Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
62.5%	25%	12.5%	4
68.7%	12.5%	18.8%	5
71.8%	6.2%	21.9%	6
73.4%	3.1%	23.5%	7
74.2%	1.6%	24.3%	8
74.6%	0.8%	24.6%	9
75%	0.4%	24.6%	10
75.1%	0.2%	24.7%	11
75.1%	0.1%	24.8%	12
75.1%	0%	24.8%	13
75.2%	0%	24.8%	14

sample29.0ms

Algorithm

intervals

Results

13.0ms	67×	body	1280	valid
5.0ms	40×	body	640	valid
3.0ms	109×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	19×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	228	6
1	228	6

prune2.0ms

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: 35.5b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 (exp.f64 x) 1.0) x)
5.8b	(-.f64 (exp.f64 x) 1.0)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`difference-of-squares_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `pow1_binary64` `flip3--_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 51

Calls

2 calls:

7.0ms	(/.f64 (-.f64 (exp.f64 x) 1.0) x)
5.0ms	(-.f64 (exp.f64 x) 1.0)

series8.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/.f64 (-.f64 (exp.f64 x) 1.0) x)
3.0ms	(-.f64 (exp.f64 x) 1.0)

simplify52.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4909	534
1	4909	534

prune75.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	52	5	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	5	58

Merged error: 0.2b

Counts

58 → 5

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
0.0b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.4b	(*.f64 x 1/6)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
5×	`add-log-exp_binary64`
2×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `associate-+r+_binary64` `-commutative_binary64`
1×	`+-commutative_binary64` `sum-log_binary64`

Counts

3 → 53

Calls

3 calls:

4.0ms	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
6.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
4.0ms	(*.f64 x 1/6)

series17.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
11.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
3.0ms	(*.f64 x 1/6)

simplify56.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4963	483
1	4963	483

prune63.0ms

Filtered

44 candidates to 62 candidates (-40.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	61	6	67

Merged error: 0.2b

Counts

67 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(*.f64 x 1/6)
14.7b	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
14.7b	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
14.7b	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `cbrt-prod_binary64`
6×	`cbrt-div_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `associate-r_binary64` `pow1/3_binary64` `associate-l_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 57

Calls

4 calls:

4.0ms	(*.f64 x 1/6)
3.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
3.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
3.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))

series26.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(*.f64 x 1/6)
8.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
8.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
8.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))

simplify29.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4958	931
1	4958	931

prune125.0ms

Filtered

58 candidates to 69 candidates (-19.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	69	6	75

Merged error: 0.2b

Counts

75 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(*.f64 x 1/6)
0.4b	(*.f64 x 1/36)
14.7b	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
14.7b	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `associate-l_binary64` `cbrt-prod_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64`
2×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 62

Calls

4 calls:

4.0ms	(*.f64 x 1/6)
4.0ms	(*.f64 x 1/36)
3.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
3.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))

series21.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(*.f64 x 1/6)
2.0ms	(*.f64 x 1/36)
8.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
8.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))

simplify46.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5084	723

prune98.0ms

Filtered

54 candidates to 74 candidates (-37.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	74	6	80

Merged error: 0.1b

Counts

80 → 6

regimes39.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.4b

bsearch6.0ms

Steps

Iters	Range		Point
5	-0.0003268625709671245	-8.946218564378357e-05	-0.00013902426818612792

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	23
1	33	23

end0.0ms

sample913.0ms

Algorithm

intervals

Results

431.0ms	2247×	body	1280	valid
213.0ms	1688×	body	640	valid
71.0ms	2815×	body	80	valid
68.0ms	808×	body	320	valid
23.0ms	442×	body	160	valid

Details

analyze4.0ms

sample29.0ms

simplify15.0ms

prune2.0ms

localize4.0ms

rewrite13.0ms

series8.0ms

simplify52.0ms

prune75.0ms

localize6.0ms

rewrite14.0ms

series17.0ms

simplify56.0ms

prune63.0ms

localize13.0ms

rewrite13.0ms

series26.0ms

simplify29.0ms

prune125.0ms

localize15.0ms

rewrite15.0ms

series21.0ms

simplify46.0ms

prune98.0ms

regimes39.0ms

bsearch6.0ms

simplify2.0ms

end0.0ms

sample913.0ms

Profiling