Details

sample127.0ms

Algorithm

intervals

Results

56.0ms	41×	body	2560	valid
40.0ms	90×	body	1280	valid
13.0ms	53×	body	640	valid
5.0ms	31×	body	320	valid
3.0ms	24×	body	160	valid
1.0ms	17×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 26.3b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.8b	(- 1.0 (cos x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
5.0ms	(- 1.0 (cos x))

series54.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify36.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	292	569
1	965	460
2	5002	460

prune181.0ms

Filtered

74 candidates to 51 candidates (68.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	60	14	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	14	75

Merged error: 0.1b

Counts

75 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.8b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.8b	(- 1.0 (cos x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
40×	`add-cube-cbrt`
38×	`exp-prod`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`prod-diff`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 132

Calls

4 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
8.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
8.0ms	(- 1.0 (cos x))

series132.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
46.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
34.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms	(- 1.0 (cos x))

simplify48.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	368	1009
1	1099	873
2	5002	871

prune317.0ms

Filtered

144 candidates to 102 candidates (70.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	138	6	144
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	145	13	158

Merged error: 0.1b

Counts

158 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x)))
0.4b	(pow (cos x) 3)
0.4b	(fma (cos x) (cos x) (* 1.0 (cos x)))
2.6b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

156×	`add-sqr-sqrt`
144×	`prod-diff`
114×	`unpow-prod-down` `*-un-lft-identity` `cube-prod`
84×	`add-cube-cbrt`
50×	`sqr-pow`
48×	`difference-of-squares`
26×	`cube-mult` `unpow3`
25×	`times-frac` `associate-/l*`
15×	`distribute-lft-out--`
12×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`difference-cubes` `pow-unpow`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `fma-udef` `div-inv` `rem-cube-cbrt`

Counts

4 → 297

Calls

4 calls:

29.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x)))
2.0ms	(pow (cos x) 3)
1.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
16.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series321.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x)))
33.0ms	(pow (cos x) 3)
47.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
53.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify130.0ms

Algorithm

egg-herbie

Counts

309 → 309

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	768	3924
1	2914	2902
2	5001	2876

prune402.0ms

Filtered

309 candidates to 100 candidates (32.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	306	3	309
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	308	14	322

Merged error: 0.1b

Counts

322 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.4b	(pow (cos x) 3)
0.4b	(pow (cos x) 3)
2.4b	(- (pow (pow 1.0 3) 3) (pow (pow (cos x) 3) 3))

rewrite364.0ms

Algorithm

rewrite-expression-head

Rules

1263×	`unpow-prod-down` `cube-prod`
900×	`prod-diff`
580×	`add-sqr-sqrt`
482×	`*-un-lft-identity`
440×	`add-cube-cbrt`
246×	`sqr-pow`
186×	`cube-mult` `unpow3`
100×	`difference-of-squares`
30×	`fma-neg`
21×	`distribute-lft-out--`
9×	`pow-unpow`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 1141

Calls

4 calls:

2.0ms	(pow (cos x) 3)
2.0ms	(pow (cos x) 3)
3.0ms	(pow (cos x) 3)
68.0ms	(- (pow (pow 1.0 3) 3) (pow (pow (cos x) 3) 3))

series169.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (cos x) 3)
30.0ms	(pow (cos x) 3)
28.0ms	(pow (cos x) 3)
83.0ms	(- (pow (pow 1.0 3) 3) (pow (pow (cos x) 3) 3))

simplify331.0ms

Algorithm

egg-herbie

Counts

1153 → 1153

Iterations

Useful iterations: 2 (130.0ms)

Iter	Nodes	Cost
0	1026	21138
1	2809	12908
2	5002	12815

prune516.0ms

Filtered

1153 candidates to 98 candidates (8.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	1151	2	1153
Fresh	0	12	12
Picked	1	0	1
Done	0	1	1
Total	1152	15	1167

Merged error: 0.1b

Counts

1167 → 15

regimes183.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.3b

bsearch91.0ms

Steps

Iters	Range		Point
10	0.00022027325057658872	62623256.830634765	0.021907997979399244
9	-17.831791951177678	-3.7534567552478157e-06	-0.02260905259882163

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	32
1	39	32

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.1s	1621×	body	2560	valid
1.3s	2741×	body	1280	valid
469.0ms	1865×	body	640	valid
192.0ms	982×	body	320	valid
56.0ms	473×	body	160	valid
22.0ms	315×	body	80	valid
13.0ms	3×	body	5120	valid

Details

sample127.0ms

simplify6.0ms

prune2.0ms

localize12.0ms

rewrite14.0ms

series54.0ms

simplify36.0ms

prune181.0ms

localize11.0ms

rewrite34.0ms

series132.0ms

simplify48.0ms

prune317.0ms

localize16.0ms

rewrite64.0ms

series321.0ms

simplify130.0ms

prune402.0ms

localize23.0ms

rewrite364.0ms

series169.0ms

simplify331.0ms

prune516.0ms

regimes183.0ms

bsearch91.0ms

simplify2.0ms

end0.0ms

sample4.3s

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