Details

Time bar (total: 4.7s)

sample79.0ms

Algorithm
intervals
Results
34.0ms92×body2560valid
17.0ms80×body1280valid
7.0ms46×body640valid
6.0ms245×body80nan
2.0ms18×body320valid
1.0ms14×body160valid
0.0ms6×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: 0.6b

localize7.0ms

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))
0.6b
(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))
6.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series117.0ms

Counts
3 → 9
Calls
3 calls:
84.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
29.0ms
(* 5.0 (* v v))
3.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify39.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0336587
11261535
25002531

prune158.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.0b
(exp (log (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
0.2b
(* 5.0 (* v v))
0.6b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-exp-log
9×add-sqr-sqrt add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×log-prod
4×exp-prod add-log-exp
3×associate-*l* exp-sum pow-prod-down prod-exp cbrt-unprod
2×log-pow
1×acos-asin rem-log-exp associate-*r* *-commutative rem-exp-log unswap-sqr
Counts
4 → 54
Calls
4 calls:
1.0ms
(log (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms
(exp (log (acos (/ (- 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)))

series111.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(log (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
8.0ms
(exp (log (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
24.0ms
(* 5.0 (* v v))
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify117.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (31.0ms)

IterNodesCost
0156537
1407466
21036448
33485442
45001442

prune138.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize9.0ms

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)))
0.6b
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite45.0ms

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:
9.0ms
(+ (pow v 2) (pow v 4))
34.0ms
(* 4.0 (+ (pow v 2) (pow v 4)))
0.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series171.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(+ (pow v 2) (pow v 4))
93.0ms
(* 4.0 (+ (pow v 2) (pow v 4)))
4.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify153.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0177315
1834276
24136273
35002273

prune119.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b
(pow (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 2)
1.0b
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down
5×pow1 add-exp-log
4×add-cbrt-cube add-log-exp
3×pow-unpow pow1/3
2×pow-pow
1×acos-asin pow-to-exp pow-exp unpow2 sqr-pow
Counts
4 → 52
Calls
4 calls:
0.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
2.0ms
(pow (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 2)
0.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

series421.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
151.0ms
(pow (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 2)
136.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
131.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

simplify65.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
0141687
1400610
21597597
35001594

prune170.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.6b

regimes214.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.5b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0136
1136

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s3068×body2560valid
556.0ms2476×body1280valid
222.0ms8249×body80nan
195.0ms1225×body640valid
70.0ms605×body320valid
34.0ms417×body160valid
10.0ms209×body80valid