Details

Time bar (total: 5.3s)

sample84.0ms

Algorithm
intervals
Results
32.0ms95×body2560valid
17.0ms78×body1280valid
11.0ms283×body80nan
6.0ms37×body640valid
3.0ms24×body320valid
1.0ms13×body160valid
0.0ms9×body80valid

simplify98.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0207
1437
2847
31557
42627
54547
628787
750017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b
(- 1.0 (* 5.0 (* v v)))
0.1b
(* 5.0 (* v v))
0.3b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
12×times-frac
11×add-exp-log add-cbrt-cube
9×pow1
6×add-log-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u difference-of-squares
3×flip3-- fma-neg associate-*l* prod-diff pow-prod-down prod-exp flip-- cbrt-unprod associate-/l*
2×associate-/r/ associate-/l/
1×cbrt-undiv acos-asin sub-neg frac-2neg diff-log div-sub div-exp associate-*r* clear-num *-commutative div-inv unswap-sqr
Counts
4 → 89
Calls
4 calls:
26.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
6.0ms
(- 1.0 (* 5.0 (* v v)))
16.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series172.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
60.0ms
(- 1.0 (* 5.0 (* v v)))
25.0ms
(* 5.0 (* v v))
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify47.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0391750
11491682
25002678

prune227.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (fma 1.0 1.0 (* (- (* 5.0 5.0)) (pow v 4))) (fma v (* 5.0 v) 1.0)) (- (* v v) 1.0))
0.0b
(/ (fma 1.0 1.0 (* (- (* 5.0 5.0)) (pow v 4))) (fma v (* 5.0 v) 1.0))
0.1b
(* (- (* 5.0 5.0)) (pow v 4))
0.3b
(acos (/ (/ (fma 1.0 1.0 (* (- (* 5.0 5.0)) (pow v 4))) (fma v (* 5.0 v) 1.0)) (- (* v v) 1.0)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
106×times-frac
83×add-sqr-sqrt
64×add-cube-cbrt *-un-lft-identity
16×add-exp-log associate-/l*
14×difference-of-squares
13×add-cbrt-cube
7×associate-*r* associate-/r* div-inv
6×associate-*l*
4×pow1 cbrt-undiv expm1-log1p-u unpow-prod-down div-exp log1p-expm1-u add-log-exp
3×prod-exp unswap-sqr
2×frac-2neg clear-num associate-/r/ sqr-pow
1×distribute-lft-neg-out distribute-lft-neg-in acos-asin pow-to-exp neg-mul-1 flip3-- distribute-rgt-neg-in pow-exp *-commutative flip-- cbrt-unprod associate-/l/
Counts
4 → 158
Calls
4 calls:
22.0ms
(/ (/ (fma 1.0 1.0 (* (- (* 5.0 5.0)) (pow v 4))) (fma v (* 5.0 v) 1.0)) (- (* v v) 1.0))
5.0ms
(/ (fma 1.0 1.0 (* (- (* 5.0 5.0)) (pow v 4))) (fma v (* 5.0 v) 1.0))
15.0ms
(* (- (* 5.0 5.0)) (pow v 4))
1.0ms
(acos (/ (/ (fma 1.0 1.0 (* (- (* 5.0 5.0)) (pow v 4))) (fma v (* 5.0 v) 1.0)) (- (* v v) 1.0)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (/ (fma 1.0 1.0 (* (- (* 5.0 5.0)) (pow v 4))) (fma v (* 5.0 v) 1.0)) (- (* v v) 1.0))
156.0ms
(/ (fma 1.0 1.0 (* (- (* 5.0 5.0)) (pow v 4))) (fma v (* 5.0 v) 1.0))
38.0ms
(* (- (* 5.0 5.0)) (pow v 4))
7.0ms
(acos (/ (/ (fma 1.0 1.0 (* (- (* 5.0 5.0)) (pow v 4))) (fma v (* 5.0 v) 1.0)) (- (* v v) 1.0)))

simplify84.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06862641
130322492
250012490

prune584.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
0.9b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.9b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b
(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite19.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 91
Calls
4 calls:
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
12.0ms
(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series48.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
21.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
18.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
5.0ms
(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify112.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (101.0ms)

IterNodesCost
01321070
1439956
22385912
35002881

prune175.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
0.9b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.9b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b
(* (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
75×sqrt-prod
63×add-sqr-sqrt
24×associate-*r* unswap-sqr
18×unpow-prod-down cube-prod
16×add-cube-cbrt *-un-lft-identity
9×add-exp-log associate-*l*
7×pow1
6×add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×prod-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×acos-asin cube-mult pow-to-exp unpow3 pow-exp *-commutative pow-prod-up cbrt-unprod
Counts
4 → 112
Calls
4 calls:
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
30.0ms
(* (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3))

series49.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
18.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
19.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
8.0ms
(* (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3))

simplify277.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
02162510
17231610
247861545
350011545

prune230.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

regimes151.0ms

Accuracy

0% (0.0b remaining)

Error of 0.5b against oracle of 0.5b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02312
12712
22812
32812

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s3031×body2560valid
569.0ms2496×body1280valid
225.0ms8117×body80nan
202.0ms1249×body640valid
68.0ms589×body320valid
36.0ms420×body160valid
10.0ms215×body80valid