Details

sample0.0hr

Algorithm

intervals

Results

0.0hr	136×	body	1280	valid
0.0hr	17×	body	2560	valid
0.0hr	61×	body	640	valid
0.0hr	25×	body	320	valid
0.0hr	14×	body	160	valid
0.0hr	3×	body	80	valid

simplify0.0hr

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0hr)

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

prune0.0hr

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: 36.1b

Counts

2 → 1

localize0.0hr

Local error

Found 2 expressions with local error:

0.6b	(- (cos (+ x eps)) (cos x))
4.8b	(cos (+ x eps))

rewrite0.0hr

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:

0.0hr	(- (cos (+ x eps)) (cos x))
0.0hr	(cos (+ x eps))

series0.0hr

Counts

2 → 6

Calls

2 calls:

0.0hr	(- (cos (+ x eps)) (cos x))
0.0hr	(cos (+ x eps))

simplify0.0hr

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (0.0hr)

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

prune0.0hr

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: 14.6b

Counts

31 → 9

localize0.0hr

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))
1.5b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite0.0hr

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:

0.0hr	(* (cos x) (cos eps))
0.0hr	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.0hr	(* (sin x) (sin eps))
0.0hr	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (cos x) (cos eps))
0.0hr	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.0hr	(* (sin x) (sin eps))
0.0hr	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify0.0hr

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (0.0hr)

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

prune0.0hr

Filtered

82 candidates to 57 candidates (30.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	69	13	82
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	76	15	91

Merged error: 14.6b

Counts

91 → 15

localize0.0hr

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(pow (* (sin x) (sin eps)) 3)
1.5b	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
26.4b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`cbrt-prod` `add-cube-cbrt`
3×	`pow-unpow` `diff-log` `associate-r` `associate-l` `sin-mult`
2×	`cube-div` `cube-mult` `sub-neg` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `associate--l+` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `cbrt-div` `flip3--` `pow1/3` `*-commutative` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

0.0hr	(* (sin x) (sin eps))
0.0hr	(pow (* (sin x) (sin eps)) 3)
0.0hr	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
0.0hr	(cbrt (pow (* (sin x) (sin eps)) 3))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (sin x) (sin eps))
0.0hr	(pow (* (sin x) (sin eps)) 3)
0.0hr	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
0.0hr	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify0.0hr

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (0.0hr)

Iter	Nodes	Cost
0	293	636
1	1142	582
2	5002	567

prune0.0hr

Filtered

90 candidates to 59 candidates (34.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	91	14	105

Merged error: 14.5b

Counts

105 → 14

localize0.0hr

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
0.4b	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
0.4b	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
1.8b	(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

82×	`pow1`
34×	`pow-prod-down`
30×	`add-exp-log` `add-cbrt-cube`
23×	`cos-mult` `sin-mult`
18×	`add-sqr-sqrt`
16×	`prod-exp` `cbrt-unprod` `associate-/l/`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt` `times-frac`
12×	`associate-r/` `associate-l/`
10×	`frac-times`
9×	`frac-sub`
8×	`pow-sqr` `pow-prod-up`
6×	`add-log-exp` `difference-of-squares`
5×	`sub-div`
4×	`pow-plus` `associate-/l*`
3×	`associate-/r*` `associate-/r/`
2×	`pow2` `flip3--` `div-sub` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip--`
1×	`cbrt-undiv` `associate--l-` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `frac-add` `clear-num` `flip-+` `div-inv` `distribute-lft-out--`

Counts

4 → 141

Calls

4 calls:

0.0hr	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
0.0hr	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
0.0hr	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
0.0hr	(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
0.0hr	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
0.0hr	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
0.0hr	(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

simplify0.0hr

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (0.0hr)

Iter	Nodes	Cost
0	620	2406
1	3205	2128
2	5002	2122

prune0.0hr

Filtered

153 candidates to 95 candidates (37.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	144	9	153
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	149	18	167

Merged error: 14.5b

Counts

167 → 18

regimes0.0hr

Accuracy

79.9% (1.9b remaining)

Error of 16.6b against oracle of 14.6b and baseline of 24.3b

bsearch0.0hr

Steps

Iters	Range		Point
6	1.4775731308786106e-05	0.00014293033519397603	1.496850468976921e-05
8	-5.122061173659024e-26	-3.1027681468238543e-30	-5.051304068891255e-26

simplify0.0hr

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0hr)

Iter	Nodes	Cost
0	49	50
1	49	50

end0.0hr

sample0.0hr

Algorithm

intervals

Results

0.0hr	4446×	body	1280	valid
0.0hr	659×	body	2560	valid
0.0hr	1868×	body	640	valid
0.0hr	651×	body	320	valid
0.0hr	283×	body	160	valid
0.0hr	93×	body	80	valid

Details

sample0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

regimes0.0hr

bsearch0.0hr

simplify0.0hr

end0.0hr

sample0.0hr

Profiling