Details

analyze496.0ms

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

sample60.0ms

Algorithm

intervals

Results

26.0ms	63×	body	1280	valid
13.0ms	55×	body	640	valid
6.0ms	36×	body	320	valid
5.0ms	91×	body	80	valid
1.0ms	11×	body	160	valid
0.0ms	1×	body	80	invalid

simplify478.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

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: 40.8b

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))
3.6b	(-.f64 (exp.f64 (*.f64 2.0 x)) 1.0)
3.6b	(-.f64 (exp.f64 x) 1.0)

rewrite47.0ms

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)))
20.0ms	(/.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)

series38.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2.0 x)) 1.0) (-.f64 (exp.f64 x) 1.0)))
9.0ms	(/.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)
12.0ms	(-.f64 (exp.f64 x) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5066	2150

prune153.0ms

Filtered

96 candidates to 133 candidates (-38.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	3	134

Merged error: 0b

Counts

134 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0)))
9.6b	(sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
3×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64` `associate-+r+_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 28

Calls

2 calls:

6.0ms	(+.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))))

series11.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(+.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))))

simplify48.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5605	475

prune36.0ms

Filtered

27 candidates to 34 candidates (-25.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	34	3	37

Merged error: 0b

Counts

37 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) 2.0)
0.0b	(+.f64 (exp.f64 x) 1.0)
3.6b	(-.f64 (pow.f64 (exp.f64 x) 2) (*.f64 1.0 1.0))
3.6b	(-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64` `difference-of-squares_binary64`
5×	`pow1_binary64` `unpow-prod-down_binary64`
4×	`pow-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow-unpow_binary64` `sqr-pow_binary64` `exp-prod_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 62

Calls

4 calls:

4.0ms	(pow.f64 (exp.f64 x) 2.0)
4.0ms	(+.f64 (exp.f64 x) 1.0)
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)

series27.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow.f64 (exp.f64 x) 2.0)
2.0ms	(+.f64 (exp.f64 x) 1.0)
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)

simplify50.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4958	602
1	4958	602

prune80.0ms

Filtered

56 candidates to 74 candidates (-32.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	74	3	77

Merged error: 0b

Counts

77 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0) (-.f64 (exp.f64 x) 1.0))) 3))
0.1b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0) (-.f64 (exp.f64 x) 1.0))) 3)
3.6b	(-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0)
3.6b	(-.f64 (exp.f64 x) 1.0)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

225×	`add-sqr-sqrt_binary64`
164×	`sqrt-prod_binary64`
162×	`*-un-lft-identity_binary64`
140×	`times-frac_binary64`
109×	`unpow-prod-down_binary64`
94×	`cbrt-prod_binary64`
92×	`difference-of-squares_binary64`
88×	`cube-prod_binary64`
62×	`add-cube-cbrt_binary64`
50×	`distribute-lft-out--_binary64`
23×	`sqr-pow_binary64`
8×	`add-log-exp_binary64` `associate-/r/_binary64`
6×	`pow1_binary64` `flip3--_binary64` `flip--_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`div-inv_binary64`
3×	`pow-unpow_binary64` `pow-pow_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cube-div_binary64` `unpow3_binary64` `sqrt-div_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `pow1/2_binary64` `rem-cbrt-cube_binary64` `sqrt-pow2_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`

Counts

4 → 241

Calls

4 calls:

19.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0) (-.f64 (exp.f64 x) 1.0))) 3))
17.0ms	(pow.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0) (-.f64 (exp.f64 x) 1.0))) 3)
7.0ms	(-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0)
5.0ms	(-.f64 (exp.f64 x) 1.0)

series57.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0) (-.f64 (exp.f64 x) 1.0))) 3))
30.0ms	(pow.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0) (-.f64 (exp.f64 x) 1.0))) 3)
5.0ms	(-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0)
2.0ms	(-.f64 (exp.f64 x) 1.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5044	5637

prune165.0ms

Filtered

111 candidates to 253 candidates (-127.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	253	0	253
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	253	3	256

Merged error: 0b

Counts

256 → 3

regimes35.0ms

Accuracy

99% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 20.3b

bsearch17.0ms

Steps

Iters	Range		Point
9	-0.00023126046997282165	-4.0086703064809486e-10	-1.397327525252979e-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

844.0ms	2309×	body	1280	valid
393.0ms	1686×	body	640	valid
130.0ms	862×	body	320	valid
122.0ms	2742×	body	80	valid
42.0ms	401×	body	160	valid
0.0ms	4×	body	80	invalid

Details

analyze496.0ms

sample60.0ms

simplify478.0ms

prune4.0ms

localize10.0ms

rewrite47.0ms

series38.0ms

simplify43.0ms

prune153.0ms

localize6.0ms

rewrite10.0ms

series11.0ms

simplify48.0ms

prune36.0ms

localize13.0ms

rewrite22.0ms

series27.0ms

simplify50.0ms

prune80.0ms

localize10.0ms

rewrite67.0ms

series57.0ms

simplify65.0ms

prune165.0ms

regimes35.0ms

bsearch17.0ms

simplify2.0ms

end0.0ms

sample1.7s

Profiling