Details

sample90.0ms

Algorithm

intervals

Results

47.0ms	140×	body	1280	valid
18.0ms	21×	body	2560	valid
13.0ms	65×	body	640	valid
3.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	2×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

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: 41.7b

Counts

2 → 1

localize9.0ms

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))

series68.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify111.0ms

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

prune80.0ms

Filtered

30 candidates to 23 candidates (76.7%)

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: 14.7b

Counts

31 → 9

localize15.0ms

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))
2.2b	(- (* (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)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos x) (cos eps))
53.0ms	(+ (* (sin x) (sin eps)) (cos x))
43.0ms	(* (sin x) (sin eps))
126.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	332	607
1	1284	576
2	5002	567

prune229.0ms

Filtered

77 candidates to 53 candidates (68.8%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	60	17	77
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	66	20	86

Merged error: 14.5b

Counts

86 → 20

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(pow (* (sin x) (sin eps)) 3)
2.2b	(- (* (cos x) (cos eps)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
25.0b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

5.0ms	(* (sin x) (sin eps))
5.0ms	(pow (* (sin x) (sin eps)) 3)
13.0ms	(- (* (cos x) (cos eps)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
3.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

series276.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin x) (sin eps))
60.0ms	(pow (* (sin x) (sin eps)) 3)
126.0ms	(- (* (cos x) (cos eps)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
44.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify49.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	374	684
1	1626	611
2	5001	597

prune239.0ms

Filtered

88 candidates to 57 candidates (64.8%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	18	19
Picked	0	1	1
Done	0	0	0
Total	88	20	108

Merged error: 14.5b

Counts

108 → 20

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
0.4b	(+ (+ (* (sin x) (sin eps)) (cos x)) (* (cos x) (cos eps)))
0.5b	(pow (* (cos x) (cos eps)) 3)
2.1b	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `difference-of-squares` `sqr-pow`
7×	`cube-div`
6×	`unpow-prod-down` `pow-unpow` `cube-prod`
5×	`cos-mult`
4×	`flip3-+` `flip-+`
3×	`pow-pow` `pow-exp` `sum-log` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `unpow3` `frac-add` `frac-sub`
1×	`difference-cubes` `+-commutative` `sub-neg` `associate-+l+` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 87

Calls

4 calls:

7.0ms	(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
9.0ms	(+ (+ (* (sin x) (sin eps)) (cos x)) (* (cos x) (cos eps)))
4.0ms	(pow (* (cos x) (cos eps)) 3)
14.0ms	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

series629.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
95.0ms	(+ (+ (* (sin x) (sin eps)) (cos x)) (* (cos x) (cos eps)))
58.0ms	(pow (* (cos x) (cos eps)) 3)
404.0ms	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

simplify86.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	531	1253
1	2604	1149
2	5002	1134

prune329.0ms

Filtered

99 candidates to 65 candidates (65.7%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	83	16	99
Fresh	10	8	18
Picked	1	0	1
Done	1	0	1
Total	95	24	119

Merged error: 14.4b

Counts

119 → 24

regimes339.0ms

Accuracy

84% (1.7b remaining)

Error of 15.7b against oracle of 14.1b and baseline of 24.6b

bsearch102.0ms

Steps

Iters	Range		Point
10	8.485467515044765e-21	4.846798205843289e-11	4.8007364015852064e-11
6	-3.029806383639767e-11	-2.792984742033529e-12	-2.950098860365708e-11

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	28
1	36	28

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4350×	body	1280	valid
545.0ms	620×	body	2560	valid
411.0ms	1939×	body	640	valid
99.0ms	708×	body	320	valid
28.0ms	292×	body	160	valid
5.0ms	91×	body	80	valid