (* x x)))))
4.0ms
(sqrt (- (* 1.0 1.0) (* (* x x) (* x x))))
25.0ms
(+ (/ 1.0 x) (/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (* x (sqrt (+ 1.0 (* x x))))))
12.0ms
(* (* x x) (* x x))

series494.0ms

Counts
4 → 12
Calls
4 calls:
199.0ms
(/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (* x (sqrt (+ 1.0 (* x x)))))
111.0ms
(sqrt (- (* 1.0 1.0) (* (* x x) (* x x))))
152.0ms
(+ (/ 1.0 x) (/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (* x (sqrt (+ 1.0 (* x x))))))
32.0ms
(* (* x x) (* x x))

simplify62.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05541134
121341053
250011045

prune366.0ms

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

sample1.3s

Algorithm
intervals
Results
679.0ms24242×body80nan
281.0ms8000×body80valid