Details

sample150.0ms

Algorithm

intervals

Results

78.0ms	53×	body	2560	valid
37.0ms	76×	body	1280	valid
19.0ms	70×	body	640	valid
5.0ms	29×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	13×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.9b	(- 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:

41.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify79.0ms

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

prune149.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 1/240 (pow x 5))
0.1b	(* 1/24 (pow x 3))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`associate-r`
12×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp` `add-cbrt-cube`
4×	`cube-prod` `sqr-pow`
2×	`pow1` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `add-log-exp`
1×	`cube-mult` `unpow3`

Counts

2 → 56

Calls

2 calls:

5.0ms	(* 1/240 (pow x 5))
7.0ms	(* 1/24 (pow x 3))

series87.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(* 1/240 (pow x 5))
36.0ms	(* 1/24 (pow x 3))

simplify184.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	208	209
1	871	193
2	4634	193
3	5001	193

prune143.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.9b	(- 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))
4.0ms	(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:

39.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
18.0ms	(exp (log (- 1.0 (cos x))))
74.0ms	(log (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))

simplify80.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (71.0ms)

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

prune239.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sin x))
0.2b	(* (- 1.0 (cos x)) (/ 1 (sin x)))
1.9b	(- 1.0 (cos x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`associate-l` `add-log-exp`
4×	`div-exp` `prod-exp`
3×	`flip3--` `associate-/r` `flip--` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 87

Calls

3 calls:

2.0ms	(/ 1 (sin x))
16.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
3.0ms	(- 1.0 (cos x))

series69.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/ 1 (sin x))
38.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
18.0ms	(- 1.0 (cos x))

simplify40.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	320	548
1	1393	482
2	5001	456

prune147.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes121.0ms

Accuracy

98.9% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 31.9b

bsearch85.0ms

Steps

Iters	Range		Point
10	2.1112891761060846e-05	363928.4733812492	0.021289844305877163
8	-0.10438916540540782	-0.00034188071245303247	-0.02428592948842055

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	33
1	46	33

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.2s	1591×	body	2560	valid
1.3s	2782×	body	1280	valid
497.0ms	1862×	body	640	valid
364.0ms	924×	body	320	valid
64.0ms	482×	body	160	valid
27.0ms	355×	body	80	valid
16.0ms	4×	body	5120	valid