Details

Time bar (total: 4.7s)

sample51.0ms

Algorithm
intervals
Results
22.0ms51×body2560valid
10.0ms45×body1280valid
7.0ms51×body640valid
2.0ms25×body320valid
2.0ms63×body80valid
1.0ms21×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

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: 32.6b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

3.2b
(- 1.0 (cos x))
16.1b
(/ (- 1.0 (cos x)) (* x x))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
101×add-sqr-sqrt
89×*-un-lft-identity
75×times-frac
55×add-cube-cbrt
18×swap-sqr associate-*r* associate-*l*
17×distribute-lft-out-- difference-of-squares
15×associate-/r*
9×prod-diff
7×add-exp-log add-cbrt-cube
6×*-commutative unswap-sqr
5×associate-/l*
4×add-log-exp
3×fma-neg
2×pow1 cbrt-undiv expm1-log1p-u flip3-- div-exp flip-- log1p-expm1-u associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num cbrt-unprod div-inv
Counts
2 → 142
Calls
2 calls:
4.0ms
(- 1.0 (cos x))
11.0ms
(/ (- 1.0 (cos x)) (* x x))

series64.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(- 1.0 (cos x))
45.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify73.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05451225
123481087
250011068

prune196.0ms

Filtered
148 candidates to 82 candidates (55.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New13711148
Fresh000
Picked101
Done000
Total13811149

Merged error: 0.2b

Counts
149 → 11

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b
(* 1/24 (pow x 2))
11.4b
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×associate-*r*
7×add-exp-log
5×add-cube-cbrt *-un-lft-identity
4×pow1 unpow-prod-down add-cbrt-cube unswap-sqr
3×associate-*l* prod-exp
2×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
1×pow-to-exp pow-prod-down pow-exp *-commutative cbrt-unprod fma-udef
Counts
2 → 40
Calls
2 calls:
6.0ms
(* 1/24 (pow x 2))
1.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series73.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(* 1/24 (pow x 2))
43.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify103.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (98.0ms)

IterNodesCost
0139205
1565173
22596173
35001172

prune95.0ms

Filtered
46 candidates to 30 candidates (65.2%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New46046
Fresh01010
Picked011
Done000
Total461157

Merged error: 0.2b

Counts
57 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
3.2b
(- 1.0 (cos x))
6.1b
(/ (- 1.0 (cos x)) (* (cbrt x) x))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
114×add-sqr-sqrt
90×*-un-lft-identity
80×times-frac
54×add-cube-cbrt
36×associate-*l*
30×cbrt-prod
18×associate-*r* distribute-lft-out-- difference-of-squares
16×associate-/r*
12×unswap-sqr
11×add-cbrt-cube
9×add-exp-log prod-diff
6×*-commutative add-log-exp
5×associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u
3×cbrt-undiv fma-neg
2×flip3-- pow1/3 div-exp flip-- cbrt-unprod associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num div-inv
Counts
4 → 175
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
4.0ms
(- 1.0 (cos x))
13.0ms
(/ (- 1.0 (cos x)) (* (cbrt x) x))

series634.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(cbrt x)
173.0ms
(cbrt x)
19.0ms
(- 1.0 (cos x))
259.0ms
(/ (- 1.0 (cos x)) (* (cbrt x) x))

simplify76.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06771606
127631430
250021423

prune482.0ms

Filtered
187 candidates to 132 candidates (70.6%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1843187
Fresh279
Picked011
Done011
Total18612198

Merged error: 0.2b

Counts
198 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
3.2b
(- 1.0 (cos x))
3.3b
(log (exp (- 1.0 (cos x))))
6.1b
(/ (log (exp (- 1.0 (cos x)))) (* (cbrt x) x))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
172×add-sqr-sqrt
144×times-frac
132×*-un-lft-identity
108×log-pow
94×add-cube-cbrt
90×exp-prod
60×associate-*l*
43×cbrt-prod
30×associate-*r*
22×pow1
20×unswap-sqr
19×distribute-lft-out-- difference-of-squares
18×prod-diff
16×associate-/r*
14×log-prod
11×exp-sum add-cbrt-cube
10×add-exp-log *-commutative
9×associate-/l*
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv fma-neg
2×sub-neg log-div exp-diff div-exp rem-log-exp cbrt-unprod
1×flip3-- frac-2neg pow1/3 diff-log div-sub prod-exp clear-num flip-- div-inv
Counts
4 → 260
Calls
4 calls:
1.0ms
(cbrt x)
5.0ms
(- 1.0 (cos x))
6.0ms
(log (exp (- 1.0 (cos x))))
16.0ms
(/ (log (exp (- 1.0 (cos x)))) (* (cbrt x) x))

series461.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(cbrt x)
18.0ms
(- 1.0 (cos x))
18.0ms
(log (exp (- 1.0 (cos x))))
249.0ms
(/ (log (exp (- 1.0 (cos x)))) (* (cbrt x) x))

simplify89.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
08562762
131162309
250032309

prune438.0ms

Filtered
272 candidates to 164 candidates (60.3%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2693272
Fresh369
Picked101
Done022
Total27311284

Merged error: 0.2b

Counts
284 → 11

regimes58.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.9b

bsearch61.0ms

Steps
ItersRangePoint
10
1.0482644148039984e-06
3857898261607.3584
0.03316890245008123
7
-0.05767290693153419
-0.00024695944164034034
-0.03185288092824355

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03515
13515

end0.0ms

sample1.6s

Algorithm
intervals
Results
717.0ms1553×body2560valid
310.0ms1341×body1280valid
224.0ms1477×body640valid
98.0ms936×body320valid
67.0ms2205×body80valid
34.0ms488×body160valid