Details

sample147.0ms

Algorithm

intervals

Results

74.0ms	53×	body	2560	valid
38.0ms	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

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

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:

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

series52.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify40.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

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

prune375.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 1/240 (pow x 5) (* 1/2 x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma 1/240 (pow x 5) (* 1/2 x))

series120.0ms

Counts

1 → 3

Calls

1 calls:

120.0ms

(fma 1/240 (pow x 5) (* 1/2 x))

simplify48.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	59
1	65	52
2	228	52
3	979	52
4	5001	52

prune61.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

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))

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:

11.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
3.0ms	(exp (log (- 1.0 (cos x))))
6.0ms	(log (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

series147.0ms

Counts

4 → 12

Calls

4 calls:

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

prune279.0ms

Pruning

14 alts after pruning (13 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))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
26×	`add-cube-cbrt`
20×	`times-frac`
16×	`add-exp-log`
13×	`associate-r`
10×	`add-cbrt-cube`
9×	`prod-diff`
6×	`pow1`
5×	`associate-l` `add-log-exp`
4×	`div-exp` `prod-exp`
3×	`expm1-log1p-u` `flip3--` `fma-neg` `associate-/r` `flip--` `log1p-expm1-u` `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 → 105

Calls

3 calls:

3.0ms	(/ 1 (sin x))
19.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
3.0ms	(- 1.0 (cos x))

series65.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/ 1 (sin x))
34.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
18.0ms	(- 1.0 (cos x))

simplify54.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	381	728
1	1613	574
2	5002	548

prune174.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes119.0ms

Accuracy

98.9% (0.4b remaining)

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

bsearch83.0ms

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	40	31
1	40	31

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.1s	1591×	body	2560	valid
1.3s	2782×	body	1280	valid
486.0ms	1862×	body	640	valid
168.0ms	924×	body	320	valid
79.0ms	482×	body	160	valid
26.0ms	355×	body	80	valid
17.0ms	4×	body	5120	valid