Details

sample89.0ms

Algorithm

intervals

Results

49.0ms	142×	body	1280	valid
15.0ms	72×	body	640	valid
12.0ms	14×	body	2560	valid
3.0ms	20×	body	320	valid
1.0ms	7×	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: 38.5b

localize8.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (cos (+ x eps)) (cos x))
3.9b	(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))
5.0ms	(cos (+ x eps))

series71.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify75.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (71.0ms)

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

prune123.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.3b

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))
3.7b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite39.0ms

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)))
4.0ms	(* (sin x) (sin eps))
23.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series305.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos x) (cos eps))
84.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
44.0ms	(* (sin x) (sin eps))
132.0ms	(- (- (* (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	5002	822

prune330.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 14.2b

localize15.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
3.6b	(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))))

series192.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(fma (sin x) (sin eps) (cos x))
142.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify116.0ms

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

prune157.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.4b	(pow (* (sin x) (sin eps)) 3)
3.7b	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
26.1b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
20×	`prod-diff`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`cbrt-prod`
13×	`associate--l+`
9×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cube-mult` `unpow-prod-down` `pow-unpow` `fma-neg` `diff-log` `unpow3` `cube-prod` `associate-r` `associate-l` `sin-mult` `sqr-pow`
2×	`cube-div` `sub-neg` `pow-pow` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt`
1×	`associate--l-` `pow-to-exp` `cbrt-div` `flip3--` `pow1/3` `*-commutative` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 109

Calls

4 calls:

4.0ms	(* (sin x) (sin eps))
3.0ms	(pow (* (sin x) (sin eps)) 3)
52.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
2.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

series288.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin x) (sin eps))
60.0ms	(pow (* (sin x) (sin eps)) 3)
132.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
46.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify58.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	433	1278
1	1704	976
2	5002	949

prune361.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.1b

regimes201.0ms

Accuracy

86.7% (1.3b remaining)

Error of 15.9b against oracle of 14.6b and baseline of 24.4b

bsearch80.0ms

Steps

Iters	Range		Point
5	1.7079491355729536e-10	3.529261774314728e-10	3.491110681506798e-10
6	-8.751105362266984e-13	-1.8057709034692785e-13	-8.668113418781679e-13

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	57
1	59	57
2	59	57

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4494×	body	1280	valid
566.0ms	658×	body	2560	valid
380.0ms	1816×	body	640	valid
104.0ms	676×	body	320	valid
32.0ms	268×	body	160	valid
10.0ms	88×	body	80	valid