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

sample30.0ms

Algorithm

intervals

Results

14.0ms	77×	body	1280	valid
7.0ms	58×	body	640	valid
2.0ms	94×	body	80	valid
1.0ms	17×	body	320	valid
1.0ms	10×	body	160	valid

simplify24.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	169	9
1	169	9

prune1.0ms

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: 38.9b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 (exp.f64 x) 1) x)
2.7b	(-.f64 (exp.f64 x) 1)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
7×	`associate-/l*_binary64`
5×	`difference-of-sqr-1_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 → 61

Calls

2 calls:

7.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
4.0ms	(-.f64 (exp.f64 x) 1)

series35.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
9.0ms	(-.f64 (exp.f64 x) 1)

simplify68.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4938	1013
1	4938	1013

prune47.0ms

Filtered

43 candidates to 67 candidates (-55.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	3	68

Merged error: 0.0b

Counts

68 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

5.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
4.0ms	(*.f64 x 1/6)

series49.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
11.0ms	(*.f64 x 1/6)

simplify99.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4907	440
1	4907	440

prune28.0ms

Filtered

32 candidates to 46 candidates (-43.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	46	3	49

Merged error: 0.0b

Counts

49 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)) x)
0.0b	(pow.f64 (exp.f64 x) 2)
0.0b	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
2.7b	(+.f64 (pow.f64 (exp.f64 x) 2) -1)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

274×	`times-frac_binary64`
238×	`*-un-lft-identity_binary64`
156×	`add-sqr-sqrt_binary64`
112×	`add-cube-cbrt_binary64`
88×	`difference-of-sqr--1_binary64`
63×	`distribute-lft-out_binary64`
46×	`associate-/l*_binary64`
25×	`unpow-prod-down_binary64`
23×	`unpow2_binary64` `sqr-pow_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r/_binary64`
7×	`flip3-+_binary64` `associate-/r*_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64` `pow-pow_binary64` `div-exp_binary64`
3×	`associate-/l/_binary64` `pow-unpow_binary64` `exp-prod_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-to-exp_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 267

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)) x)
3.0ms	(pow.f64 (exp.f64 x) 2)
14.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
6.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)

series159.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)) x)
18.0ms	(pow.f64 (exp.f64 x) 2)
47.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
19.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)

simplify132.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5758	7296

prune202.0ms

Filtered

166 candidates to 279 candidates (-68.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	277	2	279
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	278	4	282

Merged error: 0.0b

Counts

282 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) 2) 3) (pow.f64 -1 3)) (*.f64 (+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 (pow.f64 (exp.f64 x) 2) 1)) (+.f64 (exp.f64 x) 1)))
0.0b	(pow.f64 (exp.f64 x) 4)
0.0b	(pow.f64 (pow.f64 (exp.f64 x) 2) 3)
2.6b	(+.f64 (pow.f64 (pow.f64 (exp.f64 x) 2) 3) (pow.f64 -1 3))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64`
29×	`unpow-prod-down_binary64`
20×	`cube-prod_binary64`
15×	`distribute-lft-out_binary64`
14×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-/l*_binary64` `times-frac_binary64`
8×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64`
5×	`pow1_binary64` `pow-pow_binary64` `pow-exp_binary64`
4×	`sqr-pow_binary64` `frac-times_binary64`
3×	`pow-to-exp_binary64` `sum-cubes_binary64` `exp-prod_binary64`
2×	`associate-/l/_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `div-exp_binary64` `associate-l/_binary64`
1×	`associate-/r*_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `unpow3_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

4 → 115

Calls

4 calls:

32.0ms	(/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) 2) 3) (pow.f64 -1 3)) (*.f64 (+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 (pow.f64 (exp.f64 x) 2) 1)) (+.f64 (exp.f64 x) 1)))
5.0ms	(pow.f64 (exp.f64 x) 4)
4.0ms	(pow.f64 (pow.f64 (exp.f64 x) 2) 3)
17.0ms	(+.f64 (pow.f64 (pow.f64 (exp.f64 x) 2) 3) (pow.f64 -1 3))

series308.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) 2) 3) (pow.f64 -1 3)) (*.f64 (+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 (pow.f64 (exp.f64 x) 2) 1)) (+.f64 (exp.f64 x) 1)))
26.0ms	(pow.f64 (exp.f64 x) 4)
39.0ms	(pow.f64 (pow.f64 (exp.f64 x) 2) 3)
41.0ms	(+.f64 (pow.f64 (pow.f64 (exp.f64 x) 2) 3) (pow.f64 -1 3))

simplify90.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5028	2524

prune128.0ms

Filtered

76 candidates to 127 candidates (-67.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	127	4	131

Merged error: 0.0b

Counts

131 → 4

regimes20.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.4b

bsearch19.0ms

Steps

Iters	Range		Point
9	-0.0005850184536782462	-3.6316210910225665e-09	-0.00014159864022581637

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	73
1	44	73

end0.0ms

sample908.0ms

Algorithm

intervals

Results

429.0ms	2294×	body	1280	valid
199.0ms	1648×	body	640	valid
73.0ms	2828×	body	80	valid
66.0ms	813×	body	320	valid
22.0ms	417×	body	160	valid

Details

analyze4.0ms

sample30.0ms

simplify24.0ms

prune1.0ms

localize4.0ms

rewrite13.0ms

series35.0ms

simplify68.0ms

prune47.0ms

localize6.0ms

rewrite10.0ms

series49.0ms

simplify99.0ms

prune28.0ms

localize8.0ms

rewrite54.0ms

series159.0ms

simplify132.0ms

prune202.0ms

localize15.0ms

rewrite62.0ms

series308.0ms

simplify90.0ms

prune128.0ms

regimes20.0ms

bsearch19.0ms

simplify3.0ms

end0.0ms

sample908.0ms

Profiling