Details

Time bar (total: 4.3s)

sample87.0ms

Algorithm
intervals
Results
37.0ms98×body2560valid
17.0ms75×body1280valid
7.0ms246×body80nan
7.0ms40×body640valid
3.0ms27×body320valid
1.0ms10×body160valid
0.0ms6×body80valid

simplify95.0ms

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: 0.8b

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))
0.8b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite41.0ms

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:
22.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
16.0ms
(* 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:
79.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
22.0ms
(* 5.0 (* v v))
7.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify37.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0336587
11261535
25002531

prune156.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow v 2) (pow v 4))
0.0b
(* 4.0 (+ (pow v 2) (pow v 4)))
0.8b
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite70.0ms

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:
15.0ms
(+ (pow v 2) (pow v 4))
53.0ms
(* 4.0 (+ (pow v 2) (pow v 4)))
1.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series154.0ms

Counts
3 → 9
Calls
3 calls:
67.0ms
(+ (pow v 2) (pow v 4))
83.0ms
(* 4.0 (+ (pow v 2) (pow v 4)))
4.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify154.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0177315
1834276
24136273
35002273

prune120.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
1.0b
(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
1.0b
(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
1.0b
(* (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))) (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 acos-asin pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 83
Calls
4 calls:
1.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
1.0ms
(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
1.0ms
(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
12.0ms
(* (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))) (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))

series51.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
23.0ms
(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
19.0ms
(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
5.0ms
(* (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))) (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))

simplify116.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 3 (106.0ms)

IterNodesCost
0123882
1451782
22481744
35001717

prune182.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
1.0b
(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
1.0b
(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
1.0b
(* (pow (sqrt (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))) 3) (sqrt (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
75×sqrt-prod
63×add-sqr-sqrt
24×associate-*l* unswap-sqr
18×unpow-prod-down cube-prod
16×add-cube-cbrt *-un-lft-identity
9×add-exp-log associate-*r*
7×pow1
6×add-cbrt-cube
4×add-log-exp sqr-pow
3×prod-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×acos-asin cube-mult pow-to-exp pow-plus unpow3 pow-exp *-commutative pow-prod-up cbrt-unprod
Counts
4 → 105
Calls
4 calls:
1.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
1.0ms
(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
1.0ms
(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
29.0ms
(* (pow (sqrt (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))) 3) (sqrt (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))))

series50.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
18.0ms
(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
22.0ms
(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
5.0ms
(* (pow (sqrt (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))) 3) (sqrt (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))))

simplify49.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
01871710
18321369
250011319

prune226.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

regimes23.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02128
12128

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.0s2952×body2560valid
572.0ms2489×body1280valid
236.0ms7949×body80nan
218.0ms1276×body640valid
80.0ms643×body320valid
36.0ms426×body160valid
11.0ms214×body80valid