Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

sample23.0ms

Algorithm

intervals

Results

9.0ms	67×	body	1024	valid
5.0ms	139×	body	128	valid
3.0ms	30×	body	512	valid
1.0ms	20×	body	256	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 20.1b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
2.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt_binary64`
97×	`*-un-lft-identity_binary64` `times-frac_binary64`
64×	`sqrt-prod_binary64`
42×	`add-cube-cbrt_binary64`
25×	`difference-of-squares_binary64`
13×	`associate-/r*_binary64` `distribute-lft-out--_binary64`
10×	`add-exp-log_binary64`
9×	`pow1_binary64`
8×	`distribute-lft-out_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64` `div-inv_binary64` `pow-flip_binary64`
4×	`sqrt-div_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 160

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
9.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
6.0ms	(/.f64 1 (sqrt.f64 x))
39.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series181.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(sqrt.f64 (+.f64 x 1))
33.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
54.0ms	(/.f64 1 (sqrt.f64 x))
68.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify93.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4929	3368
1	4929	3368

prune139.0ms

Filtered

95 candidates to 172 candidates (-81.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	163	9	172
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	9	173

Merged error: 19.5b

Counts

173 → 9

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
8.7b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
33×	`times-frac_binary64`
26×	`sqrt-prod_binary64`
20×	`add-cube-cbrt_binary64`
15×	`difference-of-squares_binary64`
7×	`associate-/r*_binary64`
6×	`pow1_binary64` `add-exp-log_binary64`
5×	`add-log-exp_binary64` `distribute-lft-out_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64`
4×	`sqrt-div_binary64`
3×	`associate-/l*_binary64` `pow-flip_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-exp_binary64` `flip--_binary64`

Counts

3 → 94

Calls

3 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
8.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
23.0ms	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series120.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(sqrt.f64 (+.f64 x 1))
30.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
62.0ms	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify90.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4895	2003
1	4895	2003

prune85.0ms

Filtered

61 candidates to 103 candidates (-68.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	103	9	112

Merged error: 19.5b

Counts

112 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 x))
0.3b	(/.f64 1 (sqrt.f64 (sqrt.f64 x)))
0.4b	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
16.2b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite481.0ms

Algorithm

rewrite-expression-head

Rules

875×	`times-frac_binary64`
853×	`sqrt-prod_binary64`
737×	`add-sqr-sqrt_binary64`
431×	`*-un-lft-identity_binary64`
314×	`add-cube-cbrt_binary64`
115×	`difference-of-squares_binary64`
34×	`associate-/l*_binary64`
24×	`sqrt-pow1_binary64`
21×	`div-inv_binary64`
20×	`pow1_binary64`
18×	`associate-/r*_binary64`
14×	`add-exp-log_binary64` `pow-flip_binary64`
12×	`pow1/2_binary64`
11×	`add-cbrt-cube_binary64`
10×	`pow-div_binary64`
8×	`distribute-lft-out--_binary64`
6×	`add-log-exp_binary64`
5×	`div-exp_binary64`
4×	`cbrt-undiv_binary64`
2×	`distribute-lft-out_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 557

Calls

4 calls:

2.0ms	(sqrt.f64 (sqrt.f64 x))
7.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 x)))
21.0ms	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
353.0ms	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series344.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(sqrt.f64 (sqrt.f64 x))
107.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 x)))
49.0ms	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
80.0ms	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify195.0ms

Algorithm

egg-herbie

Counts

569 → 569

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5065	15867

prune199.0ms

Filtered

147 candidates to 569 candidates (-287.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	567	2	569
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	568	10	578

Merged error: 19.5b

Counts

578 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 (-.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x))))
0.4b	(/.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (sqrt.f64 x)))
14.6b	(-.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

278×	`sqrt-prod_binary64`
247×	`add-sqr-sqrt_binary64`
142×	`times-frac_binary64`
83×	`*-un-lft-identity_binary64`
63×	`difference-of-squares_binary64`
55×	`add-cube-cbrt_binary64`
32×	`associate-/l*_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`distribute-lft-out_binary64`
10×	`associate-/r*_binary64`
9×	`associate-l_binary64`
8×	`pow1_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `unswap-sqr_binary64` `sqrt-div_binary64`
4×	`associate-/l/_binary64` `associate-*r/_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`pow1/2_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `sqrt-undiv_binary64` `sqrt-unprod_binary64` `div-sub_binary64` `*-commutative_binary64`

Counts

4 → 235

Calls

4 calls:

13.0ms	(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
61.0ms	(/.f64 (-.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x))))
11.0ms	(/.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (sqrt.f64 x)))
53.0ms	(-.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

series600.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
317.0ms	(/.f64 (-.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x))))
73.0ms	(/.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (sqrt.f64 x)))
131.0ms	(-.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

simplify119.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5094	8363

prune196.0ms

Filtered

114 candidates to 247 candidates (-116.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	241	6	247
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	243	14	257

Merged error: 19.5b

Counts

257 → 14

regimes46.0ms

Accuracy

90.3% (0.6b remaining)

Error of 19.9b against oracle of 19.3b and baseline of 25.1b

bsearch30.0ms

Steps

Iters	Range		Point
8	4.164586611240553e+94	2.261788715377049e+97	5.641413807697915e+96

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	85
1	54	85

end0.0ms

sample709.0ms

Algorithm

intervals

Results

308.0ms	2206×	body	1024	valid
163.0ms	4279×	body	128	valid
104.0ms	973×	body	512	valid
37.0ms	542×	body	256	valid

Details

analyze1.0ms

sample23.0ms

simplify11.0ms

prune6.0ms

localize7.0ms

rewrite77.0ms

series181.0ms

simplify93.0ms

prune139.0ms

localize11.0ms

rewrite43.0ms

series120.0ms

simplify90.0ms

prune85.0ms

localize10.0ms

rewrite481.0ms

series344.0ms

simplify195.0ms

prune199.0ms

localize10.0ms

rewrite174.0ms

series600.0ms

simplify119.0ms

prune196.0ms

regimes46.0ms

bsearch30.0ms

simplify3.0ms

end0.0ms

sample709.0ms

Profiling