Details

sample101.0ms

Algorithm

intervals

Results

28.0ms	65×	body	10240	exit
23.0ms	54×	body	1280	valid
17.0ms	318×	body	80	valid
10.0ms	39×	body	640	valid
4.0ms	27×	body	320	valid
1.0ms	12×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (36.0ms)

Iter	Nodes	Cost
0	47	16
1	124	16
2	365	16
3	1376	16
4	5001	15

prune9.0ms

Filtered

1 candidates to 1 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: 30.2b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(exp (- (* (- 1.0 eps) x)))
0.0b	(exp (- (* (+ 1.0 eps) x)))
2.2b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
74×	`exp-neg`
72×	`frac-times`
56×	`neg-sub0` `exp-diff`
38×	`associate-*l/`
36×	`associate-*r/`
29×	`flip3--` `flip--`
27×	`flip3-+` `flip-+`
18×	`un-div-inv`
10×	`exp-prod` `*-commutative`
4×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `prod-diff`
2×	`neg-mul-1` `fma-neg`
1×	`sub-neg`

Counts

4 → 108

Calls

4 calls:

6.0ms	(* (- 1.0 eps) x)
4.0ms	(exp (- (* (- 1.0 eps) x)))
4.0ms	(exp (- (* (+ 1.0 eps) x)))
17.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series274.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (- 1.0 eps) x)
31.0ms	(exp (- (* (- 1.0 eps) x)))
26.0ms	(exp (- (* (+ 1.0 eps) x)))
189.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify128.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	1174	3388
1	4160	3137
2	5001	3061

prune269.0ms

Filtered

120 candidates to 51 candidates (42.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	117	5	122

Merged error: 0.9b

Counts

122 → 5

localize9.0ms

Local error

Found 1 expressions with local error:

5.8b	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`fma-udef`

Counts

1 → 1

Calls

1 calls:

1.0ms

(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series37.0ms

Counts

1 → 3

Calls

1 calls:

37.0ms

(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify129.0ms

Algorithm

egg-herbie

Counts

4 → 4

Iterations

Useful iterations: 3 (10.0ms)

Iter	Nodes	Cost
0	28	20
1	82	17
2	239	17
3	741	14
4	3237	14
5	5001	14

prune20.0ms

Filtered

4 candidates to 2 candidates (50.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	3	1	4
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	4	5	9

Merged error: 0.9b

Counts

9 → 5

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma (pow x 2) (- (* x 0.6666666666666667) 1.0) 2.0)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`fma-udef`

Counts

1 → 1

Calls

1 calls:

1.0ms

(fma (pow x 2) (- (* x 0.6666666666666667) 1.0) 2.0)

series38.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

(fma (pow x 2) (- (* x 0.6666666666666667) 1.0) 2.0)

simplify132.0ms

Algorithm

egg-herbie

Counts

4 → 4

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	36	22
1	98	19
2	277	19
3	822	16
4	3510	16
5	5001	16

prune14.0ms

Filtered

4 candidates to 2 candidates (50.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	4	5	9

Merged error: 0.9b

Counts

9 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(exp (- (* (- 1.0 eps) x)))
0.1b	(pow (exp -1) (* (+ 1.0 eps) x))
2.7b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (pow (exp -1) (* (+ 1.0 eps) x))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-*l/`
18×	`frac-sub`
11×	`flip3--` `flip--`
10×	`*-commutative`
9×	`exp-neg`
8×	`frac-times`
7×	`neg-sub0` `exp-diff`
6×	`flip3-+` `prod-diff` `flip-+`
5×	`exp-prod`
4×	`associate-*r/`
3×	`sqr-pow`
2×	`distribute-lft-neg-in` `pow-unpow` `distribute-rgt-neg-in` `fma-neg` `associate-r` `un-div-inv`
1×	`pow-to-exp` `neg-mul-1` `sub-neg` `pow-exp`

Counts

4 → 45

Calls

4 calls:

3.0ms	(* (- 1.0 eps) x)
4.0ms	(exp (- (* (- 1.0 eps) x)))
3.0ms	(pow (exp -1) (* (+ 1.0 eps) x))
13.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (pow (exp -1) (* (+ 1.0 eps) x))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (- 1.0 eps) x)
26.0ms	(exp (- (* (- 1.0 eps) x)))
42.0ms	(pow (exp -1) (* (+ 1.0 eps) x))
366.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (pow (exp -1) (* (+ 1.0 eps) x))))

simplify85.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	704	1174
1	2841	1070
2	5001	1052

prune163.0ms

Filtered

57 candidates to 35 candidates (61.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	1	1	2
Picked	1	0	1
Done	1	1	2
Total	58	4	62

Merged error: 0.9b

Counts

62 → 4

regimes70.0ms

Accuracy

96.6% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 15.8b

bsearch62.0ms

Steps

Iters	Range		Point
4	221.0380432921384	357.20278190505735	330.46423576118536

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	21
1	36	21

end0.0ms

sample2.9s

Algorithm

intervals

Results

787.0ms	1902×	body	10240	exit
779.0ms	1783×	body	1280	valid
564.0ms	10024×	body	80	valid
333.0ms	1268×	body	640	valid
111.0ms	639×	body	320	valid
40.0ms	347×	body	160	valid