Details

Time bar (total: 3.0s)

sample330.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
7.0ms234×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0166
1196
2216
3216

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
45×add-sqr-sqrt
41×times-frac
26×sqrt-prod
24×add-cube-cbrt
11×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
5×add-exp-log add-cbrt-cube associate-/l*
4×pow1 associate-/r* associate-/r/
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num flip--
Counts
3 → 97
Calls
3 calls:
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
17.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
27.0ms
(/ (- 1.0 x) (+ 1.0 x))

series141.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
88.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
48.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify39.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0370779
11128734
25001719

prune235.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite231.0ms

Algorithm
rewrite-expression-head
Rules
670×sqrt-prod
586×*-un-lft-identity
528×times-frac
514×add-sqr-sqrt
228×add-cube-cbrt
138×swap-sqr
82×distribute-lft-out
74×distribute-lft-out--
62×associate-*r* associate-*l*
52×difference-of-squares
25×unswap-sqr
20×add-exp-log add-cbrt-cube
16×sqrt-div associate-/l*
14×associate-/r*
12×associate-/r/
11×pow1
6×cbrt-undiv sqrt-undiv flip3-+ div-exp flip-+ div-inv
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u associate-/l/ add-log-exp
2×flip3-- frac-2neg clear-num flip--
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ pow-prod-down associate-*l/ rem-square-sqrt pow-sqr *-commutative pow-prod-up
Counts
4 → 504
Calls
4 calls:
1.0ms
(atan (sqrt (* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))))
23.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
23.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
142.0ms
(* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

series214.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(atan (sqrt (* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))))
88.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
90.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
33.0ms
(* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

simplify139.0ms

Algorithm
egg-herbie
Counts
516 → 516
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
09517951
148696800
250016798

prune817.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01414
11414

end0.0ms

sample762.0ms

Algorithm
intervals
Results
307.0ms8000×body80valid
206.0ms7914×body80nan