Details

Time bar (total: 4.5s)

sample298.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
14.0ms282×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
(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))

rewrite30.0ms

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:
10.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
14.0ms
(/ (- 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))))
50.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify37.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0354753
11071709
25001690

prune231.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(atan (sqrt (/ (- (pow 1.0 3) (pow x 3)) (* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x)))))
0.0b
(* x (+ x 1.0))
0.0b
(* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x))
0.0b
(/ (- (pow 1.0 3) (pow x 3)) (* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
34×*-un-lft-identity
32×difference-of-squares
25×times-frac associate-/l*
24×unpow-prod-down cube-prod
16×sqr-pow
13×add-exp-log flip3-+ add-cbrt-cube flip-+
10×add-cube-cbrt distribute-lft-out--
8×pow1 frac-times associate-*r* associate-/r/
6×associate-*r/ associate-*l*
4×associate-*l/ add-log-exp
3×prod-exp cbrt-unprod
2×difference-cubes cbrt-undiv distribute-rgt-in distribute-lft-in div-exp pow-prod-down *-commutative associate-/l/ distribute-lft-out unswap-sqr
1×flip3-- frac-2neg div-sub clear-num associate-/r* flip-- div-inv
Counts
4 → 135
Calls
4 calls:
0.0ms
(atan (sqrt (/ (- (pow 1.0 3) (pow x 3)) (* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x)))))
10.0ms
(* x (+ x 1.0))
24.0ms
(* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x))
53.0ms
(/ (- (pow 1.0 3) (pow x 3)) (* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x)))

series157.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(atan (sqrt (/ (- (pow 1.0 3) (pow x 3)) (* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x)))))
43.0ms
(* x (+ x 1.0))
34.0ms
(* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x))
72.0ms
(/ (- (pow 1.0 3) (pow x 3)) (* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x)))

simplify107.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07051610
137501476
250011476

prune435.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (cbrt (/ (- 1.0 x) (+ 1.0 x))) (cbrt (/ (- 1.0 x) (+ 1.0 x)))) (cbrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b
(cbrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b
(cbrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b
(cbrt (/ (- 1.0 x) (+ 1.0 x)))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
117×*-un-lft-identity
106×cbrt-prod
81×add-sqr-sqrt times-frac
45×add-cube-cbrt
29×associate-*r*
23×pow1
20×distribute-lft-out
16×distribute-lft-out-- difference-of-squares
15×cbrt-div
12×pow1/3
9×add-exp-log pow-prod-up
8×associate-/r/
6×pow-plus
5×frac-times pow-prod-down associate-*l/ add-cbrt-cube
4×flip3-+ flip-+ div-inv add-log-exp
3×associate-*r/ prod-exp pow-sqr cbrt-unprod unswap-sqr
2×pow2
1×associate-*l* pow3 *-commutative
Counts
4 → 171
Calls
4 calls:
83.0ms
(* (* (cbrt (/ (- 1.0 x) (+ 1.0 x))) (cbrt (/ (- 1.0 x) (+ 1.0 x)))) (cbrt (/ (- 1.0 x) (+ 1.0 x))))
6.0ms
(cbrt (/ (- 1.0 x) (+ 1.0 x)))
8.0ms
(cbrt (/ (- 1.0 x) (+ 1.0 x)))
6.0ms
(cbrt (/ (- 1.0 x) (+ 1.0 x)))

series443.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (* (cbrt (/ (- 1.0 x) (+ 1.0 x))) (cbrt (/ (- 1.0 x) (+ 1.0 x)))) (cbrt (/ (- 1.0 x) (+ 1.0 x))))
136.0ms
(cbrt (/ (- 1.0 x) (+ 1.0 x)))
134.0ms
(cbrt (/ (- 1.0 x) (+ 1.0 x)))
140.0ms
(cbrt (/ (- 1.0 x) (+ 1.0 x)))

simplify66.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04431980
115101830
250021741

prune496.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
85×sqrt-prod
78×*-un-lft-identity
60×add-sqr-sqrt
56×times-frac
40×add-cube-cbrt
10×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
8×sqrt-div associate-/l*
7×associate-/r*
6×pow1 add-exp-log add-cbrt-cube
4×add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv sqrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 128
Calls
4 calls:
4.0ms
(sqrt (+ 1.0 x))
4.0ms
(sqrt (- 1.0 x))
4.0ms
(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
13.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series155.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (+ 1.0 x))
31.0ms
(sqrt (- 1.0 x))
4.0ms
(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
89.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify41.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
03531256
110841184
250011121

prune284.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes33.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02113
12313
22313

end0.0ms

sample1.2s

Algorithm
intervals
Results
622.0ms8000×body80valid
396.0ms8006×body80nan