Details

sample92.0ms

Algorithm

intervals

Results

52.0ms	150×	body	1280	valid
16.0ms	19×	body	2560	valid
12.0ms	58×	body	640	valid
3.0ms	18×	body	320	valid
1.0ms	10×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 40.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
3.7b	(cos (+ x eps))

rewrite12.0ms

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))

series71.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify73.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (69.0ms)

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

prune115.0ms

Filtered

46 candidates to 31 candidates (67.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	35	11	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	11	47

Merged error: 14.1b

Counts

47 → 11

localize14.0ms

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))
1.5b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite27.0ms

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))

series298.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos x) (cos eps))
84.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
49.0ms	(* (sin x) (sin eps))
126.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify54.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (40.0ms)

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

prune303.0ms

Filtered

105 candidates to 73 candidates (69.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	93	12	105
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	100	16	116

Merged error: 13.9b

Counts

116 → 16

localize15.0ms

Local error

Found 2 expressions with local error:

0.2b	(fma (sin x) (sin eps) (cos x))
1.5b	(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))))

series191.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(fma (sin x) (sin eps) (cos x))
141.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify118.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (25.0ms)

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

prune141.0ms

Filtered

26 candidates to 21 candidates (80.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	21	5	26
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	24	18	42

Merged error: 13.8b

Counts

42 → 18

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
1.5b	(fma (cos eps) (cos x) (- (+ (* (sin x) (sin eps)) (cos x))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u`
1×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `sin-mult` `unswap-sqr`

Counts

3 → 45

Calls

3 calls:

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

series237.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(+ (* (sin x) (sin eps)) (cos x))
44.0ms	(* (sin x) (sin eps))
139.0ms	(fma (cos eps) (cos x) (- (+ (* (sin x) (sin eps)) (cos x))))

simplify77.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	205	378
1	645	339
2	2519	338
3	5001	336

prune149.0ms

Filtered

54 candidates to 43 candidates (79.6%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	3	14	17
Picked	0	1	1
Done	0	0	0
Total	55	17	72

Merged error: 13.8b

Counts

72 → 17

regimes199.0ms

Accuracy

85% (1.5b remaining)

Error of 16.0b against oracle of 14.5b and baseline of 24.3b

bsearch114.0ms

Steps

Iters	Range		Point
9	7.678987351435402e-30	2.5754526088038613e-20	2.5335197603511498e-20
8	-0.41295360884021565	-1.0220710393840792e-05	-0.00014619102741755152

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	15
1	42	15
2	42	15

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4503×	body	1280	valid
548.0ms	631×	body	2560	valid
384.0ms	1823×	body	640	valid
101.0ms	659×	body	320	valid
35.0ms	308×	body	160	valid
4.0ms	76×	body	80	valid