Details

sample32.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
22×	`log-pow`
21×	`pow1`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `associate-/r*`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`log-div` `div-sub`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 74

Calls

3 calls:

3.0ms	(+ (* re re) (* im im))
6.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
3.0ms	(sqrt (+ (* re re) (* im im)))

series29.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* re re) (* im im))
18.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify88.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	259	745
1	894	701
2	2872	696
3	5001	694

prune315.0ms

Filtered

83 candidates to 55 candidates (33.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	68	15	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	15	84

Merged error: 6.1b

Counts

84 → 15

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im)))))) (log 10.0))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

126×	`pow1`
94×	`log-pow`
72×	`times-frac`
60×	`sqrt-div`
54×	`cbrt-div`
45×	`pow1/3` `pow-prod-up`
34×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `*-un-lft-identity`
30×	`flip3-+` `pow-plus` `flip-+`
28×	`frac-times`
26×	`log-div` `div-sub`
25×	`pow-prod-down`
18×	`associate-/l*`
15×	`pow-sqr`
14×	`associate-*l/`
10×	`pow2`
9×	`sqrt-prod`
8×	`associate-*r/`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow3`
4×	`associate-/r*` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 177

Calls

4 calls:

23.0ms	(/ (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im)))))) (log 10.0))
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im)))))) (log 10.0))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
9.0ms	(sqrt (+ (* re re) (* im im)))

simplify148.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	483	3563
1	954	3472
2	3042	3077
3	5001	3047

prune789.0ms

Filtered

189 candidates to 91 candidates (51.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	183	6	189
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	188	16	204

Merged error: 6.1b

Counts

204 → 16

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 3 (/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im)))))))
0.5b	(cbrt (sqrt (+ (* re re) (* im im))))
0.6b	(/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im))))))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

172×	`times-frac`
84×	`add-sqr-sqrt`
83×	`add-cube-cbrt` `*-un-lft-identity`
68×	`log-pow`
52×	`pow1`
29×	`associate-/r*`
22×	`pow1/3`
11×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
6×	`cbrt-prod` `sqrt-prod` `div-inv`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `add-log-exp`
2×	`cbrt-div` `frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`

Counts

4 → 186

Calls

4 calls:

7.0ms	(/ 3 (/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im)))))))
4.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
4.0ms	(/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im))))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ 3 (/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im)))))))
25.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
38.0ms	(/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im))))))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify89.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	595	2629
1	2580	2514
2	5002	2508

prune1.2s

Filtered

198 candidates to 133 candidates (32.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	187	11	198
Fresh	7	8	15
Picked	1	0	1
Done	0	0	0
Total	195	19	214

Merged error: 6.0b

Counts

214 → 19

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (log 10.0) (log (* (* (cbrt (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (cbrt (sqrt (+ (* re re) (* im im)))))) (cbrt (cbrt (sqrt (+ (* re re) (* im im))))))))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

126×	`pow1`
94×	`log-pow`
72×	`times-frac`
45×	`pow1/3` `pow-prod-up`
34×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-plus`
25×	`pow-prod-down`
18×	`associate-/r*`
15×	`pow-sqr`
10×	`pow2`
9×	`sqrt-prod`
6×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
5×	`pow3`
4×	`associate-/l*` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 151

Calls

4 calls:

18.0ms	(/ (log 10.0) (log (* (* (cbrt (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (cbrt (sqrt (+ (* re re) (* im im)))))) (cbrt (cbrt (sqrt (+ (* re re) (* im im))))))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (log 10.0) (log (* (* (cbrt (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (cbrt (sqrt (+ (* re re) (* im im)))))) (cbrt (cbrt (sqrt (+ (* re re) (* im im))))))))
6.0ms	(sqrt (+ (* re re) (* im im)))
9.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify181.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 3 (161.0ms)

Iter	Nodes	Cost
0	292	2404
1	818	2301
2	3687	1960
3	5001	1914

prune748.0ms

Filtered

163 candidates to 80 candidates (50.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	3	15	18
Picked	1	0	1
Done	0	0	0
Total	165	17	182

Merged error: 6.0b

Counts

182 → 17

regimes1.4s

Accuracy

54.9% (11.0b remaining)

Error of 18.7b against oracle of 7.7b and baseline of 32.2b

bsearch303.0ms

Steps

Iters	Range		Point
6	1.3653351403313602e+73	1.322226463547956e+74	1.2936263172600616e+74
8	2.3994843959372772e-195	7.432573966013439e-193	2.676988169724194e-193
9	2.1736971780370254e-258	2.3440915256910505e-249	1.6077080132841703e-255
7	-8.271287922560956e-294	-4.441296914487316e-296	-2.3073780707255892e-294
8	-1.4022534510236193e-184	-1.2792908018706196e-188	-4.340783863196871e-187
10	-6.190653983166317e+156	-1.198940147728456e+144	-1.2150470868789148e+144

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	51
1	53	51

end0.0ms

sample675.0ms

Algorithm

intervals

Results

453.0ms

8000×

body

valid

Details

sample32.0ms

simplify3.0ms

prune4.0ms

localize10.0ms

rewrite15.0ms

series29.0ms

simplify88.0ms

prune315.0ms

localize14.0ms

rewrite44.0ms

series38.0ms

simplify148.0ms

prune789.0ms

localize15.0ms

rewrite27.0ms

series100.0ms

simplify89.0ms

prune1.2s

localize18.0ms

rewrite36.0ms

series60.0ms

simplify181.0ms

prune748.0ms

regimes1.4s

bsearch303.0ms

simplify2.0ms

end0.0ms

sample675.0ms

Profiling