Details

analyze1.0ms

Algorithm

Search

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

sample26.0ms

Algorithm

intervals

Results

9.0ms	62×	body	640	valid
5.0ms	144×	body	80	valid
5.0ms	27×	body	1280	valid
2.0ms	17×	body	320	valid
0.0ms	6×	body	160	valid

simplify7.0ms

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: 19.8b

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)))
0.3b	(/.f64 1 (sqrt.f64 x))
2.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite53.0ms

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

series30.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
5.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
8.0ms	(/.f64 1 (sqrt.f64 x))
14.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify59.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5299	2132

prune162.0ms

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: 19.3b

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)))
2.1b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite44.0ms

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))
17.0ms	(/.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)))
11.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series48.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 1 x))
26.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
7.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
11.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify53.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4950	1672
1	4950	1672

prune116.0ms

Filtered

83 candidates to 119 candidates (-43.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	126	3	129

Merged error: 0.2b

Counts

129 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

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

series50.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
8.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
28.0ms	(/.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)))

simplify78.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4915	2632
1	4915	2632

prune189.0ms

Filtered

108 candidates to 178 candidates (-64.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	170	8	178
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	172	9	181

Merged error: 0.0b

Counts

181 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.1b	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
0.4b	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac_binary64`
162×	`*-un-lft-identity_binary64`
157×	`add-sqr-sqrt_binary64`
120×	`add-cube-cbrt_binary64`
91×	`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×	`pow1_binary64` `div-inv_binary64`
8×	`div-exp_binary64`
7×	`associate-r_binary64`
6×	`associate-l_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `pow1/2_binary64` `sqrt-pow1_binary64`
2×	`1-exp_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`associate-/l/_binary64` `cbrt-unprod_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `inv-pow_binary64` `prod-exp_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 256

Calls

4 calls:

3.0ms	(sqrt.f64 (+.f64 1 x))
13.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
8.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))

series48.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 1 x))
25.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
7.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
11.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))

simplify81.0ms

Algorithm

egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4953	6059
1	4953	6059

prune261.0ms

Filtered

151 candidates to 268 candidates (-77.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	266	2	268
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	269	8	277

Merged error: 0b

Counts

277 → 8

regimes42.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	23
1	15	23

end0.0ms

sample807.0ms

Algorithm

intervals

Results

251.0ms	1768×	body	640	valid
214.0ms	1139×	body	1280	valid
165.0ms	4204×	body	80	valid
64.0ms	608×	body	320	valid
20.0ms	281×	body	160	valid

Details

analyze1.0ms

sample26.0ms

simplify7.0ms

prune4.0ms

localize12.0ms

rewrite53.0ms

series30.0ms

simplify59.0ms

prune162.0ms

localize7.0ms

rewrite44.0ms

series48.0ms

simplify53.0ms

prune116.0ms

localize8.0ms

rewrite57.0ms

series50.0ms

simplify78.0ms

prune189.0ms

localize10.0ms

rewrite43.0ms

series48.0ms

simplify81.0ms

prune261.0ms

regimes42.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample807.0ms

Profiling