Details

Time bar (total: 3.1s)

sample297.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
16.0ms280×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

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b
(/ (- 1.0 x) (+ 1.0 x))
0.0b
(atan (sqrt (/ (- 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)))
14.0ms
(/ (- 1.0 x) (+ 1.0 x))
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series147.0ms

Counts
3 → 9
Calls
3 calls:
94.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
35.0ms
(/ (- 1.0 x) (+ 1.0 x))
18.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify40.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0370779
11128734
25001719

prune240.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
18×flip3-+ flip-+
16×add-sqr-sqrt sqrt-prod associate-/r/
12×pow1 frac-times add-cube-cbrt
11×add-exp-log add-cbrt-cube
9×times-frac
6×associate-*r/ swap-sqr associate-*l/ distribute-lft-out
4×expm1-log1p-u associate-*r* associate-*l* log1p-expm1-u associate-/l* add-log-exp
3×difference-of-squares
2×cbrt-undiv rem-sqrt-square div-exp prod-exp cbrt-unprod div-inv associate-/l/
1×pow2 distribute-rgt-in flip3-- frac-2neg distribute-lft-in sqrt-pow1 pow-plus pow1/2 sqrt-div div-sub pow-prod-down clear-num associate-/r* pow-sqr *-commutative pow-prod-up flip-- unswap-sqr
Counts
4 → 117
Calls
4 calls:
12.0ms
(sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))))
0.0ms
(atan (sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))))
16.0ms
(/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))
17.0ms
(* (+ 1.0 x) (+ 1.0 x))

series158.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))))
4.0ms
(atan (sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))))
50.0ms
(/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))
17.0ms
(* (+ 1.0 x) (+ 1.0 x))

simplify74.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
05271107
12355948
25001914

prune294.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
28×times-frac
24×add-sqr-sqrt log-pow
22×add-cube-cbrt add-log-exp
17×pow1
12×exp-to-pow
8×add-exp-log add-cbrt-cube difference-of-squares
7×associate-/r*
6×exp-prod flip3-+ swap-sqr sum-log flip-+ distribute-lft-out
5×log-prod
4×expm1-log1p-u frac-times associate-*r* associate-*l* log1p-expm1-u associate-/l*
2×distribute-rgt-in distribute-lft-in associate-*r/ exp-sum associate-*l/ associate-/l/
1×cbrt-undiv pow2 flip3-- frac-2neg pow-plus div-sub div-exp rem-log-exp pow-prod-down prod-exp clear-num pow-sqr *-commutative pow-prod-up flip-- cbrt-unprod div-inv unswap-sqr
Counts
4 → 126
Calls
4 calls:
0.0ms
(atan (sqrt (/ (- (* 1.0 1.0) (* x x)) (log (exp (* (+ 1.0 x) (+ 1.0 x)))))))
9.0ms
(/ (- (* 1.0 1.0) (* x x)) (log (exp (* (+ 1.0 x) (+ 1.0 x)))))
2.0ms
(log (exp (* (+ 1.0 x) (+ 1.0 x))))
17.0ms
(* (+ 1.0 x) (+ 1.0 x))

series87.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(atan (sqrt (/ (- (* 1.0 1.0) (* x x)) (log (exp (* (+ 1.0 x) (+ 1.0 x)))))))
47.0ms
(/ (- (* 1.0 1.0) (* x x)) (log (exp (* (+ 1.0 x) (+ 1.0 x)))))
16.0ms
(log (exp (* (+ 1.0 x) (+ 1.0 x))))
17.0ms
(* (+ 1.0 x) (+ 1.0 x))

simplify74.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
04631203
122041013
25001995

prune307.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes69.0ms

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

sample1.1s

Algorithm
intervals
Results
530.0ms8000×body80valid
409.0ms7959×body80nan