Details

sample36.0ms

Algorithm

intervals

Results

12.0ms	71×	body	1280	valid
8.0ms	76×	body	10240	exit
4.0ms	43×	body	640	valid
2.0ms	100×	body	80	valid
2.0ms	28×	body	320	valid
1.0ms	14×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	4
1	8	4
2	8	4

prune2.0ms

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: 39.2b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (exp x) (- (exp x) 1.0))
3.9b	(- (exp x) 1.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `fma-neg` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 67

Calls

2 calls:

7.0ms	(/ (exp x) (- (exp x) 1.0))
5.0ms	(- (exp x) 1.0)

series44.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ (exp x) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)

simplify188.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (182.0ms)

Iter	Nodes	Cost
0	237	520
1	786	429
2	4651	416
3	5001	404

prune125.0ms

Filtered

73 candidates to 50 candidates (68.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	3	74

Merged error: 0.0b

Counts

74 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (fma 1/12 x (/ 1 x)) 1/2)
0.1b	(fma 1/12 x (/ 1 x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

2 → 28

Calls

2 calls:

3.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
1.0ms	(fma 1/12 x (/ 1 x))

series63.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
45.0ms	(fma 1/12 x (/ 1 x))

simplify40.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	90	126
1	306	119
2	1283	117
3	5001	116

prune54.0ms

Filtered

34 candidates to 26 candidates (76.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	34	3	37

Merged error: 0.0b

Counts

37 → 3

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (exp x))
0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
3.9b	(- 1 (/ 1.0 (exp x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
70×	`times-frac`
59×	`add-cube-cbrt`
39×	`prod-diff`
20×	`difference-of-squares`
11×	`associate-/r*`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`div-inv` `distribute-lft-out--` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `fma-neg` `div-exp` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--`
1×	`sub-neg` `rec-exp` `pow-flip` `diff-log` `1-exp` `inv-pow`

Counts

3 → 145

Calls

3 calls:

4.0ms	(/ 1.0 (exp x))
9.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
9.0ms	(- 1 (/ 1.0 (exp x)))

series99.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ 1.0 (exp x))
51.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
35.0ms	(- 1 (/ 1.0 (exp x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	552	1839
1	2298	1281
2	5001	1188

prune149.0ms

Filtered

154 candidates to 73 candidates (47.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	154	3	157

Merged error: 0.0b

Counts

157 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (- 1 (/ 1.0 (exp x)))) (cbrt (- 1 (/ 1.0 (exp x)))))
3.9b	(- 1 (/ 1.0 (exp x)))
3.9b	(- 1 (/ 1.0 (exp x)))
3.9b	(- 1 (/ 1.0 (exp x)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

181×	`add-sqr-sqrt`
151×	`*-un-lft-identity`
117×	`add-cube-cbrt` `prod-diff`
95×	`times-frac`
40×	`cbrt-prod`
28×	`difference-of-squares`
13×	`swap-sqr`
12×	`cbrt-div`
11×	`pow1` `associate-r` `associate-l`
10×	`add-log-exp`
9×	`flip3--` `fma-neg` `flip--` `div-inv` `distribute-lft-out--`
6×	`add-exp-log` `pow1/3`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 250

Calls

4 calls:

20.0ms	(* (cbrt (- 1 (/ 1.0 (exp x)))) (cbrt (- 1 (/ 1.0 (exp x)))))
9.0ms	(- 1 (/ 1.0 (exp x)))
9.0ms	(- 1 (/ 1.0 (exp x)))
9.0ms	(- 1 (/ 1.0 (exp x)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (cbrt (- 1 (/ 1.0 (exp x)))) (cbrt (- 1 (/ 1.0 (exp x)))))
37.0ms	(- 1 (/ 1.0 (exp x)))
35.0ms	(- 1 (/ 1.0 (exp x)))
40.0ms	(- 1 (/ 1.0 (exp x)))

simplify86.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	568	4603
1	2153	3113
2	5001	2775

prune315.0ms

Filtered

262 candidates to 106 candidates (40.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	261	1	262
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	261	4	265

Merged error: 0.0b

Counts

265 → 4

regimes56.0ms

Accuracy

96.7% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 21.3b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	10
1	19	10

end0.0ms

sample1.1s

Algorithm

intervals

Results

375.0ms	2207×	body	1280	valid
279.0ms	2487×	body	10240	exit
173.0ms	1652×	body	640	valid
62.0ms	871×	body	320	valid
55.0ms	2856×	body	80	valid
18.0ms	416×	body	160	valid