Details

sample188.0ms

Algorithm

intervals

Results

81.0ms	77×	body	2560	valid
62.0ms	110×	body	1280	valid
13.0ms	41×	body	640	valid
7.0ms	314×	pre	80	true
4.0ms	58×	body	80	overflowed
2.0ms	9×	body	320	valid
1.0ms	14×	body	80	valid
1.0ms	5×	body	160	valid

simplify98.0ms

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: 60.3b

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))
3.7b	(- (exp (* a eps)) 1.0)
3.8b	(- (exp (* b eps)) 1.0)
6.2b	(- (exp (* (+ a b) eps)) 1.0)

rewrite30.0ms

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)

series164.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
33.0ms	(- (exp (* a eps)) 1.0)
35.0ms	(- (exp (* b eps)) 1.0)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (51.0ms)

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

prune417.0ms

Filtered

150 candidates to 91 candidates (60.7%)

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: 49.1b

Counts

151 → 5

localize230.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (exp (* b eps)) 1.0)
6.2b	(- (exp (* (+ a b) eps)) 1.0)
14.4b	(* (pow a 2) (pow eps 2))
16.5b	(* (pow a 3) (pow eps 3))

rewrite32.0ms

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))
9.0ms	(* (pow a 3) (pow eps 3))

series177.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (exp (* b eps)) 1.0)
48.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow a 2) (pow eps 2))
67.0ms	(* (pow a 3) (pow eps 3))

simplify96.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (81.0ms)

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

prune642.0ms

Filtered

182 candidates to 98 candidates (53.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	177	5	182
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	178	9	187

Merged error: 48.4b

Counts

187 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
3.8b	(- (exp (* b eps)) 1.0)
6.2b	(- (exp (* (+ a b) eps)) 1.0)
14.4b	(* (pow a 2) (pow eps 2))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
28×	`add-exp-log`
26×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`prod-diff` `add-cbrt-cube`
16×	`unswap-sqr`
14×	`unpow-prod-down`
13×	`prod-exp`
10×	`unpow2` `sqr-pow`
8×	`associate-r` `associate-l` `add-log-exp`
6×	`pow-to-exp` `fma-neg` `pow-exp`
5×	`cbrt-unprod`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `associate-*r/` `div-exp` `flip--` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 136

Calls

4 calls:

16.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
5.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
8.0ms	(* (pow a 2) (pow eps 2))

series836.0ms

Counts

4 → 12

Calls

4 calls:

725.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
35.0ms	(- (exp (* b eps)) 1.0)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow a 2) (pow eps 2))

simplify96.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	732	1701
1	3704	1263
2	5001	1252

prune532.0ms

Filtered

148 candidates to 89 candidates (60.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	152	5	157

Merged error: 0.1b

Counts

157 → 5

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`times-frac`
13×	`fma-def`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`distribute-lft-out`
5×	`div-inv`
3×	`add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u`

Counts

1 → 34

Calls

1 calls:

13.0ms

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

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify69.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	107	112
1	368	101
2	1274	98
3	3144	98
4	5001	98

prune57.0ms

Filtered

37 candidates to 28 candidates (75.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	35	7	42

Merged error: 0.1b

Counts

42 → 7

regimes115.0ms

Accuracy

0% (3.4b remaining)

Error of 3.4b against oracle of 0.1b and baseline of 3.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.7s	2543×	body	2560	valid
1.9s	3450×	body	1280	valid
352.0ms	1061×	body	640	valid
210.0ms	9975×	pre	80	true
129.0ms	1973×	body	80	overflowed
77.0ms	350×	body	320	valid
31.0ms	461×	body	80	valid
19.0ms	137×	body	160	valid