Details

sample90.0ms

Algorithm

intervals

Results

46.0ms	107×	body	1280	valid
16.0ms	18×	body	2560	valid
12.0ms	51×	body	640	valid
5.0ms	29×	body	320	valid
2.0ms	41×	body	80	valid
1.0ms	10×	body	160	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: 36.3b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (sin (+ x eps)) (sin x))
3.6b	(sin (+ x eps))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

4×	`sin-sum`
2×	`+-commutative` `associate--l+`
1×	`sub-neg` `flip3--` `diff-sin` `flip--`

Counts

2 → 9

Calls

2 calls:

4.0ms	(- (sin (+ x eps)) (sin x))
3.0ms	(sin (+ x eps))

series61.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify138.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 4 (135.0ms)

Iter	Nodes	Cost
0	117	90
1	282	88
2	919	87
3	3429	86
4	5001	85

prune38.0ms

Filtered

15 candidates to 10 candidates (66.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	13	3	16

Merged error: 0.3b

Counts

16 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin eps) (cos x))
0.1b	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
0.2b	(* (cos eps) (sin x))
1.7b	(- (* (cos eps) (sin x)) (sin x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-commutative`
3×	`sin-cos-mult`
2×	`sub-neg` `associate-+r+` `flip3--` `fma-def` `fma-neg` `frac-add` `flip--`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 19

Calls

4 calls:

3.0ms	(* (sin eps) (cos x))
8.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
3.0ms	(* (cos eps) (sin x))
5.0ms	(- (* (cos eps) (sin x)) (sin x))

series268.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin eps) (cos x))
114.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
48.0ms	(* (cos eps) (sin x))
65.0ms	(- (* (cos eps) (sin x)) (sin x))

simplify85.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	227	262
1	751	252
2	3222	235
3	5001	235

prune102.0ms

Filtered

31 candidates to 22 candidates (71.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	27	4	31
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	28	6	34

Merged error: 0.3b

Counts

34 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos eps) (sin x))
0.6b	(fma (cos eps) (sin x) (sin x))
2.0b	(- (* (* (cos eps) (sin x)) (cos eps)) (sin x))
8.6b	(/ (* (sin x) (- (* (* (cos eps) (sin x)) (cos eps)) (sin x))) (fma (cos eps) (sin x) (sin x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

4×	`fma-neg` `*-commutative`
2×	`flip3--` `associate-r/` `associate-l` `flip--` `associate-/l/` `associate-/l`
1×	`sub-neg` `frac-2neg` `clear-num` `fma-udef` `div-inv`

Counts

4 → 17

Calls

4 calls:

3.0ms	(* (cos eps) (sin x))
1.0ms	(fma (cos eps) (sin x) (sin x))
7.0ms	(- (* (* (cos eps) (sin x)) (cos eps)) (sin x))
14.0ms	(/ (* (sin x) (- (* (* (cos eps) (sin x)) (cos eps)) (sin x))) (fma (cos eps) (sin x) (sin x)))

series453.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos eps) (sin x))
75.0ms	(fma (cos eps) (sin x) (sin x))
67.0ms	(- (* (* (cos eps) (sin x)) (cos eps)) (sin x))
263.0ms	(/ (* (sin x) (- (* (* (cos eps) (sin x)) (cos eps)) (sin x))) (fma (cos eps) (sin x) (sin x)))

simplify75.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	172	232
1	604	225
2	2381	208
3	5001	202

prune133.0ms

Filtered

29 candidates to 22 candidates (75.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	27	8	35

Merged error: 0.2b

Counts

35 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(fma (cos eps) (sin x) (sin x))
1.9b	(- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))
8.6b	(/ (* (sin x) (- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))) (fma (pow (cos eps) 2) (sin x) (sin x)))
8.6b	(/ (* (sin x) (/ (* (sin x) (- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))) (fma (pow (cos eps) 2) (sin x) (sin x)))) (fma (cos eps) (sin x) (sin x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

12×	`associate-/l/`
11×	`associate-*r/`
8×	`fma-neg`
7×	`associate-/l*`
5×	`associate-r` `*-commutative`
4×	`associate-l` `clear-num`
3×	`flip3--` `frac-2neg` `flip--` `div-inv`
2×	`unpow2` `sqr-pow`
1×	`sub-neg` `un-div-inv` `fma-udef`

Counts

4 → 34

Calls

4 calls:

1.0ms	(fma (cos eps) (sin x) (sin x))
9.0ms	(- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))
11.0ms	(/ (* (sin x) (- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))) (fma (pow (cos eps) 2) (sin x) (sin x)))
16.0ms	(/ (* (sin x) (/ (* (sin x) (- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))) (fma (pow (cos eps) 2) (sin x) (sin x)))) (fma (cos eps) (sin x) (sin x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

74.0ms	(fma (cos eps) (sin x) (sin x))
72.0ms	(- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))
322.0ms	(/ (* (sin x) (- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))) (fma (pow (cos eps) 2) (sin x) (sin x)))
773.0ms	(/ (* (sin x) (/ (* (sin x) (- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))) (fma (pow (cos eps) 2) (sin x) (sin x)))) (fma (cos eps) (sin x) (sin x)))

simplify37.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	252	564
1	1083	483
2	5002	463

prune208.0ms

Filtered

46 candidates to 37 candidates (80.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	42	4	46
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	44	10	54

Merged error: 0.2b

Counts

54 → 10

regimes117.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	25
1	24	25

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3322×	body	1280	valid
587.0ms	635×	body	2560	valid
434.0ms	1830×	body	640	valid
134.0ms	767×	body	320	valid
55.0ms	1102×	body	80	valid
36.0ms	344×	body	160	valid