Details

Time bar (total: 3.7s)

sample50.0ms

Algorithm
intervals
Results
24.0ms837×body80nan
9.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0127
1167
2167

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
30×add-sqr-sqrt
27×times-frac
23×add-cube-cbrt
20×sqrt-prod
8×add-log-exp
7×associate-/l*
6×add-exp-log add-cbrt-cube difference-of-squares
5×pow1
4×sqrt-div distribute-lft-out
3×flip3-- associate-/r* flip-- div-inv
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 → 91
Calls
4 calls:
2.0ms
(- 1.0 (* x x))
2.0ms
(sqrt (- 1.0 (* x x)))
26.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series337.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- 1.0 (* x x))
56.0ms
(sqrt (- 1.0 (* x x)))
110.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
128.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify43.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0409777
11409748
25001730

prune256.0ms

Filtered
103 candidates to 81 candidates (78.6%)
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
(+ (/ 1.0 x) (/ (/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (sqrt (+ 1.0 (* x x)))) x))
0.0b
(/ (/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (sqrt (+ 1.0 (* x x)))) x)
0.0b
(/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (sqrt (+ 1.0 (* x x))))
0.1b
(* (* x x) (* x x))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
360×times-frac
232×sqrt-prod
201×*-un-lft-identity
193×add-sqr-sqrt add-cube-cbrt
115×pow1
55×associate-/l*
36×pow-prod-up
31×difference-of-squares
23×add-exp-log pow-prod-down add-cbrt-cube
22×pow-sqr
18×pow-plus
13×pow2
12×sqrt-div
10×associate-/r/
9×associate-/r*
8×prod-exp cbrt-unprod div-inv
6×flip3-+ flip-+ add-log-exp
4×cbrt-undiv div-exp distribute-lft-out
3×associate-/l/
2×frac-2neg clear-num
1×+-commutative sqrt-undiv distribute-rgt-out flip3-- swap-sqr associate-*r* associate-*l* frac-add sum-log *-commutative flip-- unswap-sqr
Counts
4 → 362
Calls
4 calls:
100.0ms
(+ (/ 1.0 x) (/ (/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (sqrt (+ 1.0 (* x x)))) x))
21.0ms
(/ (/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (sqrt (+ 1.0 (* x x)))) x)
10.0ms
(/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (sqrt (+ 1.0 (* x x))))
15.0ms
(* (* x x) (* x x))

series480.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(+ (/ 1.0 x) (/ (/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (sqrt (+ 1.0 (* x x)))) x))
187.0ms
(/ (/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (sqrt (+ 1.0 (* x x)))) x)
110.0ms
(/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (sqrt (+ 1.0 (* x x))))
38.0ms
(* (* x x) (* x x))

simplify136.0ms

Algorithm
egg-herbie
Counts
374 → 374
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010866031
145105828
250025828

prune805.0ms

Filtered
374 candidates to 203 candidates (54.3%)
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
01614
11614

end0.0ms

sample1.4s

Algorithm
intervals
Results
701.0ms24046×body80nan
286.0ms8000×body80valid