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	73×	body	1280	valid
6.0ms	49×	body	640	valid
2.0ms	98×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	15×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (12.0ms)

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: 38.0b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 (exp.f64 x) 1.0) x)
4.0b	(-.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)
4.0ms	(-.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)

simplify48.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4909	534
1	4909	534

prune65.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	54	3	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	3	58

Merged error: 0.1b

Counts

58 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.3b	(*.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:

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

series11.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
3.0ms	(*.f64 x 1/6)

simplify51.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5037	298

prune40.0ms

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: 0.1b

Counts

49 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (exp.f64 x) x)
3.6b	(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1.0 x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
3×	`associate-/r_binary64` `add-exp-log_binary64` `associate-/l_binary64` `div-inv_binary64`
2×	`pow1_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-rgt-out--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

2 → 49

Calls

2 calls:

4.0ms	(/.f64 (exp.f64 x) x)
15.0ms	(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1.0 x))

series11.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(/.f64 (exp.f64 x) x)
6.0ms	(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1.0 x))

simplify46.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4909	495
1	4909	495

prune51.0ms

Filtered

45 candidates to 55 candidates (-22.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	55	3	58

Merged error: 0.0b

Counts

58 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 1.0 3)) (.f64 x (+.f64 (pow.f64 (exp.f64 x) 2) (.f64 1.0 (+.f64 (exp.f64 x) 1.0)))))
0.0b	(pow.f64 (exp.f64 x) 3)
0.0b	(.f64 x (+.f64 (pow.f64 (exp.f64 x) 2) (.f64 1.0 (+.f64 (exp.f64 x) 1.0))))
3.9b	(-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 1.0 3))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
48×	`difference-of-squares_binary64`
42×	`*-un-lft-identity_binary64`
39×	`unpow-prod-down_binary64` `cube-prod_binary64`
25×	`sqr-pow_binary64` `associate-/l*_binary64` `times-frac_binary64`
15×	`distribute-lft-out--_binary64`
12×	`add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64`
4×	`associate-*r/_binary64` `pow-pow_binary64`
3×	`difference-cubes_binary64` `pow-unpow_binary64` `associate-r_binary64` `associate-l_binary64` `exp-prod_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow-exp_binary64` `unpow3_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 151

Calls

4 calls:

21.0ms	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 1.0 3)) (.f64 x (+.f64 (pow.f64 (exp.f64 x) 2) (.f64 1.0 (+.f64 (exp.f64 x) 1.0)))))
4.0ms	(pow.f64 (exp.f64 x) 3)
8.0ms	(.f64 x (+.f64 (pow.f64 (exp.f64 x) 2) (.f64 1.0 (+.f64 (exp.f64 x) 1.0))))
12.0ms	(-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 1.0 3))

series65.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 1.0 3)) (.f64 x (+.f64 (pow.f64 (exp.f64 x) 2) (.f64 1.0 (+.f64 (exp.f64 x) 1.0)))))
6.0ms	(pow.f64 (exp.f64 x) 3)
14.0ms	(.f64 x (+.f64 (pow.f64 (exp.f64 x) 2) (.f64 1.0 (+.f64 (exp.f64 x) 1.0))))
8.0ms	(-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 1.0 3))

simplify63.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4977	2854
1	4977	2854

prune150.0ms

Filtered

95 candidates to 163 candidates (-71.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	162	4	166

Merged error: 0.0b

Counts

166 → 4

regimes38.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.6b

bsearch9.0ms

Steps

Iters	Range		Point
7	-0.00017326833653887792	-5.890329637648454e-06	-0.00016629416446113426

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	35
1	42	35

end0.0ms

sample916.0ms

Algorithm

intervals

Results

443.0ms	2280×	body	1280	valid
204.0ms	1647×	body	640	valid
68.0ms	2849×	body	80	valid
67.0ms	790×	body	320	valid
25.0ms	434×	body	160	valid

Details

analyze4.0ms

sample30.0ms

simplify15.0ms

prune2.0ms

localize6.0ms

rewrite13.0ms

series8.0ms

simplify48.0ms

prune65.0ms

localize6.0ms

rewrite10.0ms

series11.0ms

simplify51.0ms

prune40.0ms

localize5.0ms

rewrite21.0ms

series11.0ms

simplify46.0ms

prune51.0ms

localize12.0ms

rewrite53.0ms

series65.0ms

simplify63.0ms

prune150.0ms

regimes38.0ms

bsearch9.0ms

simplify2.0ms

end0.0ms

sample916.0ms

Profiling