Details

sample134.0ms

Algorithm

intervals

Results

67.0ms	53×	body	2560	valid
40.0ms	94×	body	1280	valid
13.0ms	58×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	14×	body	160	valid
1.0ms	12×	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

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.9b	(- 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))
4.0ms	(- 1.0 (cos x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

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

prune189.0ms

Filtered

74 candidates to 51 candidates (68.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.2b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.9b	(- 1.0 (cos x))

rewrite33.0ms

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))
10.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series130.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (- 1.0 (cos x)) (sin x))
45.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
33.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify40.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (30.0ms)

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

prune356.0ms

Filtered

144 candidates to 101 candidates (70.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.4b	(pow E (/ (- 1.0 (cos x)) (sin x)))
1.2b	(log (pow E (/ (- 1.0 (cos x)) (sin x))))
1.9b	(- 1.0 (cos x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt` `*-un-lft-identity`
33×	`add-cube-cbrt`
30×	`times-frac`
19×	`pow-unpow`
9×	`add-exp-log` `prod-diff`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`log-prod`
6×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `rem-log-exp` `pow-exp` `log1p-expm1-u`
3×	`fma-neg` `div-sub` `associate-/r*`
2×	`pow-to-exp` `e-exp-1` `flip3--` `flip--` `div-inv` `associate-/l/` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `sub-neg` `log-div` `pow-pow` `frac-2neg` `diff-log` `div-exp` `clear-num` `log-pow`

Counts

4 → 127

Calls

4 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(pow E (/ (- 1.0 (cos x)) (sin x)))
3.0ms	(log (pow E (/ (- 1.0 (cos x)) (sin x))))
5.0ms	(- 1.0 (cos x))

series407.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (- 1.0 (cos x)) (sin x))
120.0ms	(pow E (/ (- 1.0 (cos x)) (sin x)))
226.0ms	(log (pow E (/ (- 1.0 (cos x)) (sin x))))
23.0ms	(- 1.0 (cos x))

simplify50.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	454	1004
1	1687	868
2	5002	864

prune347.0ms

Filtered

139 candidates to 95 candidates (68.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- 1.0 (cos x)))
0.3b	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
1.2b	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
1.9b	(- 1.0 (cos x))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

231×	`times-frac`
166×	`add-sqr-sqrt` `*-un-lft-identity`
136×	`exp-prod`
120×	`add-cube-cbrt`
69×	`log-pow`
23×	`distribute-lft-out--` `difference-of-squares`
16×	`associate-/r/`
9×	`prod-diff` `div-inv`
8×	`flip3--` `flip--`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `associate-/l*`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 227

Calls

4 calls:

7.0ms	(/ (sin x) (- 1.0 (cos x)))
14.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
21.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
5.0ms	(- 1.0 (cos x))

series142.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (sin x) (- 1.0 (cos x)))
40.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
43.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
19.0ms	(- 1.0 (cos x))

simplify62.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	593	1886
1	2179	1647
2	5002	1502

prune602.0ms

Filtered

239 candidates to 181 candidates (75.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

regimes159.0ms

Accuracy

98.1% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 30.1b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	25
1	29	25

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.2s	1544×	body	2560	valid
1.2s	2798×	body	1280	valid
434.0ms	1928×	body	640	valid
137.0ms	915×	body	320	valid
46.0ms	441×	body	160	valid
30.0ms	369×	body	80	valid
19.0ms	5×	body	5120	valid