Details

sample36.0ms

Algorithm

intervals

Results

10.0ms	64×	body	1280	valid
8.0ms	77×	body	10240	exit
5.0ms	50×	body	640	valid
2.0ms	105×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	13×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 37.9b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
3.9b	(- (exp x) 1.0)

rewrite13.0ms

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)

series45.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ (exp x) (- (exp x) 1.0))
15.0ms	(- (exp x) 1.0)

simplify187.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (181.0ms)

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

prune130.0ms

Filtered

73 candidates to 50 candidates (68.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	4	74

Merged error: 0.0b

Counts

74 → 4

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
0.1b	(fma 1/6 (pow x 3) x)
11.6b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-cbrt-cube`
4×	`add-exp-log`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 49

Calls

3 calls:

4.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
1.0ms	(fma 1/6 (pow x 3) x)
1.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series140.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
73.0ms	(fma 1/6 (pow x 3) x)
27.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify93.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	178	458
1	614	416
2	3125	414
3	5002	414

prune150.0ms

Filtered

58 candidates to 45 candidates (77.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	57	5	62

Merged error: 0.0b

Counts

62 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

11.6b	(fma 1/2 (pow x 2) (* (* (cbrt (fma 1/6 (pow x 3) x)) (cbrt (fma 1/6 (pow x 3) x))) (cbrt (fma 1/6 (pow x 3) x))))
14.6b	(cbrt (fma 1/6 (pow x 3) x))
14.6b	(cbrt (fma 1/6 (pow x 3) x))
14.6b	(cbrt (fma 1/6 (pow x 3) x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(fma 1/2 (pow x 2) (* (* (cbrt (fma 1/6 (pow x 3) x)) (cbrt (fma 1/6 (pow x 3) x))) (cbrt (fma 1/6 (pow x 3) x))))
1.0ms	(cbrt (fma 1/6 (pow x 3) x))
1.0ms	(cbrt (fma 1/6 (pow x 3) x))
1.0ms	(cbrt (fma 1/6 (pow x 3) x))

series366.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(fma 1/2 (pow x 2) (* (* (cbrt (fma 1/6 (pow x 3) x)) (cbrt (fma 1/6 (pow x 3) x))) (cbrt (fma 1/6 (pow x 3) x))))
110.0ms	(cbrt (fma 1/6 (pow x 3) x))
110.0ms	(cbrt (fma 1/6 (pow x 3) x))
115.0ms	(cbrt (fma 1/6 (pow x 3) x))

simplify68.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	173	599
1	495	548
2	2018	508
3	5001	470

prune225.0ms

Filtered

61 candidates to 55 candidates (90.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	61	5	66

Merged error: 0.0b

Counts

66 → 5

localize5.0ms

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))

rewrite4.0ms

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))

series61.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
46.0ms	(fma 1/12 x (/ 1 x))

simplify39.0ms

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

prune52.0ms

Filtered

34 candidates to 26 candidates (76.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	34	5	39

Merged error: 0.0b

Counts

39 → 5

regimes59.0ms

Accuracy

95% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 11.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	17
1	20	17

end0.0ms

sample1.1s

Algorithm

intervals

Results

388.0ms	2316×	body	1280	valid
284.0ms	2599×	body	10240	exit
185.0ms	1662×	body	640	valid
59.0ms	817×	body	320	valid
53.0ms	2809×	body	80	valid
18.0ms	397×	body	160	valid