Details

sample243.0ms

Algorithm

intervals

Results

88.0ms	84×	body	2560	valid
65.0ms	70×	body	10240	exit
59.0ms	125×	body	1280	valid
6.0ms	326×	pre	80	true
5.0ms	18×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	6×	body	160	valid
1.0ms	10×	body	80	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 (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: 61.5b

Counts

2 → 1

localize21.0ms

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)
4.6b	(- (exp (* b eps)) 1.0)
4.8b	(- (exp (* (+ a b) eps)) 1.0)

rewrite31.0ms

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:

11.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
5.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series165.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
33.0ms	(- (exp (* a eps)) 1.0)
31.0ms	(- (exp (* b eps)) 1.0)
51.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	488	1660
1	2051	1241
2	5003	1216

prune464.0ms

Filtered

150 candidates to 91 candidates (60.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	147	4	151

Merged error: 49.3b

Counts

151 → 4

localize31.0ms

Local error

Found 4 expressions with local error:

4.6b	(- (exp (* b eps)) 1.0)
4.8b	(- (exp (* (+ a b) eps)) 1.0)
13.4b	(* (pow a 2) (pow eps 2))
15.0b	(* (pow a 3) (pow eps 3))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `unswap-sqr`
28×	`add-exp-log` `add-cube-cbrt` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`prod-diff` `prod-exp`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`add-cbrt-cube` `add-log-exp`
6×	`fma-neg`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-prod-down` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 170

Calls

4 calls:

5.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow a 2) (pow eps 2))
10.0ms	(* (pow a 3) (pow eps 3))

series181.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (exp (* b eps)) 1.0)
50.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow a 2) (pow eps 2))
68.0ms	(* (pow a 3) (pow eps 3))

simplify94.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	564	1114
1	2481	873
2	5002	825

prune734.0ms

Filtered

182 candidates to 98 candidates (53.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	179	3	182
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	179	7	186

Merged error: 49.1b

Counts

186 → 7

localize35.0ms

Local error

Found 4 expressions with local error:

4.6b	(- (exp (* eps b)) 1.0)
4.8b	(- (exp (* (+ a b) eps)) 1.0)
13.4b	(* (pow a 2) (pow eps 2))
15.0b	(* (pow a 3) (pow eps 3))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `unswap-sqr`
28×	`add-exp-log` `add-cube-cbrt` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`prod-diff` `prod-exp`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`add-cbrt-cube` `add-log-exp`
6×	`fma-neg`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-prod-down` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 170

Calls

4 calls:

5.0ms	(- (exp (* eps b)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
8.0ms	(* (pow a 2) (pow eps 2))
10.0ms	(* (pow a 3) (pow eps 3))

series180.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (exp (* eps b)) 1.0)
49.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow a 2) (pow eps 2))
66.0ms	(* (pow a 3) (pow eps 3))

simplify89.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	559	1168
1	2620	884
2	5002	872

prune773.0ms

Filtered

182 candidates to 96 candidates (52.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	182	7	189

Merged error: 49.1b

Counts

189 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

2.9b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))
4.8b	(- (exp (* (+ a b) eps)) 1.0)
14.1b	(* (pow eps 2) (pow b 2))
15.6b	(* (pow eps 3) (pow b 3))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
40×	`add-exp-log`
32×	`unswap-sqr`
28×	`unpow-prod-down`
23×	`*-un-lft-identity`
22×	`prod-exp`
21×	`add-cube-cbrt`
20×	`associate-r` `associate-l` `add-cbrt-cube` `sqr-pow`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
9×	`prod-diff`
6×	`cbrt-unprod` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--`
2×	`cube-mult` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `associate-/r/` `*-commutative` `associate-/l/`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 169

Calls

4 calls:

17.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 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))
10.0ms	(* (pow eps 3) (pow b 3))

series1.4s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))
44.0ms	(- (exp (* (+ a b) eps)) 1.0)
37.0ms	(* (pow eps 2) (pow b 2))
61.0ms	(* (pow eps 3) (pow b 3))

simplify142.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (123.0ms)

Iter	Nodes	Cost
0	785	1816
1	4673	1415
2	5001	1412

prune715.0ms

Filtered

181 candidates to 103 candidates (56.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	2	2	4
Picked	1	0	1
Done	2	0	2
Total	184	4	188

Merged error: 0.0b

Counts

188 → 4

regimes88.0ms

Accuracy

0% (3.4b remaining)

Error of 3.5b against oracle of 0.1b and baseline of 3.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.5s	2572×	body	2560	valid
1.7s	1979×	body	10240	exit
1.7s	3484×	body	1280	valid
280.0ms	1019×	body	640	valid
166.0ms	9981×	pre	80	true
62.0ms	332×	body	320	valid
27.0ms	466×	body	80	valid
15.0ms	129×	body	160	valid