Details

sample97.0ms

Algorithm

intervals

Results

50.0ms	152×	body	1280	valid
19.0ms	22×	body	2560	valid
11.0ms	51×	body	640	valid
3.0ms	18×	body	320	valid
1.0ms	11×	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 (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

localize15.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
3.6b	(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:

7.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series64.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(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

prune136.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	20	10	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	10	31

Merged error: 14.5b

Counts

31 → 10

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))
1.6b	(- (- (* (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))
7.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms	(* (sin x) (sin eps))
8.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series286.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos x) (cos eps))
75.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
47.0ms	(* (sin x) (sin eps))
122.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify111.0ms

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

prune493.0ms

Filtered

82 candidates to 57 candidates (69.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	68	14	82
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	74	18	92

Merged error: 14.3b

Counts

92 → 18

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps)))))
0.2b	(* (sin x) (sin eps))
1.6b	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
2.6b	(log (exp (* (sin x) (sin eps))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

6.0ms	(- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps)))))
5.0ms	(* (sin x) (sin eps))
9.0ms	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
2.0ms	(log (exp (* (sin x) (sin eps))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps)))))
45.0ms	(* (sin x) (sin eps))
128.0ms	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
43.0ms	(log (exp (* (sin x) (sin eps))))

simplify81.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	266	688
1	792	625
2	3018	609
3	5001	609

prune351.0ms

Filtered

78 candidates to 55 candidates (70.5%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	17	17
Picked	0	1	1
Done	0	0	0
Total	77	19	96

Merged error: 14.3b

Counts

96 → 19

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(cbrt (pow (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x))) 3))
0.4b	(pow (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x))) 3)
1.6b	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

5.0ms	(* (sin x) (sin eps))
9.0ms	(cbrt (pow (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x))) 3))
9.0ms	(pow (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x))) 3)
9.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sin x) (sin eps))
134.0ms	(cbrt (pow (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x))) 3))
171.0ms	(pow (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x))) 3)
136.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

simplify57.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	439	1402
1	1856	1327
2	5003	1321

prune331.0ms

Filtered

99 candidates to 62 candidates (62.6%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	95	4	99
Fresh	5	12	17
Picked	0	1	1
Done	0	1	1
Total	100	18	118

Merged error: 14.2b

Counts

118 → 18

regimes285.0ms

Accuracy

87.8% (1.2b remaining)

Error of 16.0b against oracle of 14.8b and baseline of 24.7b

bsearch137.0ms

Steps

Iters	Range		Point
10	0.0003689785113026431	114238954.84408061	0.000373531228165614
10	-1.6204037746650976e-06	-3.4634588385797854e-17	-1.2838162386962672e-08

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	29
1	41	29

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.5s	4452×	body	1280	valid
571.0ms	669×	body	2560	valid
400.0ms	1825×	body	640	valid
97.0ms	673×	body	320	valid
29.0ms	290×	body	160	valid
5.0ms	91×	body	80	valid

Details

sample97.0ms

simplify4.0ms

prune4.0ms

localize15.0ms

rewrite11.0ms

series64.0ms

simplify110.0ms

prune136.0ms

localize14.0ms

rewrite26.0ms

series286.0ms

simplify111.0ms

prune493.0ms

localize17.0ms

rewrite23.0ms

series297.0ms

simplify81.0ms

prune351.0ms

localize16.0ms

rewrite34.0ms

series491.0ms

simplify57.0ms

prune331.0ms

regimes285.0ms

bsearch137.0ms

simplify1.0ms

end0.0ms

sample2.9s

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