Details

sample99.0ms

Algorithm

intervals

Results

43.0ms	134×	body	1280	valid
19.0ms	22×	body	2560	valid
13.0ms	61×	body	640	valid
11.0ms	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

prune3.0ms

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: 40.0b

Counts

2 → 1

localize9.0ms

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))

series62.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify86.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 3 (22.0ms)

Iter	Nodes	Cost
0	130	175
1	267	165
2	741	164
3	2284	163
4	5002	163

prune136.0ms

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: 13.1b

Counts

31 → 12

localize16.0ms

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))
4.0ms	(- (* (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))

series272.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos x) (cos eps))
77.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
45.0ms	(* (sin x) (sin eps))
110.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify110.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	300	631
1	1047	598
2	4388	582
3	5002	582

prune348.0ms

Filtered

82 candidates to 58 candidates (70.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	67	15	82
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	75	19	94

Merged error: 13.0b

Counts

94 → 19

localize14.0ms

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)))

rewrite23.0ms

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

series244.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos x) (cos eps))
50.0ms	(+ (* (sin x) (sin eps)) (cos x))
45.0ms	(* (sin x) (sin eps))
109.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	328	606
1	1270	572
2	5002	565

prune325.0ms

Filtered

77 candidates to 53 candidates (68.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	69	8	77
Fresh	8	10	18
Picked	1	0	1
Done	0	0	0
Total	78	18	96

Merged error: 12.9b

Counts

96 → 18

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:

10.0ms	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
5.0ms	(* (sin x) (sin eps))
11.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
6.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

series392.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
45.0ms	(* (sin x) (sin eps))
109.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
110.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

simplify71.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	236	887
1	727	801
2	2817	794
3	5002	794

prune297.0ms

Filtered

91 candidates to 59 candidates (64.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	90	19	109

Merged error: 12.9b

Counts

109 → 19

regimes294.0ms

Accuracy

86.9% (1.3b remaining)

Error of 15.9b against oracle of 14.6b and baseline of 24.6b

bsearch139.0ms

Steps

Iters	Range		Point
10	2.38166625324972e-08	1325.407106289753	2.5115276673854185e-08
10	-41296.44367278978	-5.93144934820363e-07	-6.015306453223413e-07

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	16
1	33	16

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4554×	body	1280	valid
518.0ms	596×	body	2560	valid
393.0ms	1840×	body	640	valid
92.0ms	653×	body	320	valid
33.0ms	283×	body	160	valid
4.0ms	74×	body	80	valid

Details

sample99.0ms

simplify4.0ms

prune3.0ms

localize9.0ms

rewrite10.0ms

series62.0ms

simplify86.0ms

prune136.0ms

localize16.0ms

rewrite23.0ms

series272.0ms

simplify110.0ms

prune348.0ms

localize14.0ms

rewrite23.0ms

series244.0ms

simplify41.0ms

prune325.0ms

localize17.0ms

rewrite34.0ms

series392.0ms

simplify71.0ms

prune297.0ms

regimes294.0ms

bsearch139.0ms

simplify1.0ms

end0.0ms

sample2.8s

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