Details

sample227.0ms

Algorithm

intervals

Results

79.0ms	80×	body	2560	valid
59.0ms	116×	body	1280	valid
55.0ms	69×	body	10240	exit
8.0ms	31×	body	640	valid
6.0ms	325×	pre	80	true
2.0ms	11×	body	320	valid
1.0ms	13×	body	80	valid
1.0ms	5×	body	160	valid

simplify93.0ms

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 (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: 60.6b

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))
2.6b	(- (exp (* b eps)) 1.0)
3.8b	(- (exp (* a eps)) 1.0)
5.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite42.0ms

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:

15.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
10.0ms	(- (exp (* b eps)) 1.0)
6.0ms	(- (exp (* a eps)) 1.0)
8.0ms	(- (exp (* (+ a b) eps)) 1.0)

series175.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
32.0ms	(- (exp (* b eps)) 1.0)
40.0ms	(- (exp (* a eps)) 1.0)
48.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	339	733
1	1408	673
2	5002	672

prune461.0ms

Filtered

88 candidates to 66 candidates (25.0%)

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: 50.0b

Counts

89 → 5

localize31.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (exp (* a eps)) 1.0)
5.4b	(- (exp (* (+ a b) eps)) 1.0)
12.2b	(* (pow eps 2) (pow b 2))
14.2b	(* (pow eps 3) (pow b 3))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
28×	`add-exp-log`
26×	`unpow-prod-down`
25×	`unswap-sqr`
24×	`*-un-lft-identity`
18×	`prod-exp` `sqr-pow`
16×	`add-cube-cbrt` `pow-unpow` `associate-r` `associate-l` `pow-prod-down`
12×	`pow1` `pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`add-cbrt-cube` `add-log-exp`
4×	`pow-pow`
2×	`sub-neg` `flip3--` `diff-log` `unpow3` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 137

Calls

4 calls:

6.0ms	(- (exp (* a eps)) 1.0)
8.0ms	(- (exp (* (+ a b) eps)) 1.0)
10.0ms	(* (pow eps 2) (pow b 2))
10.0ms	(* (pow eps 3) (pow b 3))

series184.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (exp (* a eps)) 1.0)
49.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow eps 2) (pow b 2))
68.0ms	(* (pow eps 3) (pow b 3))

simplify70.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	498	723
1	2000	631
2	5002	613

prune495.0ms

Filtered

149 candidates to 82 candidates (45.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	145	4	149
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	146	8	154

Merged error: 49.2b

Counts

154 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (exp (* a eps)) 1.0)
4.7b	(* (* (pow eps 3) b) b)
5.4b	(- (exp (* (+ a b) eps)) 1.0)
12.2b	(* (pow eps 2) (pow b 2))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
35×	`associate-l`
26×	`add-exp-log` `unswap-sqr`
21×	`*-un-lft-identity`
19×	`unpow-prod-down`
16×	`prod-exp`
15×	`add-cube-cbrt`
14×	`associate-r`
13×	`pow1` `sqr-pow`
11×	`pow-prod-down` `add-cbrt-cube`
10×	`unpow2`
8×	`pow-unpow` `add-log-exp`
7×	`pow-to-exp` `pow-exp`
4×	`cbrt-unprod`
3×	`*-commutative`
2×	`sub-neg` `flip3--` `pow-pow` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`unpow3`

Counts

4 → 128

Calls

4 calls:

6.0ms	(- (exp (* a eps)) 1.0)
11.0ms	(* (* (pow eps 3) b) b)
11.0ms	(- (exp (* (+ a b) eps)) 1.0)
10.0ms	(* (pow eps 2) (pow b 2))

series159.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (exp (* a eps)) 1.0)
39.0ms	(* (* (pow eps 3) b) b)
50.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow eps 2) (pow b 2))

simplify66.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	508	680
1	2062	569
2	5001	557

prune493.0ms

Filtered

140 candidates to 82 candidates (41.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	135	5	140
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	140	8	148

Merged error: 48.4b

Counts

148 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (exp (* a eps)) 1.0)
4.7b	(* (* (pow eps 3) b) b)
5.4b	(- (exp (* (+ a b) eps)) 1.0)
5.8b	(* b (pow eps 2))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
30×	`associate-l`
19×	`add-exp-log`
16×	`*-un-lft-identity`
14×	`associate-r` `unswap-sqr`
12×	`add-cube-cbrt`
11×	`pow1` `add-cbrt-cube`
10×	`prod-exp`
9×	`unpow-prod-down`
8×	`add-log-exp`
5×	`sqr-pow`
4×	`pow-prod-down` `cbrt-unprod`
3×	`*-commutative`
2×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `flip--` `distribute-lft-out--` `unpow2` `difference-of-squares`
1×	`unpow3`

Counts

4 → 98

Calls

4 calls:

6.0ms	(- (exp (* a eps)) 1.0)
10.0ms	(* (* (pow eps 3) b) b)
11.0ms	(- (exp (* (+ a b) eps)) 1.0)
6.0ms	(* b (pow eps 2))

series155.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (exp (* a eps)) 1.0)
40.0ms	(* (* (pow eps 3) b) b)
50.0ms	(- (exp (* (+ a b) eps)) 1.0)
27.0ms	(* b (pow eps 2))

simplify57.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	418	537
1	1718	457
2	5001	449

prune384.0ms

Filtered

110 candidates to 71 candidates (35.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	112	6	118

Merged error: 48.4b

Counts

118 → 6

regimes167.0ms

Accuracy

57% (3.7b remaining)

Error of 52.2b against oracle of 48.5b and baseline of 57.2b

bsearch352.0ms

Steps

Iters	Range		Point
8	1.390978468581987e+50	8.50227910835678e+52	4.3090365317377904e+51
9	-1.2967359649109884e+81	-2.872156065838817e+75	-1.5373949796703815e+77

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	45
1	75	45

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.5s	2594×	body	2560	valid
1.8s	2007×	body	10240	exit
1.7s	3414×	body	1280	valid
300.0ms	1071×	body	640	valid
177.0ms	10008×	pre	80	true
63.0ms	349×	body	320	valid
25.0ms	456×	body	80	valid
14.0ms	117×	body	160	valid