Details

Time bar (total: 4.6s)

sample292.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
7.0ms275×body80nan

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0166
1196
2216
3216

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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))

rewrite25.0ms

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))))
8.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
11.0ms
(/ (- 1.0 x) (+ 1.0 x))

series151.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
94.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
52.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify41.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0370779
11128734
25001719

prune242.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x)))))
0.0b
(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))
0.0b
(/ 1 (sqrt (+ 1.0 x)))
0.0b
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
148×add-sqr-sqrt
144×*-un-lft-identity
134×times-frac
84×sqrt-prod
72×add-cube-cbrt
41×associate-*r*
32×add-exp-log
27×associate-*l*
20×add-cbrt-cube
18×distribute-lft-out
15×distribute-lft-out-- difference-of-squares unswap-sqr
14×associate-/r*
11×pow1 sqrt-div div-exp
8×prod-exp associate-/r/ associate-/l*
6×cbrt-undiv
4×expm1-log1p-u flip3-+ cbrt-unprod flip-+ log1p-expm1-u div-inv add-log-exp
3×rec-exp pow-flip sqrt-pow1 1-exp
2×frac-times frac-2neg pow1/2 associate-*r/ pow-prod-down associate-*l/ clear-num associate-/l/
1×flip3-- div-sub *-commutative flip-- inv-pow
Counts
4 → 244
Calls
4 calls:
16.0ms
(sqrt (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x)))))
39.0ms
(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))
7.0ms
(/ 1 (sqrt (+ 1.0 x)))
10.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(sqrt (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x)))))
33.0ms
(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))
56.0ms
(/ 1 (sqrt (+ 1.0 x)))
95.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

simplify104.0ms

Algorithm
egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
08322377
138952084
250011955

prune502.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))
0.0b
(/ 1 (sqrt (+ 1.0 x)))
0.0b
(expm1 (log1p (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))))
0.0b
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
148×add-sqr-sqrt
144×*-un-lft-identity
134×times-frac
83×sqrt-prod
72×add-cube-cbrt
41×associate-*r*
32×add-exp-log
27×associate-*l*
20×add-cbrt-cube
18×distribute-lft-out
15×distribute-lft-out-- difference-of-squares unswap-sqr
14×associate-/r*
11×div-exp
8×pow1 sqrt-div prod-exp associate-/r/ associate-/l*
6×cbrt-undiv
4×expm1-log1p-u flip3-+ cbrt-unprod flip-+ log1p-expm1-u div-inv add-log-exp
3×rec-exp pow-flip 1-exp
2×frac-2neg clear-num associate-/l/
1×frac-times expm1-log1p flip3-- sqrt-pow1 pow1/2 div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- inv-pow expm1-udef
Counts
4 → 239
Calls
4 calls:
36.0ms
(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))
7.0ms
(/ 1 (sqrt (+ 1.0 x)))
1.0ms
(expm1 (log1p (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))))
10.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

series356.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))
52.0ms
(/ 1 (sqrt (+ 1.0 x)))
170.0ms
(expm1 (log1p (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))))
95.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

simplify99.0ms

Algorithm
egg-herbie
Counts
251 → 251
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
08732373
139922067
250011916

prune575.0ms

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

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
124×*-un-lft-identity
85×add-sqr-sqrt
81×times-frac
78×sqrt-prod
58×exp-prod
48×add-cube-cbrt
30×log-pow
21×distribute-lft-out
17×distribute-lft-out-- difference-of-squares
8×associate-/r/
6×pow1 add-exp-log add-cbrt-cube
5×associate-/l* add-log-exp
4×expm1-log1p-u flip3-+ associate-/r* flip-+ log1p-expm1-u div-inv
3×log-prod
2×rem-sqrt-square associate-/l/
1×cbrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp rem-log-exp clear-num flip-- rem-exp-log
Counts
4 → 170
Calls
4 calls:
8.0ms
(sqrt (/ (- 1.0 x) (+ x 1.0)))
15.0ms
(log (exp (sqrt (/ (- 1.0 x) (+ x 1.0)))))
10.0ms
(exp (sqrt (/ (- 1.0 x) (+ x 1.0))))
9.0ms
(/ (- 1.0 x) (+ x 1.0))

series417.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(sqrt (/ (- 1.0 x) (+ x 1.0)))
99.0ms
(log (exp (sqrt (/ (- 1.0 x) (+ x 1.0)))))
189.0ms
(exp (sqrt (/ (- 1.0 x) (+ x 1.0))))
34.0ms
(/ (- 1.0 x) (+ x 1.0))

simplify53.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
05281348
116411273
250011222

prune461.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes15.0ms

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
02013
12013

end0.0ms

sample700.0ms

Algorithm
intervals
Results
306.0ms8000×body80valid
201.0ms8017×body80nan