Details

sample96.0ms

Algorithm

intervals

Results

46.0ms	134×	body	1280	valid
19.0ms	22×	body	2560	valid
13.0ms	61×	body	640	valid
3.0ms	24×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 40.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (cos (+ x eps)) (cos x))
4.1b	(cos (+ x eps))

rewrite10.0ms

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))

series14.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

simplify108.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

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

prune116.0ms

Filtered

30 candidates to 23 candidates (23.3%)

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: 13.1b

Counts

31 → 12

localize13.0ms

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))
2.5b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite23.0ms

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)))
4.0ms	(* (sin x) (sin eps))
8.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series58.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
18.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
9.0ms	(* (sin x) (sin eps))
23.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify109.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (29.0ms)

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

prune348.0ms

Filtered

82 candidates to 57 candidates (30.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	68	14	82
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	76	18	94

Merged error: 13.0b

Counts

94 → 18

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.5b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite26.0ms

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))
11.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
11.0ms	(+ (* (sin x) (sin eps)) (cos x))
9.0ms	(* (sin x) (sin eps))
22.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify40.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (34.0ms)

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

prune314.0ms

Filtered

77 candidates to 53 candidates (31.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	69	8	77
Fresh	8	9	17
Picked	1	0	1
Done	0	0	0
Total	78	17	95

Merged error: 12.9b

Counts

95 → 17

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
0.2b	(* (sin x) (sin eps))
2.5b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
2.5b	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

13.0ms	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
5.0ms	(* (sin x) (sin eps))
8.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
6.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

series86.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
9.0ms	(* (sin x) (sin eps))
23.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
23.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

simplify72.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	239	889
1	734	805
2	2890	794
3	5001	794

prune301.0ms

Filtered

91 candidates to 59 candidates (35.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	91	17	108

Merged error: 12.9b

Counts

108 → 17

regimes276.0ms

Accuracy

84.5% (1.6b remaining)

Error of 16.1b against oracle of 14.5b and baseline of 24.6b

bsearch152.0ms

Steps

Iters	Range		Point
10	2.38166625324972e-08	1325.407106289753	8.297309089062768e-07
10	-41296.44367278978	-5.93144934820363e-07	-8.698733813856477e-07

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	17
1	36	17

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.6s	4554×	body	1280	valid
505.0ms	596×	body	2560	valid
388.0ms	1840×	body	640	valid
92.0ms	653×	body	320	valid
28.0ms	283×	body	160	valid
4.0ms	74×	body	80	valid

Details

sample96.0ms

simplify4.0ms

prune4.0ms

localize8.0ms

rewrite10.0ms

series14.0ms

simplify108.0ms

prune116.0ms

localize13.0ms

rewrite23.0ms

series58.0ms

simplify109.0ms

prune348.0ms

localize13.0ms

rewrite26.0ms

series50.0ms

simplify40.0ms

prune314.0ms

localize17.0ms

rewrite34.0ms

series86.0ms

simplify72.0ms

prune301.0ms

regimes276.0ms

bsearch152.0ms

simplify1.0ms

end0.0ms

sample2.8s

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