Details

sample95.0ms

Algorithm

intervals

Results

41.0ms	121×	body	1280	valid
21.0ms	24×	body	2560	valid
13.0ms	63×	body	640	valid
5.0ms	34×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	4×	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: 41.2b

Counts

2 → 1

localize16.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (cos (+ x eps)) (cos x))
4.1b	(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))

series86.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(- (cos (+ x eps)) (cos x))
19.0ms	(cos (+ x eps))

simplify115.0ms

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

prune103.0ms

Filtered

30 candidates to 23 candidates (23.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	21	9	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	9	31

Merged error: 15.7b

Counts

31 → 9

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))
2.4b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite26.0ms

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)))
7.0ms	(* (sin x) (sin eps))
9.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series378.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos x) (cos eps))
108.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
55.0ms	(* (sin x) (sin eps))
166.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify116.0ms

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

prune353.0ms

Filtered

82 candidates to 57 candidates (30.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	76	15	91

Merged error: 15.5b

Counts

91 → 15

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))
2.4b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite24.0ms

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

series344.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (cos x) (cos eps))
68.0ms	(+ (* (sin x) (sin eps)) (cos x))
62.0ms	(* (sin x) (sin eps))
165.0ms	(- (* (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	574
2	5002	565

prune327.0ms

Filtered

77 candidates to 54 candidates (29.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	71	6	77
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	74	18	92

Merged error: 15.5b

Counts

92 → 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))
2.4b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
2.5b	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

rewrite31.0ms

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))
9.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
6.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

series563.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
60.0ms	(* (sin x) (sin eps))
165.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
167.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

simplify75.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (19.0ms)

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

prune302.0ms

Filtered

91 candidates to 59 candidates (35.2%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	2	15	17
Picked	0	1	1
Done	0	0	0
Total	91	18	109

Merged error: 15.5b

Counts

109 → 18

regimes284.0ms

Accuracy

85.4% (1.5b remaining)

Error of 16.0b against oracle of 14.5b and baseline of 24.9b

bsearch155.0ms

Steps

Iters	Range		Point
11	1.5451037603674646e-14	53342933.17227377	4.014258208791341e-07
8	-0.04031575958609914	-1.0196708217400701e-06	-1.2748310744836653e-06

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	17
1	35	17

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.6s	4479×	body	1280	valid
546.0ms	630×	body	2560	valid
421.0ms	1847×	body	640	valid
100.0ms	677×	body	320	valid
28.0ms	276×	body	160	valid
5.0ms	91×	body	80	valid

Details

sample95.0ms

simplify4.0ms

prune4.0ms

localize16.0ms

rewrite11.0ms

series86.0ms

simplify115.0ms

prune103.0ms

localize14.0ms

rewrite26.0ms

series378.0ms

simplify116.0ms

prune353.0ms

localize13.0ms

rewrite24.0ms

series344.0ms

simplify43.0ms

prune327.0ms

localize17.0ms

rewrite31.0ms

series563.0ms

simplify75.0ms

prune302.0ms

regimes284.0ms

bsearch155.0ms

simplify1.0ms

end0.0ms

sample3.0s

Profiling