Details

sample93.0ms

Algorithm

intervals

Results

49.0ms	146×	body	1280	valid
18.0ms	17×	body	2560	valid
12.0ms	59×	body	640	valid
4.0ms	25×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	2×	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

localize8.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
3.1b	(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))

series70.0ms

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

prune121.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(fma (sin x) (sin eps) (cos x))
2.3b	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `prod-diff` `log1p-expm1-u`
2×	`fma-udef`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `cos-mult` `*-commutative` `flip--` `cbrt-unprod` `associate--r+` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

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

series225.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(* (cos x) (cos eps))
50.0ms	(fma (sin x) (sin eps) (cos x))
131.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

simplify113.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	235	486
1	832	409
2	4806	406
3	5001	406

prune217.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.2b	(fma (sin x) (sin eps) (cos x))
0.2b	(fma (sin x) (sin eps) (cos x))
2.3b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

3×	`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

3 → 30

Calls

3 calls:

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

series241.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(fma (sin x) (sin eps) (cos x))
55.0ms	(fma (sin x) (sin eps) (cos x))
137.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify117.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	87	285
1	240	248
2	795	248
3	3587	245
4	5001	245

prune205.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.1b

localize17.0ms

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))
2.3b	(- (- (* (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))
9.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series293.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos x) (cos eps))
82.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
48.0ms	(* (sin x) (sin eps))
125.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify47.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	381	989
1	1342	838
2	5002	822

prune269.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 14.1b

regimes208.0ms

Accuracy

87.5% (1.2b remaining)

Error of 15.5b against oracle of 14.3b and baseline of 23.9b

bsearch140.0ms

Steps

Iters	Range		Point
9	6.68940051768271e-13	7.712829756242493e-08	2.1724003884687943e-10
10	-199130166725.20535	-0.00043085380315138777	-0.00043665739839330274

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	22
1	42	22
2	42	22

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4447×	body	1280	valid
535.0ms	623×	body	2560	valid
394.0ms	1889×	body	640	valid
106.0ms	674×	body	320	valid
29.0ms	299×	body	160	valid
4.0ms	68×	body	80	valid