Details

sample131.0ms

Algorithm

intervals

Results

62.0ms	51×	body	2560	valid
42.0ms	98×	body	1280	valid
13.0ms	55×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	11×	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: 29.9b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.6b	(- 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:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series53.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify78.0ms

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

prune163.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.1b	(/ (sin x) (- 1.0 (cos x)))
1.6b	(- 1.0 (cos x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
105×	`add-sqr-sqrt` `*-un-lft-identity`
71×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 159

Calls

3 calls:

9.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
6.0ms	(/ (sin x) (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

series91.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
34.0ms	(/ (sin x) (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))

simplify59.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	510	1595
1	2396	1452
2	5002	1339

prune264.0ms

Filtered

168 candidates to 86 candidates (51.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

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)))
1.6b	(- 1.0 (cos x))

rewrite22.0ms

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))))
2.0ms	(log (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

series149.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
18.0ms	(exp (log (- 1.0 (cos x))))
75.0ms	(log (- 1.0 (cos x)))
23.0ms	(- 1.0 (cos x))

simplify80.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (72.0ms)

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

prune265.0ms

Filtered

110 candidates to 72 candidates (65.5%)

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)))
0.2b	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
0.9b	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
1.6b	(- 1.0 (cos x))

rewrite79.0ms

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)))))
26.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
7.0ms	(- 1.0 (cos x))

series133.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (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))))))
18.0ms	(- 1.0 (cos x))

simplify54.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (40.0ms)

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

prune593.0ms

Filtered

219 candidates to 168 candidates (76.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

regimes85.0ms

Accuracy

98.6% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.7b

bsearch80.0ms

Steps

Iters	Range		Point
9	7.206039552426127e-07	5.540917366542361	0.025530887226718046
10	-204248214.92732975	-1.534026600097144e-05	-0.02247239573488662

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	25
1	44	25

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.3s	1591×	body	2560	valid
1.3s	2753×	body	1280	valid
446.0ms	1868×	body	640	valid
155.0ms	916×	body	320	valid
60.0ms	522×	body	160	valid
32.0ms	347×	body	80	valid
13.0ms	3×	body	5120	valid