Details

sample200.0ms

Algorithm

intervals

Results

89.0ms	78×	body	2560	valid
65.0ms	113×	body	1280	valid
13.0ms	33×	body	640	valid
7.0ms	324×	pre	80	true
5.0ms	68×	body	80	overflowed
2.0ms	8×	body	320	valid
1.0ms	19×	body	80	valid
1.0ms	5×	body	160	valid

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	258	13
3	766	13
4	3895	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: 59.1b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.4b	(- (exp (* b eps)) 1.0)
4.9b	(- (exp (* a eps)) 1.0)
7.7b	(- (exp (* (+ a b) eps)) 1.0)

rewrite33.0ms

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 (* b eps)) 1.0)
8.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series171.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
32.0ms	(- (exp (* b eps)) 1.0)
41.0ms	(- (exp (* a eps)) 1.0)
46.0ms	(- (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

prune397.0ms

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: 48.0b

Counts

151 → 5

localize30.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (exp (* b eps)) 1.0)
7.7b	(- (exp (* (+ a b) eps)) 1.0)
14.5b	(* (pow a 2) (pow eps 2))
14.6b	(* (pow a 3) (pow eps 3))

rewrite31.0ms

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))

series178.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (exp (* b eps)) 1.0)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
37.0ms	(* (pow a 2) (pow eps 2))
65.0ms	(* (pow a 3) (pow eps 3))

simplify99.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (79.0ms)

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

prune639.0ms

Filtered

182 candidates to 98 candidates (53.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	177	5	182
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	179	8	187

Merged error: 47.0b

Counts

187 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (* 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)))
4.4b	(- (exp (* b eps)) 1.0)
7.7b	(- (exp (* (+ a b) eps)) 1.0)
14.5b	(* (pow a 2) (pow eps 2))

rewrite34.0ms

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:

13.0ms	(/ (* 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)
7.0ms	(* (pow a 2) (pow eps 2))

series869.0ms

Counts

4 → 12

Calls

4 calls:

756.0ms	(/ (* 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)))
31.0ms	(- (exp (* b eps)) 1.0)
51.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow a 2) (pow eps 2))

simplify102.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	732	1665
1	3649	1263
2	5002	1252

prune680.0ms

Filtered

148 candidates to 89 candidates (60.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	153	3	156

Merged error: 0.0b

Counts

156 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite13.0ms

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:

12.0ms

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

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify71.0ms

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

prune56.0ms

Filtered

37 candidates to 28 candidates (75.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	36	1	37
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	36	4	40

Merged error: 0.0b

Counts

40 → 4

regimes71.0ms

Accuracy

0% (3.2b remaining)

Error of 3.3b against oracle of 0.1b and baseline of 3.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.8s	2571×	body	2560	valid
2.1s	3457×	body	1280	valid
382.0ms	1056×	body	640	valid
219.0ms	9992×	pre	80	true
147.0ms	1989×	body	80	overflowed
88.0ms	345×	body	320	valid
37.0ms	443×	body	80	valid
21.0ms	131×	body	160	valid

Details

sample200.0ms

simplify105.0ms

prune3.0ms

localize17.0ms

rewrite33.0ms

series171.0ms

simplify66.0ms

prune397.0ms

localize30.0ms

rewrite31.0ms

series178.0ms

simplify99.0ms

prune639.0ms

localize33.0ms

rewrite34.0ms

series869.0ms

simplify102.0ms

prune680.0ms

localize5.0ms

rewrite13.0ms

series10.0ms

simplify71.0ms

prune56.0ms

regimes71.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.1s

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