Details

Time bar (total: 5.8s)

sample81.0ms

Algorithm
intervals
Results
34.0ms94×body2560valid
20.0ms90×body1280valid
6.0ms40×body640valid
6.0ms234×body80nan
2.0ms16×body320valid
0.0ms6×body160valid
0.0ms10×body80valid

simplify94.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1427
2777
31467
42427
54177
627897
750017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.1b
(* 5.0 (* v v))
0.4b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×times-frac
10×add-exp-log add-cbrt-cube
8×pow1
4×associate-/r* difference-of-squares
3×associate-*l* pow-prod-down prod-exp cbrt-unprod associate-/l* add-log-exp
2×flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv acos-asin frac-2neg div-sub div-exp associate-*r* clear-num *-commutative div-inv unswap-sqr
Counts
3 → 63
Calls
3 calls:
10.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
7.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series108.0ms

Counts
3 → 9
Calls
3 calls:
81.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
24.0ms
(* 5.0 (* v v))
3.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify42.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0336587
11261535
25002531

prune157.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 4.0 (+ (pow v 2) (pow v 4)))
0.0b
(+ (pow v 2) (pow v 4))
0.4b
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
7×add-sqr-sqrt
5×pow1 add-exp-log add-cube-cbrt add-cbrt-cube add-log-exp
4×associate-*r*
3×associate-*l*
2×flip3-+ associate-*r/ flip-+ distribute-lft-out
1×+-commutative distribute-rgt-in acos-asin distribute-lft-in pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
3 → 43
Calls
3 calls:
32.0ms
(* 4.0 (+ (pow v 2) (pow v 4)))
9.0ms
(+ (pow v 2) (pow v 4))
1.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series179.0ms

Counts
3 → 9
Calls
3 calls:
100.0ms
(* 4.0 (+ (pow v 2) (pow v 4)))
72.0ms
(+ (pow v 2) (pow v 4))
7.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify152.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0177315
1834276
24136273
35002273

prune116.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ PI 2) (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
0.0b
(* 4.0 (+ (pow v 2) (pow v 4)))
0.0b
(+ (pow v 2) (pow v 4))
0.4b
(asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×*-un-lft-identity
8×add-log-exp
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
4×associate-*r*
3×associate-*l*
2×asin-acos flip3-+ associate-*r/ flip-+ distribute-lft-out difference-of-squares
1×+-commutative distribute-rgt-in sub-neg flip3-- distribute-lft-in times-frac diff-log pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod distribute-lft-out-- associate--r- unswap-sqr
Counts
4 → 59
Calls
4 calls:
11.0ms
(- (/ PI 2) (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
37.0ms
(* 4.0 (+ (pow v 2) (pow v 4)))
10.0ms
(+ (pow v 2) (pow v 4))
0.0ms
(asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series197.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(- (/ PI 2) (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
91.0ms
(* 4.0 (+ (pow v 2) (pow v 4)))
72.0ms
(+ (pow v 2) (pow v 4))
4.0ms
(asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify203.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0250546
11032503
24958497
35001497

prune173.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (- (pow (/ PI 2) 3) (pow (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)) 3)) (+ (* (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)) (+ (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)) (/ PI 2))) (* (/ PI 2) (/ PI 2))))
1.0b
(pow (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)) 3)
1.0b
(pow (/ PI 2) 3)
1.4b
(+ (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)) (/ PI 2))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
244×add-sqr-sqrt
149×times-frac
102×*-un-lft-identity
96×difference-of-squares
88×unpow-prod-down cube-prod
60×add-cube-cbrt
42×sqr-pow
33×associate-/l*
20×distribute-lft-out--
10×add-exp-log add-cbrt-cube
8×associate-*r/ associate-/r/
6×pow1 pow-unpow frac-add add-log-exp
5×flip3-+ flip-+
4×difference-cubes
3×pow-exp associate-/r* div-inv rem-cube-cbrt
2×cbrt-undiv cube-mult frac-times pow-to-exp pow-pow unpow3 div-exp associate-*l/ associate-/l/
1×+-commutative cube-div associate-+l- asin-acos flip3-- frac-2neg div-sub clear-num sum-log flip-- distribute-lft-out
Counts
4 → 240
Calls
4 calls:
134.0ms
(/ (- (pow (/ PI 2) 3) (pow (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)) 3)) (+ (* (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)) (+ (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)) (/ PI 2))) (* (/ PI 2) (/ PI 2))))
1.0ms
(pow (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)) 3)
4.0ms
(pow (/ PI 2) 3)
6.0ms
(+ (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)) (/ PI 2))

series525.0ms

Counts
4 → 10
Calls
4 calls:
452.0ms
(/ (- (pow (/ PI 2) 3) (pow (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)) 3)) (+ (* (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)) (+ (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)) (/ PI 2))) (* (/ PI 2) (/ PI 2))))
47.0ms
(pow (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)) 3)
0.0ms
(pow (/ PI 2) 3)
26.0ms
(+ (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)) (/ PI 2))

simplify211.0ms

Algorithm
egg-herbie
Counts
250 → 250
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09429216
147128977
250018977

prune677.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

regimes53.0ms

Accuracy

0% (0.0b remaining)

Error of 0.8b against oracle of 0.7b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04369
14969
24969

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.0s3042×body2560valid
744.0ms2524×body1280valid
222.0ms8044×body80nan
191.0ms1176×body640valid
70.0ms615×body320valid
34.0ms425×body160valid
10.0ms218×body80valid