Details

analyze2.0ms

Algorithm

Search

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

sample30.0ms

Algorithm

intervals

Results

10.0ms	69×	body	640	valid
7.0ms	37×	body	1280	valid
5.0ms	117×	body	80	valid
3.0ms	26×	body	320	valid
1.0ms	7×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	76	17
1	76	17

prune3.0ms

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: 25.0b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 1 (sqrt.f64 x))
1.9b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite52.0ms

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))
6.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(/.f64 1 (sqrt.f64 x))
31.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt.f64 (+.f64 x 1))
17.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
26.0ms	(/.f64 1 (sqrt.f64 x))
39.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify92.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4932	3393
1	4932	3393

prune139.0ms

Filtered

95 candidates to 174 candidates (-83.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	163	11	174
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	11	175

Merged error: 24.4b

Counts

175 → 11

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.1b	(/.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)))
2.0b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite42.0ms

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:

3.0ms	(sqrt.f64 (+.f64 1 x))
19.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
8.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series168.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt.f64 (+.f64 1 x))
89.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
25.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
37.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify66.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5469	2677

prune111.0ms

Filtered

83 candidates to 119 candidates (-43.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	128	2	130

Merged error: 0.3b

Counts

130 → 2

localize9.0ms

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)))
0.2b	(/.f64 (/.f64 1 (+.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)))

rewrite57.0ms

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))
13.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
20.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
8.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

series176.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
33.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
90.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
30.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

simplify77.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5317	4167

prune377.0ms

Filtered

108 candidates to 178 candidates (-64.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	168	10	178
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	169	11	180

Merged error: 0.0b

Counts

180 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac_binary64`
159×	`*-un-lft-identity_binary64`
156×	`add-sqr-sqrt_binary64`
119×	`add-cube-cbrt_binary64`
87×	`sqrt-prod_binary64`
49×	`distribute-lft-out_binary64`
21×	`associate-/l*_binary64`
20×	`associate-/r/_binary64`
19×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
12×	`flip3-+_binary64` `flip-+_binary64`
11×	`associate-/r*_binary64`
10×	`div-inv_binary64`
9×	`pow1_binary64`
8×	`div-exp_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
4×	`cbrt-undiv_binary64` `unswap-sqr_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64`
2×	`pow1/2_binary64` `1-exp_binary64` `associate-*r/_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`associate-/l/_binary64` `cbrt-unprod_binary64` `sqrt-unprod_binary64` `inv-pow_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 252

Calls

4 calls:

3.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
12.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
8.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

series171.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
78.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
39.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
29.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

simplify192.0ms

Algorithm

egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4946	9704
1	4946	9704

prune254.0ms

Filtered

145 candidates to 264 candidates (-82.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	260	4	264
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	265	10	275

Merged error: 0b

Counts

275 → 10

regimes26.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	25
1	15	25

end0.0ms

sample853.0ms

Algorithm

intervals

Results

279.0ms	1797×	body	640	valid
221.0ms	1112×	body	1280	valid
163.0ms	4139×	body	80	valid
76.0ms	645×	body	320	valid
23.0ms	307×	body	160	valid

Details

analyze2.0ms

sample30.0ms

simplify15.0ms

prune3.0ms

localize12.0ms

rewrite52.0ms

series97.0ms

simplify92.0ms

prune139.0ms

localize8.0ms

rewrite42.0ms

series168.0ms

simplify66.0ms

prune111.0ms

localize9.0ms

rewrite57.0ms

series176.0ms

simplify77.0ms

prune377.0ms

localize11.0ms

rewrite45.0ms

series171.0ms

simplify192.0ms

prune254.0ms

regimes26.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample853.0ms

Profiling