Details

sample98.0ms

Algorithm

intervals

Results

54.0ms	158×	body	1280	valid
17.0ms	19×	body	2560	valid
12.0ms	52×	body	640	valid
2.0ms	15×	body	320	valid
1.0ms	10×	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 (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: 37.9b

Counts

2 → 1

localize14.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (cos (+ x eps)) (cos x))
3.9b	(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))

series15.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify110.0ms

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

prune76.0ms

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: 15.0b

Counts

31 → 12

localize14.0ms

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))
1.2b	(- (- (* (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))
9.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series60.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
16.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
9.0ms	(* (sin x) (sin eps))
26.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify117.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

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

prune262.0ms

Filtered

82 candidates to 56 candidates (31.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	69	13	82
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	78	16	94

Merged error: 14.9b

Counts

94 → 16

localize13.0ms

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))
1.3b	(- (* (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:

5.0ms	(+ (* (sin x) (sin eps)) (cos x))
4.0ms	(* (cos x) (cos eps))
4.0ms	(* (sin x) (sin eps))
8.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* (sin x) (sin eps)) (cos x))
8.0ms	(* (cos x) (cos eps))
9.0ms	(* (sin x) (sin eps))
23.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (35.0ms)

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

prune123.0ms

Filtered

77 candidates to 53 candidates (31.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	69	8	77
Fresh	8	7	15
Picked	1	0	1
Done	0	0	0
Total	78	15	93

Merged error: 14.8b

Counts

93 → 15

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
1.3b	(- (* (cos x) (cos eps)) (+ (log (exp (* (sin x) (sin eps)))) (cos x)))
2.6b	(log (exp (* (sin x) (sin eps))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
5.0ms	(* (sin x) (sin eps))
8.0ms	(- (* (cos x) (cos eps)) (+ (log (exp (* (sin x) (sin eps)))) (cos x)))
2.0ms	(log (exp (* (sin x) (sin eps))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
9.0ms	(* (sin x) (sin eps))
23.0ms	(- (* (cos x) (cos eps)) (+ (log (exp (* (sin x) (sin eps)))) (cos x)))
10.0ms	(log (exp (* (sin x) (sin eps))))

simplify43.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	334	635
1	1247	561
2	5001	547

prune69.0ms

Filtered

80 candidates to 56 candidates (30.0%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	80	15	95

Merged error: 14.8b

Counts

95 → 15

regimes218.0ms

Accuracy

84% (1.6b remaining)

Error of 16.0b against oracle of 14.4b and baseline of 24.6b

bsearch90.0ms

Steps

Iters	Range		Point
11	9.473727641852153e-27	3305.2465175981883	1.6930971516324064e-07
9	-0.00034267683325015424	-3.7179396000055786e-10	-5.059992202592463e-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

1.6s	4409×	body	1280	valid
572.0ms	642×	body	2560	valid
434.0ms	1909×	body	640	valid
101.0ms	666×	body	320	valid
31.0ms	292×	body	160	valid
5.0ms	82×	body	80	valid

Details

sample98.0ms

simplify4.0ms

prune3.0ms

localize14.0ms

rewrite10.0ms

series15.0ms

simplify110.0ms

prune76.0ms

localize14.0ms

rewrite23.0ms

series60.0ms

simplify117.0ms

prune262.0ms

localize13.0ms

rewrite23.0ms

series52.0ms

simplify43.0ms

prune123.0ms

localize17.0ms

rewrite20.0ms

series50.0ms

simplify43.0ms

prune69.0ms

regimes218.0ms

bsearch90.0ms

simplify2.0ms

end0.0ms

sample3.0s

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