Details

sample90.0ms

Algorithm

intervals

Results

47.0ms	145×	body	1280	valid
19.0ms	22×	body	2560	valid
12.0ms	61×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	1×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (cos (+ x eps)) (cos x))
3.5b	(cos (+ x eps))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `cos-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

7.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series72.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify74.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	192	385
1	523	285
2	2519	275
3	5001	220

prune123.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
1.2b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`prod-diff` `add-log-exp`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `fma-neg` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `associate--l+` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms	(* (sin x) (sin eps))
10.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series307.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos x) (cos eps))
85.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
45.0ms	(* (sin x) (sin eps))
134.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify51.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	381	988
1	1342	837
2	5002	822

prune321.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (cos x) (cos eps) (- (* (sin eps) (sin x))))
0.2b	(* (sin eps) (sin x))
1.2b	(- (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (cos x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`prod-diff`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-r` `associate-l` `log1p-expm1-u`
2×	`fma-udef`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `sin-mult` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 60

Calls

3 calls:

1.0ms	(fma (cos x) (cos eps) (- (* (sin eps) (sin x))))
5.0ms	(* (sin eps) (sin x))
4.0ms	(- (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (cos x))

series272.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(fma (cos x) (cos eps) (- (* (sin eps) (sin x))))
45.0ms	(* (sin eps) (sin x))
139.0ms	(- (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (cos x))

simplify128.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	254	758
1	853	610
2	4301	593
3	5001	546

prune234.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
1.2b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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

2 → 20

Calls

2 calls:

1.0ms	(fma (sin x) (sin eps) (cos x))
1.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series192.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(fma (sin x) (sin eps) (cos x))
141.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify119.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	87	209
1	240	182
2	795	182
3	3587	180
4	5001	180

prune91.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.9b

regimes191.0ms

Accuracy

87.2% (1.3b remaining)

Error of 15.8b against oracle of 14.5b and baseline of 24.7b

bsearch156.0ms

Steps

Iters	Range		Point
10	8.960609758249674e-23	4.5131138850246713e-07	1.2305748660245976e-07
11	-1.5073415317839904e-10	-5.397704668065765e-30	-1.4155618696900624e-10

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	49
1	59	49
2	59	49

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4460×	body	1280	valid
569.0ms	663×	body	2560	valid
400.0ms	1836×	body	640	valid
96.0ms	675×	body	320	valid
28.0ms	287×	body	160	valid
5.0ms	79×	body	80	valid