Details

Time bar (total: 5.6s)

sample97.0ms

Algorithm
intervals
Results
40.0ms95×body2560valid
21.0ms77×body1280valid
10.0ms265×body80nan
8.0ms43×body640valid
3.0ms20×body320valid
2.0ms14×body160valid
0.0ms7×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

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: 0.2b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(- 1.0 (* 5.0 (* v v)))
0.1b
(* 5.0 (* v v))
0.2b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity
5×add-log-exp
3×expm1-log1p-u fma-neg associate-*l* prod-diff pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
1×acos-asin sub-neg flip3-- diff-log associate-*r* *-commutative flip-- unswap-sqr
Counts
3 → 51
Calls
3 calls:
3.0ms
(- 1.0 (* 5.0 (* v v)))
5.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series89.0ms

Counts
3 → 9
Calls
3 calls:
61.0ms
(- 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)))

simplify71.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
0201333
1620291
22691289
35001272

prune91.0ms

Filtered
60 candidates to 41 candidates (68.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New58260
Fresh000
Picked011
Done000
Total58361

Merged error: 0.2b

Counts
61 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(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))))
1.0b
(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)))))

rewrite12.0ms

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

series42.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
17.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
17.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
4.0ms
(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify111.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (100.0ms)

IterNodesCost
01321070
1439956
22385912
35002881

prune145.0ms

Filtered
103 candidates to 56 candidates (54.4%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1021103
Fresh101
Picked101
Done011
Total1042106

Merged error: 0.2b

Counts
106 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(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))))
1.0b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b
(* (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5) (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
28×cbrt-prod
20×sqrt-prod
18×unpow-prod-down
15×unswap-sqr
13×add-cube-cbrt *-un-lft-identity associate-*l*
9×add-exp-log associate-*r*
7×pow1
5×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 pow-to-exp pow-plus pow-exp *-commutative pow-prod-up cbrt-unprod
Counts
4 → 93
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))))
9.0ms
(* (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5) (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))

series42.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
17.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
17.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
4.0ms
(* (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5) (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))

simplify87.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
01941758
15851648
227471502
350021468

prune257.0ms

Filtered
105 candidates to 72 candidates (68.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1032105
Fresh000
Picked101
Done011
Total1043107

Merged error: 0.2b

Counts
107 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5))
1.0b
(cbrt (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5))
1.0b
(cbrt (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5))
1.0b
(* (cbrt (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5)) (cbrt (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
225×cbrt-prod
103×unpow-prod-down
100×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity unswap-sqr
35×sqrt-prod
19×sqr-pow
18×swap-sqr
16×associate-*r* associate-*l*
11×pow1
9×pow1/3
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 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 175
Calls
4 calls:
4.0ms
(cbrt (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5))
3.0ms
(cbrt (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5))
4.0ms
(cbrt (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5))
19.0ms
(* (cbrt (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5)) (cbrt (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5)))

series838.0ms

Counts
4 → 12
Calls
4 calls:
209.0ms
(cbrt (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5))
206.0ms
(cbrt (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5))
212.0ms
(cbrt (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5))
210.0ms
(* (cbrt (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5)) (cbrt (pow (cbrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5)))

simplify127.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 3 (81.0ms)

IterNodesCost
02445153
17104984
232704743
350014730

prune495.0ms

Filtered
187 candidates to 112 candidates (59.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1852187
Fresh011
Picked101
Done011
Total1864190

Merged error: 0.2b

Counts
190 → 4

regimes87.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify5.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0107
1107

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.1s2914×body2560valid
681.0ms2511×body1280valid
311.0ms8014×body80nan
256.0ms1265×body640valid
93.0ms644×body320valid
45.0ms430×body160valid
14.0ms236×body80valid