Details

sample114.0ms

Algorithm

intervals

Results

48.0ms	40×	body	2560	valid
40.0ms	101×	body	1280	valid
11.0ms	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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series59.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
25.0ms	(- 1.0 (cos x))

simplify81.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373

prune167.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

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))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `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 → 112

Calls

4 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
12.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series139.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (- 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))))
23.0ms	(- 1.0 (cos x))

simplify90.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	303	818
1	799	768
2	2970	766
3	5001	766

prune331.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (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))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`log-prod`
25×	`exp-sum`
24×	`add-cube-cbrt` `times-frac`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`exp-prod` `flip3--` `exp-diff` `flip--`
3×	`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 → 98

Calls

4 calls:

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

series151.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
24.0ms	(exp (log (- 1.0 (cos x))))
70.0ms	(log (- 1.0 (cos x)))
23.0ms	(- 1.0 (cos x))

simplify83.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	289	829
1	791	761
2	2667	734
3	5001	708

prune270.0ms

Filtered

110 candidates to 69 candidates (62.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

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))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 207

Calls

4 calls:

6.0ms	(/ (sin x) (- 1.0 (cos x)))
24.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
31.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
3.0ms	(- 1.0 (cos x))

series140.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (sin x) (- 1.0 (cos x)))
47.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
34.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
23.0ms	(- 1.0 (cos x))

simplify58.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	526	1686
1	1918	1532
2	5001	1387

prune584.0ms

Filtered

219 candidates to 168 candidates (76.7%)

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.2b

regimes365.0ms

Accuracy

98.8% (0.4b remaining)

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

bsearch63.0ms

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	38	20
1	38	20

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	1580×	body	2560	valid
1.2s	2771×	body	1280	valid
411.0ms	1826×	body	640	valid
141.0ms	946×	body	320	valid
71.0ms	510×	body	160	valid
22.0ms	365×	body	80	valid
8.0ms	2×	body	5120	valid