Details

Time bar (total: 3.5s)

sample347.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
9.0ms283×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0166
1196
2216
3216

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

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×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 → 91
Calls
3 calls:
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
17.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
26.0ms
(/ (- 1.0 x) (+ 1.0 x))

series141.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
89.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
48.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify38.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0354753
11071709
25001690

prune212.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite294.0ms

Algorithm
rewrite-expression-head
Rules
1273×sqrt-prod
651×*-un-lft-identity
606×add-sqr-sqrt
596×times-frac
263×add-cube-cbrt
143×swap-sqr
90×distribute-lft-out
81×distribute-lft-out--
65×associate-*r* associate-*l*
59×difference-of-squares
36×unswap-sqr
23×sqrt-div
20×pow1
16×associate-/l*
14×associate-/r* associate-/r/
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 pow1/2
7×flip3-+ flip-+ div-inv
5×rem-sqrt-square pow-prod-up
4×associate-/l/ add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv sqrt-undiv flip3-- frac-2neg div-exp clear-num flip--
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 590
Calls
4 calls:
23.0ms
(sqrt (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
23.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
25.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
172.0ms
(* (sqrt (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))) (sqrt (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))

series410.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(sqrt (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
88.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
87.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
95.0ms
(* (sqrt (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))) (sqrt (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))

simplify136.0ms

Algorithm
egg-herbie
Counts
602 → 602
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
06427500
129516977
250016908

prune988.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes66.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0116
1116

end0.0ms

sample781.0ms

Algorithm
intervals
Results
312.0ms8000×body80valid
208.0ms8109×body80nan