Details

sample228.0ms

Algorithm

intervals

Results

73.0ms	72×	body	2560	valid
65.0ms	133×	body	1280	valid
56.0ms	63×	body	10240	exit
9.0ms	33×	body	640	valid
5.0ms	319×	pre	80	true
1.0ms	5×	body	320	valid
0.0ms	9×	body	80	valid
0.0ms	4×	body	160	valid

simplify94.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	245	13
3	697	13
4	3463	13
5	5001	13

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: 61.8b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.3b	(- (exp (* b eps)) 1.0)
2.4b	(- (exp (* a eps)) 1.0)
3.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`flip3--` `flip--`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`frac-times`
3×	`diff-log`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

10.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series172.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
32.0ms	(- (exp (* b eps)) 1.0)
39.0ms	(- (exp (* a eps)) 1.0)
47.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	346	733
1	1449	673
2	5001	673

prune311.0ms

Filtered

88 candidates to 66 candidates (75.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Merged error: 50.5b

Counts

89 → 5

localize33.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
3.5b	(- (exp (* (+ a b) eps)) 1.0)
11.6b	(* (pow eps 2) (pow b 2))
12.1b	(* (pow eps 3) (pow b 3))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
33×	`unswap-sqr`
30×	`add-exp-log`
28×	`unpow-prod-down`
25×	`associate-l`
23×	`associate-r`
20×	`*-un-lft-identity` `sqr-pow`
19×	`prod-exp`
16×	`add-cube-cbrt`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`add-cbrt-cube` `unpow2`
6×	`pow1` `add-log-exp`
4×	`frac-times` `flip3--` `flip--`
3×	`flip3-+` `pow-prod-down` `*-commutative` `cbrt-unprod` `flip-+`
2×	`cube-mult` `unpow3` `associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `diff-log`

Counts

4 → 154

Calls

4 calls:

17.0ms	(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
8.0ms	(* (pow eps 2) (pow b 2))
9.0ms	(* (pow eps 3) (pow b 3))

series376.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
53.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow eps 2) (pow b 2))
69.0ms	(* (pow eps 3) (pow b 3))

simplify142.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (125.0ms)

Iter	Nodes	Cost
0	724	1457
1	3905	1310
2	5003	1267

prune622.0ms

Filtered

166 candidates to 91 candidates (54.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	162	9	171

Merged error: 50.3b

Counts

171 → 9

localize40.0ms

Local error

Found 4 expressions with local error:

11.6b	(* (pow eps 2) (pow b 2))
12.1b	(* (pow eps 3) (pow b 3))
12.1b	(* (pow eps 3) (pow b 3))
12.1b	(* (pow eps 3) (pow b 3))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

114×	`add-sqr-sqrt`
64×	`unswap-sqr`
56×	`unpow-prod-down`
52×	`add-exp-log`
44×	`associate-r` `associate-l`
42×	`cube-prod`
40×	`sqr-pow`
36×	`prod-exp`
26×	`add-cube-cbrt` `*-un-lft-identity`
24×	`pow-to-exp` `pow-exp`
12×	`add-cbrt-cube`
10×	`unpow2`
6×	`cube-mult` `unpow3`
4×	`pow1` `pow-prod-down` `*-commutative` `cbrt-unprod` `add-log-exp`

Counts

4 → 228

Calls

4 calls:

7.0ms	(* (pow eps 2) (pow b 2))
9.0ms	(* (pow eps 3) (pow b 3))
10.0ms	(* (pow eps 3) (pow b 3))
10.0ms	(* (pow eps 3) (pow b 3))

series237.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (pow eps 2) (pow b 2))
63.0ms	(* (pow eps 3) (pow b 3))
68.0ms	(* (pow eps 3) (pow b 3))
70.0ms	(* (pow eps 3) (pow b 3))

simplify78.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	318	1172
1	1651	1067
2	5002	952

prune962.0ms

Filtered

240 candidates to 110 candidates (45.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	240	0	240
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	240	9	249

Merged error: 50.3b

Counts

249 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (exp (* a eps)) 1.0)
3.2b	(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
3.5b	(- (exp (* (+ a b) eps)) 1.0)
11.6b	(* (pow eps 2) (pow b 2))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
18×	`add-exp-log`
17×	`unswap-sqr`
16×	`*-un-lft-identity`
14×	`unpow-prod-down`
13×	`associate-l`
11×	`associate-r`
10×	`add-cube-cbrt` `prod-exp` `unpow2` `sqr-pow`
8×	`add-cbrt-cube` `add-log-exp`
6×	`pow1` `pow-to-exp` `pow-exp`
5×	`flip3--` `flip--`
4×	`frac-times`
3×	`flip3-+` `flip-+` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `cbrt-unprod`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 109

Calls

4 calls:

4.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow eps 2) (pow b 2))

series345.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (exp (* a eps)) 1.0)
227.0ms	(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
48.0ms	(- (exp (* (+ a b) eps)) 1.0)
34.0ms	(* (pow eps 2) (pow b 2))

simplify105.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	612	1201
1	3063	1069
2	5002	1065

prune476.0ms

Filtered

121 candidates to 75 candidates (62.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	115	6	121
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	119	11	130

Merged error: 49.4b

Counts

130 → 11

regimes284.0ms

Accuracy

45.2% (4.6b remaining)

Error of 53.3b against oracle of 48.7b and baseline of 57.1b

bsearch278.0ms

Steps

Iters	Range		Point
9	2.797292414147033e+40	1.5507233175302914e+47	8.895710189523327e+43
5	-3688053911496.1914	-937727910791.0848	-2942943340030.655

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	96
1	87	96
2	87	96

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.5s	2595×	body	2560	valid
1.8s	2073×	body	10240	exit
1.7s	3407×	body	1280	valid
305.0ms	1082×	body	640	valid
176.0ms	10075×	pre	80	true
67.0ms	365×	body	320	valid
23.0ms	424×	body	80	valid
18.0ms	129×	body	160	valid