Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

sample21.0ms

Algorithm

intervals

Results

7.0ms	54×	body	1280	valid
4.0ms	46×	body	640	valid
3.0ms	130×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	13×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

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: 30.1b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1.0))
3.1b	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `difference-of-squares_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `distribute-lft-out--_binary64`
2×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

2 → 34

Calls

2 calls:

3.0ms	(sqrt.f64 (+.f64 x 1.0))
9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

series24.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(sqrt.f64 (+.f64 x 1.0))
15.0ms	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

simplify58.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4975	520
1	4975	520

prune51.0ms

Filtered

30 candidates to 40 candidates (-33.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	4	41

Merged error: 0.2b

Counts

41 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1.0))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))
0.2b	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
24×	`sqrt-prod_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 71

Calls

3 calls:

3.0ms	(sqrt.f64 (+.f64 x 1.0))
8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))
10.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x)))

series27.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(sqrt.f64 (+.f64 x 1.0))
8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))
14.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x)))

simplify33.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5038	1051

prune102.0ms

Filtered

59 candidates to 80 candidates (-35.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	75	9	84

Merged error: 0.0b

Counts

84 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1.0 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1.0 x))) (sqrt.f64 (cbrt.f64 (+.f64 1.0 x)))) (sqrt.f64 x)))
0.2b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1.0 x))) (sqrt.f64 (cbrt.f64 (+.f64 1.0 x))))
0.3b	(cbrt.f64 (+.f64 1.0 x))
0.3b	(cbrt.f64 (+.f64 1.0 x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
13×	`cbrt-prod_binary64`
10×	`associate-r_binary64`
9×	`times-frac_binary64` `sqrt-prod_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`cbrt-div_binary64` `pow1_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64`
3×	`associate-/r_binary64` `distribute-lft-out_binary64` `associate-l_binary64` `unswap-sqr_binary64` `associate-/l_binary64`
2×	`associate-*r/_binary64` `pow1/3_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

4 → 86

Calls

4 calls:

11.0ms	(/.f64 1.0 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1.0 x))) (sqrt.f64 (cbrt.f64 (+.f64 1.0 x)))) (sqrt.f64 x)))
9.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1.0 x))) (sqrt.f64 (cbrt.f64 (+.f64 1.0 x))))
3.0ms	(cbrt.f64 (+.f64 1.0 x))
3.0ms	(cbrt.f64 (+.f64 1.0 x))

series104.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/.f64 1.0 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1.0 x))) (sqrt.f64 (cbrt.f64 (+.f64 1.0 x)))) (sqrt.f64 x)))
14.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1.0 x))) (sqrt.f64 (cbrt.f64 (+.f64 1.0 x))))
8.0ms	(cbrt.f64 (+.f64 1.0 x))
8.0ms	(cbrt.f64 (+.f64 1.0 x))

simplify75.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4896	2095
1	4896	2095

prune170.0ms

Filtered

83 candidates to 98 candidates (-18.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	97	10	107

Merged error: 0.0b

Counts

107 → 10

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
0.2b	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
0.2b	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity_binary64`
274×	`sqrt-prod_binary64`
157×	`times-frac_binary64`
119×	`add-sqr-sqrt_binary64`
116×	`distribute-lft-out_binary64`
88×	`add-cube-cbrt_binary64`
41×	`swap-sqr_binary64`
27×	`associate-r_binary64` `associate-l_binary64`
20×	`pow1_binary64`
14×	`associate-/r/_binary64`
12×	`associate-/r*_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1/2_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64`
7×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
6×	`associate-/l*_binary64`
5×	`pow-prod-up_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`cbrt-undiv_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `associate-r/_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 250

Calls

4 calls:

11.0ms	(sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
10.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
13.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
37.0ms	(*.f64 (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
18.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
13.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
18.0ms	(*.f64 (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))

simplify89.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4946	4249
1	4946	4249

prune265.0ms

Filtered

142 candidates to 262 candidates (-84.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	259	3	262
Fresh	4	3	7
Picked	1	0	1
Done	0	2	2
Total	264	8	272

Merged error: 0.0b

Counts

272 → 8

regimes43.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

end0.0ms

sample597.0ms

Algorithm

intervals

Results

222.0ms	1750×	body	1280	valid
122.0ms	1220×	body	640	valid
105.0ms	4106×	body	80	valid
43.0ms	608×	body	320	valid
15.0ms	316×	body	160	valid

Details

analyze2.0ms

sample21.0ms

simplify8.0ms

prune2.0ms

localize5.0ms

rewrite13.0ms

series24.0ms

simplify58.0ms

prune51.0ms

localize7.0ms

rewrite24.0ms

series27.0ms

simplify33.0ms

prune102.0ms

localize9.0ms

rewrite28.0ms

series104.0ms

simplify75.0ms

prune170.0ms

localize8.0ms

rewrite85.0ms

series79.0ms

simplify89.0ms

prune265.0ms

regimes43.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample597.0ms

Profiling