Details

sample93.0ms

Algorithm

intervals

Results

48.0ms	140×	body	1280	valid
19.0ms	22×	body	2560	valid
11.0ms	58×	body	640	valid
3.0ms	23×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	4×	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: 40.3b

localize8.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
2.8b	(cos (+ x eps))

rewrite25.0ms

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:

15.0ms	(- (cos (+ x eps)) (cos x))
9.0ms	(cos (+ x eps))

series71.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify72.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (68.0ms)

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

prune115.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.2b

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))
2.0b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite103.0ms

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:

10.0ms	(* (cos x) (cos eps))
17.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
12.0ms	(* (sin x) (sin eps))
62.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series307.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos x) (cos eps))
86.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
51.0ms	(* (sin x) (sin eps))
130.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify46.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (38.0ms)

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

prune297.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
2.0b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite1.0ms

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:

0.0ms	(fma (sin x) (sin eps) (cos x))
0.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series199.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(fma (sin x) (sin eps) (cos x))
145.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify122.0ms

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

prune133.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
0.1b	(fma (sin x) (sin eps) (cos x))
1.9b	(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))
2.0b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `log-prod` `log-pow` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
2×	`exp-sum`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 52

Calls

4 calls:

2.0ms	(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
0.0ms	(fma (sin x) (sin eps) (cos x))
3.0ms	(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))
0.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series491.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
54.0ms	(fma (sin x) (sin eps) (cos x))
147.0ms	(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))
142.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify42.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	137	627
1	357	554
2	1340	554
3	5002	551

prune215.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 15.9b

regimes172.0ms

Accuracy

87.6% (1.2b remaining)

Error of 15.6b against oracle of 14.3b and baseline of 24.4b

bsearch80.0ms

Steps

Iters	Range		Point
5	1.317141247235427e-05	4.932692811293218e-05	1.3396711044516438e-05
9	-3096.4512561506854	-5.8848704152608634e-05	-0.00018949125417145804

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	26
1	35	26

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4420×	body	1280	valid
548.0ms	653×	body	2560	valid
380.0ms	1863×	body	640	valid
103.0ms	703×	body	320	valid
25.0ms	263×	body	160	valid
5.0ms	98×	body	80	valid