Details

sample94.0ms

Algorithm

intervals

Results

55.0ms	156×	body	1280	valid
15.0ms	18×	body	2560	valid
11.0ms	50×	body	640	valid
3.0ms	18×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	5×	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: 42.4b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (cos (+ x eps)) (cos x))
3.6b	(cos (+ x eps))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `cos-sum` `add-cbrt-cube`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

6.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series73.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (cos (+ x eps)) (cos x))
24.0ms	(cos (+ x eps))

simplify115.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	134	176
1	281	167
2	840	164
3	2958	164
4	5002	164

prune91.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	19	11	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	11	31

Merged error: 15.3b

Counts

31 → 11

localize15.0ms

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))
3.4b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`diff-log`
3×	`sub-neg` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 70

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))

series292.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (cos x) (cos eps))
81.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
47.0ms	(* (sin x) (sin eps))
125.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify118.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	600
2	4487	582
3	5002	582

prune234.0ms

Filtered

82 candidates to 56 candidates (68.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	69	13	82
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	77	16	93

Merged error: 15.1b

Counts

93 → 16

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
3.5b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
3×	`cos-mult`
2×	`flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip--` `sin-mult` `associate--r+`

Counts

4 → 65

Calls

4 calls:

5.0ms	(+ (* (sin x) (sin eps)) (cos x))
4.0ms	(* (cos x) (cos eps))
5.0ms	(* (sin x) (sin eps))
9.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ (* (sin x) (sin eps)) (cos x))
44.0ms	(* (cos x) (cos eps))
44.0ms	(* (sin x) (sin eps))
130.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	332	607
1	1284	574
2	5002	565

prune236.0ms

Filtered

77 candidates to 54 candidates (70.1%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	70	7	77
Fresh	4	11	15
Picked	0	1	1
Done	0	0	0
Total	74	19	93

Merged error: 15.0b

Counts

93 → 19

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.4b	(pow (cos x) 3)
0.6b	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
3.3b	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
18×	`unpow-prod-down` `cube-prod`
16×	`difference-of-squares`
11×	`add-log-exp`
10×	`add-cube-cbrt` `sqr-pow`
6×	`pow1` `add-exp-log` `pow-unpow` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`cube-div`
2×	`cube-mult` `pow-to-exp` `sub-neg` `associate-+l+` `flip3--` `pow-pow` `diff-log` `unpow3` `pow-exp` `sum-log` `cos-mult` `flip--` `sin-mult` `rem-cube-cbrt`
1×	`difference-cubes` `+-commutative` `associate-+l-` `flip3-+` `frac-sub` `flip-+` `distribute-lft-out` `sub-div`

Counts

4 → 100

Calls

4 calls:

13.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
3.0ms	(pow (cos x) 3)
6.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
16.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series842.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
33.0ms	(pow (cos x) 3)
108.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
602.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify102.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	599	1433
1	2889	1321
2	5002	1280

prune331.0ms

Filtered

112 candidates to 63 candidates (56.3%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	101	11	112
Fresh	10	7	17
Picked	1	0	1
Done	0	1	1
Total	112	19	131

Merged error: 15.0b

Counts

131 → 19

regimes252.0ms

Accuracy

81.1% (1.8b remaining)

Error of 16.6b against oracle of 14.7b and baseline of 24.5b

bsearch112.0ms

Steps

Iters	Range		Point
8	7.752825356470831e-10	4.272590306110455e-05	2.855283971320616e-06
8	-2.977617103627092e-24	-7.6462987371367345e-28	-2.9391443929978567e-24

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	15
1	34	15

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	4371×	body	1280	valid
601.0ms	677×	body	2560	valid
406.0ms	1872×	body	640	valid
116.0ms	706×	body	320	valid
29.0ms	279×	body	160	valid
5.0ms	95×	body	80	valid

Details

sample94.0ms

simplify5.0ms

prune2.0ms

localize9.0ms

rewrite11.0ms

series73.0ms

simplify115.0ms

prune91.0ms

localize15.0ms

rewrite24.0ms

series292.0ms

simplify118.0ms

prune234.0ms

localize15.0ms

rewrite24.0ms

series268.0ms

simplify43.0ms

prune236.0ms

localize26.0ms

rewrite41.0ms

series842.0ms

simplify102.0ms

prune331.0ms

regimes252.0ms

bsearch112.0ms

simplify1.0ms

end0.0ms

sample2.9s

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