Details

sample98.0ms

Algorithm

intervals

Results

55.0ms	142×	body	1280	valid
15.0ms	68×	body	640	valid
14.0ms	16×	body	2560	valid
3.0ms	21×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	3×	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: 38.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
4.7b	(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))

series70.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(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

prune93.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	18	12	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	12	31

Merged error: 11.5b

Counts

31 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

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

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))

series309.0ms

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))
135.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify116.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (31.0ms)

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

prune232.0ms

Filtered

82 candidates to 57 candidates (69.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	71	11	82
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	80	14	94

Merged error: 11.3b

Counts

94 → 14

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.3b	(pow (cos x) 3)
0.5b	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
1.8b	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite38.0ms

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:

8.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
2.0ms	(pow (cos x) 3)
6.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
18.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series854.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
28.0ms	(pow (cos x) 3)
110.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
612.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify104.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (91.0ms)

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

prune418.0ms

Filtered

112 candidates to 63 candidates (56.3%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	100	12	112
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	106	20	126

Merged error: 11.2b

Counts

126 → 20

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (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))
2.0b	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

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))
7.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

series391.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
45.0ms	(* (sin x) (sin eps))
132.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
128.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

simplify99.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	300	825
1	970	767
2	3675	746
3	5002	745

prune201.0ms

Filtered

85 candidates to 58 candidates (68.2%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	18	19
Picked	0	1	1
Done	0	0	0
Total	85	20	105

Merged error: 11.2b

Counts

105 → 20

regimes279.0ms

Accuracy

83.3% (1.7b remaining)

Error of 15.7b against oracle of 14.0b and baseline of 23.9b

bsearch138.0ms

Steps

Iters	Range		Point
10	9.184627563245358e-19	1.8195783874717837e-07	3.2579410132536815e-08
7	-9.926686819785067e-05	-1.6277076070161703e-06	-1.649759884777939e-06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	73
1	52	73

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	4439×	body	1280	valid
534.0ms	609×	body	2560	valid
445.0ms	1908×	body	640	valid
104.0ms	682×	body	320	valid
34.0ms	268×	body	160	valid
5.0ms	94×	body	80	valid

Details

sample98.0ms

simplify5.0ms

prune2.0ms

localize8.0ms

rewrite11.0ms

series70.0ms

simplify115.0ms

prune93.0ms

localize15.0ms

rewrite24.0ms

series309.0ms

simplify116.0ms

prune232.0ms

localize25.0ms

rewrite38.0ms

series854.0ms

simplify104.0ms

prune418.0ms

localize22.0ms

rewrite27.0ms

series391.0ms

simplify99.0ms

prune201.0ms

regimes279.0ms

bsearch138.0ms

simplify2.0ms

end0.0ms

sample2.9s

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