Details

Time bar (total: 4.2s)

sample87.0ms

Algorithm
intervals
Results
40.0ms102×body2560valid
17.0ms73×body1280valid
8.0ms288×body80nan
7.0ms41×body640valid
3.0ms22×body320valid
1.0ms12×body160valid
0.0ms6×body80valid

simplify98.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0207
1437
2847
31557
42627
54547
628787
750017

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.5b

Counts
2 → 1

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))
0.5b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite17.0ms

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×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u 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 → 69
Calls
3 calls:
8.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
5.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series112.0ms

Counts
3 → 9
Calls
3 calls:
83.0ms
(/ (- 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)))

simplify41.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0349623
11288567
25001565

prune148.0ms

Filtered
78 candidates to 61 candidates (78.2%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New74478
Fresh000
Picked101
Done000
Total75479

Merged error: 0.5b

Counts
79 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b
(* 5.0 (* v v))
0.5b
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
65×add-sqr-sqrt
57×*-un-lft-identity
55×add-cube-cbrt
49×times-frac
39×prod-diff
13×fma-neg
11×add-exp-log add-cbrt-cube
9×pow1
6×add-log-exp difference-of-squares
5×div-inv
4×expm1-log1p-u associate-/r* log1p-expm1-u
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 distribute-lft-out-- associate--r- unswap-sqr
Counts
4 → 139
Calls
4 calls:
9.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
8.0ms
(/ (- 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)))

series146.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
83.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
28.0ms
(* 5.0 (* v v))
4.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify71.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05762948
119411851
250011839

prune257.0ms

Filtered
151 candidates to 97 candidates (64.2%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1492151
Fresh213
Picked011
Done000
Total1514155

Merged error: 0.5b

Counts
155 → 4

localize8.0ms

Local error

Found 1 expressions with local error:

0.5b
(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log acos-asin add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
1.0ms
(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

series6.0ms

Counts
1 → 3
Calls
1 calls:
6.0ms
(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

simplify94.0ms

Algorithm
egg-herbie
Counts
13 → 13
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03093
15482
215382
342382
4190982
5500182

prune35.0ms

Filtered
13 candidates to 10 candidates (76.9%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New13013
Fresh022
Picked011
Done011
Total13417

Merged error: 0.5b

Counts
17 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (cbrt (/ PI 2)) (cbrt (/ PI 2)))
1.0b
(cbrt (/ PI 2))
1.0b
(cbrt (/ PI 2))
1.0b
(cbrt (/ PI 2))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
103×cbrt-prod
81×add-sqr-sqrt
69×times-frac
57×add-cube-cbrt *-un-lft-identity
16×swap-sqr associate-*r* associate-*l*
11×pow1
9×pow1/3 unswap-sqr
7×cbrt-div div-inv
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 152
Calls
4 calls:
12.0ms
(* (cbrt (/ PI 2)) (cbrt (/ PI 2)))
2.0ms
(cbrt (/ PI 2))
2.0ms
(cbrt (/ PI 2))
2.0ms
(cbrt (/ PI 2))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(* (cbrt (/ PI 2)) (cbrt (/ PI 2)))
0.0ms
(cbrt (/ PI 2))
0.0ms
(cbrt (/ PI 2))
0.0ms
(cbrt (/ PI 2))

simplify72.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
02271159
17621102
227121005
350011001

prune470.0ms

Filtered
156 candidates to 122 candidates (78.2%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1551156
Fresh101
Picked011
Done022
Total1564160

Merged error: 0.5b

Counts
160 → 4

regimes53.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0149
1149

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s2922×body2560valid
573.0ms2479×body1280valid
239.0ms7924×body80nan
218.0ms1288×body640valid
80.0ms642×body320valid
38.0ms455×body160valid
10.0ms214×body80valid