Details

sample227.0ms

Algorithm

intervals

Results

79.0ms	80×	body	2560	valid
58.0ms	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

simplify103.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	258	13
3	766	13
4	3895	13
5	5001	13

prune4.0ms

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

localize19.0ms

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)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
45×	`prod-diff`
39×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-log-exp`
9×	`flip3--` `fma-neg` `flip--`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`diff-log`
2×	`associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

18.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
7.0ms	(- (exp (* b eps)) 1.0)
7.0ms	(- (exp (* a eps)) 1.0)
10.0ms	(- (exp (* (+ a b) eps)) 1.0)

series179.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
38.0ms	(- (exp (* b eps)) 1.0)
36.0ms	(- (exp (* a eps)) 1.0)
54.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	481	1660
1	1994	1241
2	5001	1216

prune583.0ms

Filtered

150 candidates to 91 candidates (39.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	145	5	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	146	5	151

Merged error: 50.0b

Counts

151 → 5

localize27.0ms

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))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
30×	`add-cube-cbrt`
28×	`add-exp-log`
26×	`unpow-prod-down`
25×	`unswap-sqr`
18×	`prod-diff` `prod-exp` `sqr-pow`
16×	`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`
6×	`fma-neg`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `unpow3` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 169

Calls

4 calls:

7.0ms	(- (exp (* a eps)) 1.0)
10.0ms	(- (exp (* (+ a b) eps)) 1.0)
13.0ms	(* (pow eps 2) (pow b 2))
10.0ms	(* (pow eps 3) (pow b 3))

series190.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (exp (* a eps)) 1.0)
51.0ms	(- (exp (* (+ a b) eps)) 1.0)
33.0ms	(* (pow eps 2) (pow b 2))
70.0ms	(* (pow eps 3) (pow b 3))

simplify85.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	592	1065
1	2351	825
2	5002	802

prune651.0ms

Filtered

181 candidates to 100 candidates (44.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	177	4	181
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	178	8	186

Merged error: 49.2b

Counts

186 → 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))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
35×	`-un-lft-identity` `associate-l*`
29×	`add-cube-cbrt`
26×	`add-exp-log` `unswap-sqr`
19×	`unpow-prod-down`
18×	`prod-diff`
16×	`prod-exp`
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`
6×	`fma-neg`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`*-commutative`
2×	`sub-neg` `flip3--` `pow-pow` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`unpow3`

Counts

4 → 160

Calls

4 calls:

8.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(* (* (pow eps 3) b) b)
10.0ms	(- (exp (* (+ a b) eps)) 1.0)
11.0ms	(* (pow eps 2) (pow b 2))

series169.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (exp (* a eps)) 1.0)
41.0ms	(* (* (pow eps 3) b) b)
53.0ms	(- (exp (* (+ a b) eps)) 1.0)
34.0ms	(* (pow eps 2) (pow b 2))

simplify92.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	601	1022
1	2395	763
2	5001	747

prune680.0ms

Filtered

172 candidates to 100 candidates (41.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	167	5	172
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	172	8	180

Merged error: 48.4b

Counts

180 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

3.4b	(* (pow eps 3) b)
3.8b	(- (exp (* a eps)) 1.0)
4.7b	(* (* (pow eps 3) b) b)
5.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
35×	`associate-l`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`prod-diff`
13×	`unswap-sqr`
11×	`pow1` `add-cbrt-cube`
10×	`prod-exp`
9×	`unpow-prod-down` `associate-r`
8×	`add-log-exp`
6×	`fma-neg`
5×	`sqr-pow`
4×	`expm1-log1p-u` `pow-prod-down` `cbrt-unprod` `log1p-expm1-u`
3×	`*-commutative`
2×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-exp` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 129

Calls

4 calls:

6.0ms	(* (pow eps 3) b)
8.0ms	(- (exp (* a eps)) 1.0)
11.0ms	(* (* (pow eps 3) b) b)
13.0ms	(- (exp (* (+ a b) eps)) 1.0)

series172.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (pow eps 3) b)
39.0ms	(- (exp (* a eps)) 1.0)
50.0ms	(* (* (pow eps 3) b) b)
52.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify67.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	438	862
1	1573	649
2	5002	642

prune539.0ms

Filtered

141 candidates to 92 candidates (34.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	137	4	141
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	143	6	149

Merged error: 48.4b

Counts

149 → 6

regimes183.0ms

Accuracy

57.2% (3.7b remaining)

Error of 52.2b against oracle of 48.5b and baseline of 57.1b

bsearch351.0ms

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	63	43
1	63	43

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.6s	2594×	body	2560	valid
1.8s	2007×	body	10240	exit
1.7s	3414×	body	1280	valid
309.0ms	1071×	body	640	valid
196.0ms	10008×	pre	80	true
66.0ms	349×	body	320	valid
24.0ms	456×	body	80	valid
14.0ms	117×	body	160	valid