Details

sample98.0ms

Algorithm

intervals

Results

56.0ms	155×	body	1280	valid
16.0ms	70×	body	640	valid
13.0ms	15×	body	2560	valid
1.0ms	9×	body	320	valid
1.0ms	6×	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

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: 37.5b

Counts

2 → 1

localize14.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (cos (+ x eps)) (cos x))
2.8b	(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))

series68.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify114.0ms

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

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: 15.1b

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))
1.6b	(- (- (* (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:

5.0ms	(* (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))

series316.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos x) (cos eps))
86.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
47.0ms	(* (sin x) (sin eps))
137.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify117.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	304	633
1	1061	602
2	4487	583
3	5002	583

prune233.0ms

Filtered

82 candidates to 56 candidates (68.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	68	14	82
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	74	19	93

Merged error: 14.9b

Counts

93 → 19

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
1.6b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite28.0ms

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:

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

series286.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos x) (cos eps))
58.0ms	(+ (* (sin x) (sin eps)) (cos x))
46.0ms	(* (sin x) (sin eps))
136.0ms	(- (* (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	576
2	5002	567

prune230.0ms

Filtered

77 candidates to 53 candidates (68.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	67	10	77
Fresh	9	9	18
Picked	1	0	1
Done	0	0	0
Total	77	19	96

Merged error: 14.8b

Counts

96 → 19

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(pow (* (sin x) (sin eps)) 3)
1.6b	(- (* (cos x) (cos eps)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
24.0b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
3×	`pow-unpow` `associate-r` `associate-l` `sin-mult`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `diff-log` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cos-mult` `frac-sub` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `flip3--` `flip3-+` `pow1/3` `sum-log` `*-commutative` `flip--` `rem-cbrt-cube` `flip-+` `associate--r+` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

5.0ms	(* (sin x) (sin eps))
5.0ms	(pow (* (sin x) (sin eps)) 3)
11.0ms	(- (* (cos x) (cos eps)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
3.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

series310.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (sin x) (sin eps))
71.0ms	(pow (* (sin x) (sin eps)) 3)
135.0ms	(- (* (cos x) (cos eps)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
51.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify53.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	374	684
1	1626	611
2	5001	597

prune214.0ms

Filtered

88 candidates to 59 candidates (67.0%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	1	17	18
Picked	0	1	1
Done	0	0	0
Total	87	20	107

Merged error: 14.8b

Counts

107 → 20

regimes208.0ms

Accuracy

83.5% (1.7b remaining)

Error of 15.9b against oracle of 14.2b and baseline of 24.3b

bsearch134.0ms

Steps

Iters	Range		Point
10	7.970030559222916e-26	3.536164573354348e-13	3.396231196767326e-13
8	-0.00010711273713490883	-5.6941803921493696e-08	-5.489479542724413e-07

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	28
1	38	28

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.7s	4483×	body	1280	valid
529.0ms	575×	body	2560	valid
443.0ms	1875×	body	640	valid
120.0ms	697×	body	320	valid
34.0ms	299×	body	160	valid
4.0ms	71×	body	80	valid

Details

sample98.0ms

simplify5.0ms

prune2.0ms

localize14.0ms

rewrite11.0ms

series68.0ms

simplify114.0ms

prune93.0ms

localize15.0ms

rewrite24.0ms

series316.0ms

simplify117.0ms

prune233.0ms

localize14.0ms

rewrite28.0ms

series286.0ms

simplify43.0ms

prune230.0ms

localize17.0ms

rewrite25.0ms

series310.0ms

simplify53.0ms

prune214.0ms

regimes208.0ms

bsearch134.0ms

simplify2.0ms

end0.0ms

sample3.0s

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