Details

analyze1.0ms

Algorithm

Search

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

sample27.0ms

Algorithm

intervals

Results

10.0ms	69×	body	640	valid
5.0ms	31×	body	1280	valid
5.0ms	130×	body	80	valid
1.0ms	14×	body	320	valid
1.0ms	12×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	74	11
1	74	11

prune4.0ms

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: 20.2b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
3.1b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite59.0ms

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`
12×	`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×	`div-exp_binary64` `sqrt-div_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64`
2×	`flip3-+_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 162

Calls

4 calls:

3.0ms	(sqrt.f64 (+.f64 x 1))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))
37.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series31.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
5.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
9.0ms	(/.f64 1 (sqrt.f64 x))
12.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify58.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5299	2132

prune159.0ms

Filtered

95 candidates to 174 candidates (-83.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	164	10	174
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	165	10	175

Merged error: 19.6b

Counts

175 → 10

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.2b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
3.1b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
39×	`sqrt-prod_binary64`
36×	`*-un-lft-identity_binary64`
12×	`difference-of-squares_binary64`
11×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/l*_binary64` `times-frac_binary64`
9×	`pow1_binary64` `distribute-lft-out--_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64` `sqrt-div_binary64`
5×	`distribute-lft-out_binary64`
4×	`associate-*r/_binary64` `unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64` `flip--_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-unprod_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 107

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 1 x))
18.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series58.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 1 x))
30.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
11.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
12.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify54.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4950	1672
1	4950	1672

prune120.0ms

Filtered

83 candidates to 119 candidates (-43.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	126	3	129

Merged error: 0.3b

Counts

129 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64`
78×	`times-frac_binary64`
55×	`sqrt-prod_binary64`
47×	`add-sqr-sqrt_binary64`
45×	`distribute-lft-out_binary64`
39×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`
27×	`associate-/l*_binary64`
20×	`add-cbrt-cube_binary64`
14×	`div-exp_binary64`
9×	`pow1_binary64`
8×	`associate-/r/_binary64`
7×	`associate-/r_binary64` `associate-r*_binary64` `cbrt-undiv_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `associate-l_binary64` `flip-+_binary64`
5×	`prod-exp_binary64`
4×	`associate-*r/_binary64` `unswap-sqr_binary64` `div-inv_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `rec-exp_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sqrt-unprod_binary64` `inv-pow_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 166

Calls

4 calls:

8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
21.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
9.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
32.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))

simplify71.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4915	2632
1	4915	2632

prune185.0ms

Filtered

105 candidates to 178 candidates (-69.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	171	7	178
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	172	9	181

Merged error: 0.0b

Counts

181 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt_binary64`
82×	`times-frac_binary64`
66×	`*-un-lft-identity_binary64`
54×	`add-exp-log_binary64`
53×	`add-cube-cbrt_binary64`
38×	`sqrt-prod_binary64`
29×	`associate-l_binary64`
28×	`associate-r_binary64`
22×	`add-cbrt-cube_binary64`
20×	`div-exp_binary64`
19×	`unswap-sqr_binary64`
17×	`prod-exp_binary64`
15×	`pow1_binary64`
12×	`associate-/r/_binary64`
11×	`flip3-+_binary64` `flip-+_binary64` `associate-*l/_binary64`
10×	`associate-/r*_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
8×	`distribute-lft-out_binary64` `frac-add_binary64`
6×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `pow-flip_binary64`
5×	`cbrt-unprod_binary64`
4×	`add-log-exp_binary64` `inv-pow_binary64` `div-inv_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`associate-*r/_binary64` `sqrt-unprod_binary64` `un-div-inv_binary64` `frac-times_binary64`

Counts

4 → 213

Calls

4 calls:

9.0ms	(/.f64 1 (+.f64 (+.f64 1 x) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
24.0ms	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 1 x) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
11.0ms	(*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
5.0ms	(/.f64 1 (sqrt.f64 x))

series51.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/.f64 1 (+.f64 (+.f64 1 x) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
24.0ms	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 1 x) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
9.0ms	(*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
9.0ms	(/.f64 1 (sqrt.f64 x))

simplify48.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5122	3455

prune209.0ms

Filtered

140 candidates to 225 candidates (-60.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	222	3	225
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	227	7	234

Merged error: 0b

Counts

234 → 7

regimes41.0ms

Accuracy

0% (0.2b 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	16	17
1	16	17

end0.0ms

sample792.0ms

Algorithm

intervals

Results

257.0ms	1833×	body	640	valid
209.0ms	1140×	body	1280	valid
152.0ms	4101×	body	80	valid
63.0ms	610×	body	320	valid
22.0ms	316×	body	160	valid

Details

analyze1.0ms

sample27.0ms

simplify8.0ms

prune4.0ms

localize7.0ms

rewrite59.0ms

series31.0ms

simplify58.0ms

prune159.0ms

localize7.0ms

rewrite43.0ms

series58.0ms

simplify54.0ms

prune120.0ms

localize8.0ms

rewrite56.0ms

series56.0ms

simplify71.0ms

prune185.0ms

localize9.0ms

rewrite59.0ms

series51.0ms

simplify48.0ms

prune209.0ms

regimes41.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample792.0ms

Profiling