Details

sample210.0ms

Algorithm

intervals

Results

69.0ms	74×	body	2560	valid
57.0ms	117×	body	1280	valid
49.0ms	57×	body	10240	exit
10.0ms	37×	body	640	valid
5.0ms	313×	pre	80	true
2.0ms	10×	body	320	valid
1.0ms	14×	body	80	valid
0.0ms	4×	body	160	valid

simplify96.0ms

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

prune3.0ms

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: 60.4b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.2b	(- (exp (* a eps)) 1.0)
2.6b	(- (exp (* b eps)) 1.0)
3.7b	(- (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 (* a eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series168.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
36.0ms	(- (exp (* a eps)) 1.0)
32.0ms	(- (exp (* b eps)) 1.0)
51.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

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

prune330.0ms

Filtered

88 candidates to 66 candidates (75.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 49.0b

Counts

89 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

3.7b	(- (exp (* (+ a b) eps)) 1.0)
3.7b	(* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
14.1b	(* (pow a 3) (pow eps 3))
15.2b	(* (pow a 2) (pow eps 2))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
33×	`unswap-sqr`
30×	`add-exp-log`
28×	`unpow-prod-down`
25×	`associate-r`
23×	`associate-l`
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×	`sub-neg` `flip3-+` `pow-prod-down` `*-commutative` `cbrt-unprod` `flip-+`
2×	`distribute-rgt-in` `cube-mult` `distribute-lft-in` `unpow3` `associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log`

Counts

4 → 156

Calls

4 calls:

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

series262.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (exp (* (+ a b) eps)) 1.0)
120.0ms	(* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
61.0ms	(* (pow a 3) (pow eps 3))
36.0ms	(* (pow a 2) (pow eps 2))

simplify124.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	674	1509
1	3516	1362
2	5002	1319

prune629.0ms

Filtered

168 candidates to 91 candidates (54.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	165	3	168
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	166	6	172

Merged error: 48.5b

Counts

172 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

3.0b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
3.7b	(- (exp (* (+ a b) eps)) 1.0)
3.7b	(* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
15.2b	(* (pow a 2) (pow eps 2))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 128

Calls

4 calls:

20.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
14.0ms	(* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
8.0ms	(* (pow a 2) (pow eps 2))

series1.0s

Counts

4 → 12

Calls

4 calls:

826.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
46.0ms	(- (exp (* (+ a b) eps)) 1.0)
114.0ms	(* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
36.0ms	(* (pow a 2) (pow eps 2))

simplify134.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	839	2225
1	4667	1897
2	5001	1897

prune594.0ms

Filtered

140 candidates to 88 candidates (62.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	143	3	146

Merged error: 0.0b

Counts

146 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 19

Calls

1 calls:

16.0ms

(+ (/ 1 b) (/ 1 a))

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

(+ (/ 1 b) (/ 1 a))

simplify66.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (27.0ms)

Iter	Nodes	Cost
0	101	104
1	345	94
2	1153	91
3	2775	90
4	5001	90

prune34.0ms

Filtered

22 candidates to 14 candidates (63.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	22	3	25

Merged error: 0.0b

Counts

25 → 3

regimes69.0ms

Accuracy

0% (2.8b remaining)

Error of 3.2b against oracle of 0.4b and baseline of 3.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.6s	2654×	body	2560	valid
1.7s	1929×	body	10240	exit
1.7s	3427×	body	1280	valid
282.0ms	1037×	body	640	valid
166.0ms	9933×	pre	80	true
58.0ms	335×	body	320	valid
22.0ms	429×	body	80	valid
14.0ms	122×	body	160	valid