Details

analyze497.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

sample58.0ms

Algorithm

intervals

Results

24.0ms	63×	body	1280	valid
14.0ms	60×	body	640	valid
5.0ms	93×	body	80	valid
3.0ms	21×	body	320	valid
2.0ms	19×	body	160	valid
0.0ms	1×	body	80	invalid

simplify501.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5131	12

prune4.0ms

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: 40.4b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2.0 x)) 1.0) (-.f64 (exp.f64 x) 1.0)))
0.0b	(/.f64 (-.f64 (exp.f64 (*.f64 2.0 x)) 1.0) (-.f64 (exp.f64 x) 1.0))
5.3b	(-.f64 (exp.f64 (*.f64 2.0 x)) 1.0)
5.4b	(-.f64 (exp.f64 x) 1.0)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64`
75×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`sqrt-prod_binary64`
27×	`add-cube-cbrt_binary64`
24×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r_binary64` `pow1_binary64` `flip3--_binary64` `associate-/l_binary64` `flip--_binary64`
4×	`associate-/r/_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sqrt-div_binary64`

Counts

4 → 121

Calls

4 calls:

10.0ms	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2.0 x)) 1.0) (-.f64 (exp.f64 x) 1.0)))
10.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2.0 x)) 1.0) (-.f64 (exp.f64 x) 1.0))
4.0ms	(-.f64 (exp.f64 (*.f64 2.0 x)) 1.0)
7.0ms	(-.f64 (exp.f64 x) 1.0)

series58.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2.0 x)) 1.0) (-.f64 (exp.f64 x) 1.0)))
10.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2.0 x)) 1.0) (-.f64 (exp.f64 x) 1.0))
3.0ms	(-.f64 (exp.f64 (*.f64 2.0 x)) 1.0)
28.0ms	(-.f64 (exp.f64 x) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5066	2150

prune157.0ms

Filtered

96 candidates to 133 candidates (-38.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	2	134

Merged error: 0.0b

Counts

134 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(.f64 x (+.f64 (.f64 x 0.5) 1.0))
9.9b	(sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-r_binary64` `associate-l_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `add-log-exp_binary64` `associate-*r/_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

2 → 37

Calls

2 calls:

7.0ms	(.f64 x (+.f64 (.f64 x 0.5) 1.0))
3.0ms	(sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0))))

series22.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(.f64 x (+.f64 (.f64 x 0.5) 1.0))
9.0ms	(sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0))))

simplify47.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5592	490

prune43.0ms

Filtered

31 candidates to 43 candidates (-38.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	42	3	45

Merged error: 0b

Counts

45 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0)))))
0.8b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0))))) (sqrt.f64 (sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (*.f64 x 0.5) 1.0))))))
9.9b	(sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0))))
9.9b	(sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod_binary64`
54×	`add-sqr-sqrt_binary64`
38×	`sqrt-pow1_binary64`
32×	`sqrt-div_binary64`
31×	`pow1_binary64`
20×	`*-un-lft-identity_binary64` `pow1/2_binary64` `add-cube-cbrt_binary64`
15×	`swap-sqr_binary64`
9×	`flip3-+_binary64` `associate-r_binary64` `pow-prod-up_binary64` `associate-l_binary64` `unswap-sqr_binary64` `flip-+_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`add-log-exp_binary64` `rem-sqrt-square_binary64` `frac-times_binary64`
2×	`associate-r/_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 134

Calls

4 calls:

4.0ms	(sqrt.f64 (sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0)))))
14.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0))))) (sqrt.f64 (sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (*.f64 x 0.5) 1.0))))))
3.0ms	(sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0))))
3.0ms	(sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0))))

series34.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt.f64 (sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0)))))
7.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0))))) (sqrt.f64 (sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (*.f64 x 0.5) 1.0))))))
7.0ms	(sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0))))
7.0ms	(sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0))))

simplify54.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4924	2304
1	4924	2304

prune136.0ms

Filtered

80 candidates to 146 candidates (-82.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	146	3	149

Merged error: 0b

Counts

149 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) 2)
0.0b	(pow.f64 (exp.f64 x) 2.0)
5.3b	(-.f64 (pow.f64 (exp.f64 x) 2) (*.f64 1.0 1.0))
5.3b	(-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64` `pow-pow_binary64` `unpow-prod-down_binary64`
7×	`difference-of-squares_binary64`
6×	`pow-unpow_binary64` `pow1_binary64` `exp-prod_binary64`
4×	`sqr-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `unpow2_binary64` `flip--_binary64` `pow-exp_binary64`
1×	`distribute-lft-out--_binary64`

Counts

4 → 71

Calls

4 calls:

4.0ms	(pow.f64 (exp.f64 x) 2)
4.0ms	(pow.f64 (exp.f64 x) 2.0)
6.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (*.f64 1.0 1.0))
6.0ms	(-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0)

series30.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (exp.f64 x) 2)
16.0ms	(pow.f64 (exp.f64 x) 2.0)
5.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (*.f64 1.0 1.0))
5.0ms	(-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0)

simplify33.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4908	612
1	4908	612

prune85.0ms

Filtered

60 candidates to 83 candidates (-38.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	83	3	86

Merged error: 0b

Counts

86 → 3

regimes35.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.6b

bsearch20.0ms

Steps

Iters	Range		Point
10	-0.0130322730991205	-2.77060252745321e-13	-1.4142710662085361e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	35
1	49	35

end0.0ms

sample1.7s

Algorithm

intervals

Results

857.0ms	2329×	body	1280	valid
379.0ms	1642×	body	640	valid
131.0ms	839×	body	320	valid
123.0ms	2770×	body	80	valid
44.0ms	420×	body	160	valid
0.0ms	3×	body	80	invalid

Details

analyze497.0ms

sample58.0ms

simplify501.0ms

prune4.0ms

localize10.0ms

rewrite37.0ms

series58.0ms

simplify42.0ms

prune157.0ms

localize6.0ms

rewrite11.0ms

series22.0ms

simplify47.0ms

prune43.0ms

localize9.0ms

rewrite29.0ms

series34.0ms

simplify54.0ms

prune136.0ms

localize14.0ms

rewrite21.0ms

series30.0ms

simplify33.0ms

prune85.0ms

regimes35.0ms

bsearch20.0ms

simplify2.0ms

end0.0ms

sample1.7s

Profiling