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

sample17.0ms

Algorithm

intervals

Results

11.0ms

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

prune1.0ms

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 3 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
14×	`sqrt-prod_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))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
8.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series26.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
5.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
18.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify27.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5024	990

prune55.0ms

Filtered

57 candidates to 80 candidates (-40.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	4	81

Merged error: 0b

Counts

81 → 4

localize6.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64`
51×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
33×	`distribute-lft-out_binary64`
27×	`add-cube-cbrt_binary64`
24×	`associate-r_binary64`
20×	`sqrt-prod_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64`
4×	`flip3-+_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64` `flip-+_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64` `associate-/l*_binary64`
2×	`cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `div-inv_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 122

Calls

4 calls:

3.0ms	(sqrt.f64 (+.f64 x 1))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
14.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
9.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series43.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
20.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
13.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify63.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4944	1583
1	4944	1583

prune81.0ms

Filtered

88 candidates to 134 candidates (-52.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	134	4	138

Merged error: 0b

Counts

138 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

602×	`*-un-lft-identity_binary64`
594×	`times-frac_binary64`
560×	`sqrt-prod_binary64`
394×	`add-sqr-sqrt_binary64`
280×	`distribute-lft-out_binary64`
252×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
28×	`sqrt-div_binary64`
24×	`associate-/r/_binary64`
18×	`associate-/r*_binary64`
14×	`flip3-+_binary64` `flip-+_binary64`
12×	`div-inv_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64`

Counts

4 → 445

Calls

4 calls:

6.0ms	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
9.0ms	(/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
25.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
16.0ms	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
30.0ms	(/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
18.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

simplify110.0ms

Algorithm

egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5096	10285

prune236.0ms

Filtered

151 candidates to 457 candidates (-202.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	457	0	457
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	457	4	461

Merged error: 0b

Counts

461 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

119×	`*-un-lft-identity_binary64`
92×	`add-sqr-sqrt_binary64`
79×	`sqrt-prod_binary64`
76×	`times-frac_binary64`
57×	`distribute-lft-out_binary64`
47×	`add-cube-cbrt_binary64`
42×	`associate-r_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-l_binary64` `unswap-sqr_binary64` `associate-/l_binary64`
4×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 160

Calls

4 calls:

3.0ms	(sqrt.f64 (+.f64 x 1))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
9.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
20.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
5.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
31.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
17.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4945	2366
1	4945	2366

prune78.0ms

Filtered

98 candidates to 172 candidates (-75.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	172	4	176

Merged error: 0b

Counts

176 → 4

regimes38.0ms

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	11	10
1	11	10

end0.0ms

sample303.0ms

Algorithm

intervals

Results

210.0ms	7999×	body	80	valid
0.0ms	1×	body	1280	valid

Details

analyze2.0ms

sample17.0ms

simplify5.0ms

prune1.0ms

localize5.0ms

rewrite20.0ms

series26.0ms

simplify27.0ms

prune55.0ms

localize6.0ms

rewrite37.0ms

series43.0ms

simplify63.0ms

prune81.0ms

localize8.0ms

rewrite89.0ms

series76.0ms

simplify110.0ms

prune236.0ms

localize7.0ms

rewrite46.0ms

series56.0ms

simplify66.0ms

prune78.0ms

regimes38.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample303.0ms

Profiling