Details

sample118.0ms

Algorithm

intervals

Results

49.0ms	40×	body	2560	valid
42.0ms	101×	body	1280	valid
12.0ms	51×	body	640	valid
4.0ms	29×	body	320	valid
2.0ms	18×	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

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.6b	(- 1.0 (cos x))

rewrite15.0ms

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:

9.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series58.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(/ (- 1.0 (cos x)) (sin x))
25.0ms	(- 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

prune178.0ms

Filtered

74 candidates to 51 candidates (68.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.7b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.6b	(- 1.0 (cos x))

rewrite45.0ms

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:

9.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
16.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series133.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (- 1.0 (cos x)) (sin x))
40.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
38.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms	(- 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

prune343.0ms

Filtered

144 candidates to 102 candidates (70.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
2.6b	(- 1.0 (cos x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

10.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
3.0ms	(exp (log (- 1.0 (cos x))))
7.0ms	(log (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series146.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
17.0ms	(exp (log (- 1.0 (cos x))))
73.0ms	(log (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))

simplify39.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	354	1019
1	1045	861
2	5001	817

prune287.0ms

Filtered

130 candidates to 82 candidates (63.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- 1.0 (cos x)))
0.3b	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
1.7b	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
2.6b	(- 1.0 (cos x))

rewrite81.0ms

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)))
25.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
28.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
3.0ms	(- 1.0 (cos x))

series130.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (sin x) (- 1.0 (cos x)))
46.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
33.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
18.0ms	(- 1.0 (cos x))

simplify69.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (46.0ms)

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

prune591.0ms

Filtered

239 candidates to 181 candidates (75.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.2b

regimes150.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.1b

bsearch64.0ms

Steps

Iters	Range		Point
10	9.558161037350472e-13	0.8818080259852756	0.019937101609103888
5	-0.041603525395973645	-0.015510049556855336	-0.023610592701318548

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	18
1	32	18

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.1s	1580×	body	2560	valid
1.2s	2771×	body	1280	valid
449.0ms	1826×	body	640	valid
338.0ms	946×	body	320	valid
63.0ms	510×	body	160	valid
24.0ms	365×	body	80	valid
8.0ms	2×	body	5120	valid