Details

Time bar (total: 4.5s)

sample80.0ms

Algorithm
intervals
Results
34.0ms103×body2560valid
17.0ms77×body1280valid
7.0ms42×body640valid
7.0ms245×body80nan
2.0ms21×body320valid
0.0ms6×body160valid
0.0ms7×body80valid

simplify105.0ms

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

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b
(* 5.0 (* v v))
0.4b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite18.0ms

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))
6.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series113.0ms

Counts
3 → 9
Calls
3 calls:
84.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
25.0ms
(* 5.0 (* v v))
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify42.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0336587
11261535
25002531

prune163.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.2b
(* 5.0 (* v v))
0.4b
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
13×times-frac
11×add-exp-log add-cbrt-cube
9×pow1
6×add-log-exp difference-of-squares
4×associate-/r*
3×flip3-- associate-*l* pow-prod-down prod-exp flip-- cbrt-unprod associate-/l*
2×asin-acos associate-/r/ associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp associate-*r* clear-num *-commutative div-inv distribute-lft-out-- associate--r- unswap-sqr
Counts
4 → 79
Calls
4 calls:
9.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
10.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
6.0ms
(* 5.0 (* v v))
1.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series150.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
36.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
25.0ms
(* 5.0 (* v v))
3.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify49.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0409840
11459784
25001780

prune221.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ PI 2) (asin (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))))
0.0b
(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
0.2b
(* 5.0 (* v v))
0.4b
(asin (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
103×times-frac
74×add-sqr-sqrt
58×*-un-lft-identity
56×add-cube-cbrt
20×add-exp-log
18×associate-/r*
14×add-cbrt-cube difference-of-squares
10×pow1
9×associate-/r/
7×div-exp
6×add-log-exp
5×flip3-- flip-- div-inv
3×cbrt-undiv associate-*l* pow-prod-down prod-exp cbrt-unprod associate-/l*
2×rec-exp asin-acos 1-exp
1×sub-neg pow-flip frac-2neg diff-log associate-*r* clear-num *-commutative distribute-lft-out-- inv-pow associate--r- unswap-sqr
Counts
4 → 139
Calls
4 calls:
10.0ms
(- (/ PI 2) (asin (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))))
11.0ms
(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
10.0ms
(* 5.0 (* v v))
0.0ms
(asin (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

series153.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- (/ PI 2) (asin (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))))
86.0ms
(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
25.0ms
(* 5.0 (* v v))
4.0ms
(asin (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

simplify79.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06641841
128581678
250011576

prune279.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
15×associate-*r*
14×add-exp-log
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-cbrt-cube
7×unswap-sqr
6×associate-*l* prod-exp add-log-exp
4×pow1 sqr-pow
2×pow-to-exp pow-exp *-commutative cbrt-unprod unpow2
1×+-commutative asin-acos flip3-+ sum-log flip-+ distribute-lft-out
Counts
4 → 72
Calls
4 calls:
3.0ms
(+ (* 4.0 (pow v 2)) (* 4.0 (pow v 4)))
5.0ms
(* 4.0 (pow v 4))
6.0ms
(* 4.0 (pow v 2))
11.0ms
(asin (- (+ (* 4.0 (pow v 2)) (* 4.0 (pow v 4))) 1.0))

series176.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(+ (* 4.0 (pow v 2)) (* 4.0 (pow v 4)))
43.0ms
(* 4.0 (pow v 4))
25.0ms
(* 4.0 (pow v 2))
4.0ms
(asin (- (+ (* 4.0 (pow v 2)) (* 4.0 (pow v 4))) 1.0))

simplify44.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0270417
11087365
25001360

prune191.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

regimes89.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.5b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0189
1189

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s2939×body2560valid
587.0ms2517×body1280valid
231.0ms8010×body80nan
214.0ms1267×body640valid
80.0ms648×body320valid
35.0ms418×body160valid
10.0ms211×body80valid