Details

sample91.0ms

Algorithm

intervals

Results

48.0ms	136×	body	1280	valid
14.0ms	17×	body	2560	valid
13.0ms	64×	body	640	valid
4.0ms	31×	body	320	valid
1.0ms	8×	body	160	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: 39.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
2.7b	(cos (+ x eps))

rewrite26.0ms

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:

16.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

series63.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (cos (+ x eps)) (cos x))
19.0ms	(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

prune114.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
3.2b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite112.0ms

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:

17.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
12.0ms	(* (cos x) (cos eps))
12.0ms	(* (sin x) (sin eps))
68.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series275.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
36.0ms	(* (cos x) (cos eps))
46.0ms	(* (sin x) (sin eps))
114.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify49.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	381	988
1	1342	837
2	5001	822

prune304.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.4b

localize18.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
3.2b	(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))))

series182.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(fma (sin x) (sin eps) (cos x))
134.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify120.0ms

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

prune156.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
0.1b	(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
3.2b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))
3.2b	(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))

rewrite7.0ms

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:

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

series444.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(fma (sin x) (sin eps) (cos x))
128.0ms	(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
134.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))
129.0ms	(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))

simplify45.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (39.0ms)

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

prune221.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.3b

regimes188.0ms

Accuracy

87.7% (1.3b remaining)

Error of 15.6b against oracle of 14.4b and baseline of 24.8b

bsearch115.0ms

Steps

Iters	Range		Point
6	5.214836503720958e-10	3.7141773282228235e-09	3.588703897944784e-09
9	-2.2082264187638084e-10	-1.8774124276059505e-19	-8.396995804045069e-12

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	25
1	39	25

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4399×	body	1280	valid
578.0ms	660×	body	2560	valid
388.0ms	1881×	body	640	valid
100.0ms	692×	body	320	valid
27.0ms	283×	body	160	valid
4.0ms	85×	body	80	valid