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
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

sample13.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	9	8
1	9	8

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: 0.2b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
20×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
10×	`sqrt-prod_binary64`
6×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/l*_binary64`
2×	`flip3-+_binary64` `pow1_binary64` `associate-/r/_binary64` `flip-+_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 55

Calls

2 calls:

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

series27.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
22.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify42.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4950	826
1	4950	826

prune66.0ms

Filtered

42 candidates to 61 candidates (-45.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	4	62

Merged error: 0b

Counts

62 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.4b	(/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
0.4b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
0.8b	(/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

154×	`*-un-lft-identity_binary64`
150×	`add-sqr-sqrt_binary64`
131×	`sqrt-prod_binary64`
130×	`times-frac_binary64`
73×	`add-cube-cbrt_binary64`
60×	`distribute-lft-out_binary64`
33×	`associate-r_binary64` `associate-l_binary64`
32×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
18×	`associate-/r*_binary64`
15×	`unswap-sqr_binary64`
11×	`div-exp_binary64`
10×	`sqrt-div_binary64`
9×	`pow1_binary64`
8×	`associate-/r/_binary64` `prod-exp_binary64`
6×	`cbrt-undiv_binary64` `associate-/l*_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `div-inv_binary64`
3×	`1-exp_binary64` `rec-exp_binary64` `pow-flip_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `rem-sqrt-square_binary64` `inv-pow_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 235

Calls

4 calls:

6.0ms	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
9.0ms	(/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
36.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
12.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
28.0ms	(/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
16.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
24.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5045	4244

prune284.0ms

Filtered

139 candidates to 247 candidates (-77.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	247	4	251

Merged error: 0b

Counts

251 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
0.6b	(cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
0.6b	(cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
0.6b	(cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

227×	`*-un-lft-identity_binary64`
204×	`cbrt-prod_binary64`
164×	`add-sqr-sqrt_binary64`
156×	`times-frac_binary64`
108×	`distribute-lft-out_binary64`
86×	`add-cube-cbrt_binary64`
54×	`sqrt-prod_binary64`
39×	`swap-sqr_binary64`
27×	`associate-r_binary64` `associate-l_binary64`
14×	`associate-/r/_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64` `unswap-sqr_binary64`
7×	`cbrt-div_binary64` `flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `associate-r/_binary64` `pow-plus_binary64` `prod-exp_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 222

Calls

4 calls:

31.0ms	(*.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
8.0ms	(cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
8.0ms	(cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
8.0ms	(cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series664.0ms

Counts

4 → 12

Calls

4 calls:

292.0ms	(*.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
124.0ms	(cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
124.0ms	(cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
123.0ms	(cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

simplify79.0ms

Algorithm

egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5044	10675

prune797.0ms

Filtered

151 candidates to 234 candidates (-55.0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	234	4	238

Merged error: 0b

Counts

238 → 4

localize7.0ms

Local error

Found 1 expressions with local error:

2.6b	(-.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
4×	`difference-of-squares_binary64` `sqrt-prod_binary64`
3×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
1×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`

Counts

1 → 18

Calls

1 calls:

7.0ms

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

series6.0ms

Counts

1 → 3

Calls

1 calls:

6.0ms

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

simplify46.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5327	233

prune21.0ms

Filtered

16 candidates to 21 candidates (-31.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	21	4	25

Merged error: 0b

Counts

25 → 4

regimes59.0ms

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	9	8
1	9	8

end0.0ms

sample306.0ms

Algorithm

intervals

Results

216.0ms	7996×	body	80	valid
1.0ms	4×	body	1280	valid

Details

analyze2.0ms

sample13.0ms

simplify5.0ms

prune2.0ms

localize5.0ms

rewrite17.0ms

series27.0ms

simplify42.0ms

prune66.0ms

localize9.0ms

rewrite76.0ms

series79.0ms

simplify61.0ms

prune284.0ms

localize12.0ms

rewrite74.0ms

series664.0ms

simplify79.0ms

prune797.0ms

localize7.0ms

rewrite7.0ms

series6.0ms

simplify46.0ms

prune21.0ms

regimes59.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample306.0ms

Profiling