Details

Time bar (total: 4.8s)

sample100.0ms

Algorithm
intervals
Results
40.0ms89×body2560valid
25.0ms85×body1280valid
10.0ms250×body80nan
8.0ms36×body640valid
4.0ms24×body320valid
1.0ms11×body160valid
1.0ms11×body80valid

simplify96.0ms

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: 0.7b

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))
0.7b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite16.0ms

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)))

series110.0ms

Counts
3 → 9
Calls
3 calls:
81.0ms
(/ (- 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)))

simplify44.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0349623
11288567
25001565

prune150.0ms

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: 0.7b

Counts
79 → 4

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))
0.8b
(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:
8.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
9.0ms
(- (/ 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)))

series144.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
30.0ms
(- (/ PI 2) (asin (/ (- 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)))

simplify70.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05762948
119411851
250031839

prune275.0ms

Filtered
151 candidates to 97 candidates (64.2%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1474151
Fresh213
Picked101
Done000
Total1505155

Merged error: 0.7b

Counts
155 → 5

localize8.0ms

Local error

Found 1 expressions with local error:

0.7b
(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)))

series7.0ms

Counts
1 → 3
Calls
1 calls:
7.0ms
(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

prune49.0ms

Filtered
13 candidates to 10 candidates (76.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New11213
Fresh044
Picked101
Done000
Total12618

Merged error: 0.7b

Counts
18 → 6

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
0.0b
(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
0.7b
(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
4×expm1-log1p-u
3×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
1×acos-asin log1p-udef expm1-log1p log1p-expm1 expm1-udef
Counts
3 → 32
Calls
3 calls:
1.0ms
(log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
1.0ms
(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
1.0ms
(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

series270.0ms

Counts
3 → 9
Calls
3 calls:
107.0ms
(log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
156.0ms
(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
7.0ms
(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

simplify96.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
056296
188258
2187256
3462256
41961256
55001256

prune92.0ms

Filtered
41 candidates to 27 candidates (65.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New39241
Fresh145
Picked101
Done000
Total41647

Merged error: 0.7b

Counts
47 → 6

regimes120.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.6b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s2956×body2560valid
732.0ms2509×body1280valid
322.0ms7941×body80nan
264.0ms1245×body640valid
98.0ms636×body320valid
46.0ms436×body160valid
13.0ms218×body80valid