Details

Time bar (total: 3.3s)

sample277.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
6.0ms245×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

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite31.0ms

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:
10.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
15.0ms
(/ (- 1.0 x) (+ 1.0 x))

series145.0ms

Counts
3 → 9
Calls
3 calls:
92.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
49.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify42.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0370779
11128734
25001719

prune251.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
192×sqrt-prod
172×add-sqr-sqrt
148×*-un-lft-identity
140×times-frac
74×add-cube-cbrt
44×associate-*r*
30×associate-*l*
24×unswap-sqr
18×distribute-lft-out
15×distribute-lft-out-- difference-of-squares
14×associate-/r*
12×add-exp-log sqrt-div
10×pow1 add-cbrt-cube
8×associate-/r/ associate-/l*
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u div-inv add-log-exp
3×pow-flip sqrt-pow1 pow1/2 div-exp pow-prod-down
2×cbrt-undiv frac-2neg clear-num associate-/l/
1×frac-times rec-exp flip3-- sqrt-unprod 1-exp div-sub associate-*r/ associate-*l/ prod-exp *-commutative flip-- cbrt-unprod inv-pow
Counts
4 → 245
Calls
4 calls:
16.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))
0.0ms
(atan (* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))))
7.0ms
(/ 1 (sqrt (+ 1.0 x)))
76.0ms
(* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x)))))

series237.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))
5.0ms
(atan (* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))))
51.0ms
(/ 1 (sqrt (+ 1.0 x)))
92.0ms
(* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x)))))

simplify76.0ms

Algorithm
egg-herbie
Counts
257 → 257
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
06952826
125352590
250012546

prune589.0ms

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

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
96×*-un-lft-identity
64×add-sqr-sqrt
60×times-frac
58×exp-prod
52×sqrt-prod
38×add-cube-cbrt
30×log-pow
16×distribute-lft-out
13×distribute-lft-out-- difference-of-squares
6×add-exp-log associate-/r/ add-cbrt-cube
5×pow1 associate-/l* add-log-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u
3×log-prod flip3-+ flip-+ div-inv
2×associate-/l/
1×cbrt-undiv flip3-- frac-2neg div-sub div-exp rem-log-exp clear-num flip-- rem-exp-log
Counts
4 → 139
Calls
4 calls:
0.0ms
(atan (log (exp (sqrt (/ (- 1.0 x) (+ x 1.0))))))
25.0ms
(exp (sqrt (/ (- 1.0 x) (+ x 1.0))))
25.0ms
(log (exp (sqrt (/ (- 1.0 x) (+ x 1.0)))))
13.0ms
(/ (- 1.0 x) (+ x 1.0))

series300.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan (log (exp (sqrt (/ (- 1.0 x) (+ x 1.0))))))
178.0ms
(exp (sqrt (/ (- 1.0 x) (+ x 1.0))))
88.0ms
(log (exp (sqrt (/ (- 1.0 x) (+ x 1.0)))))
32.0ms
(/ (- 1.0 x) (+ x 1.0))

simplify47.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
05081098
115761016
25001977

prune393.0ms

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
01912
11912

end0.0ms

sample692.0ms

Algorithm
intervals
Results
300.0ms8000×body80valid
201.0ms7995×body80nan