Details

analyze6.0ms

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

sample21.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	11	12
1	11	12

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))))

rewrite24.0ms

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:

4.0ms	(sqrt.f64 (+.f64 x 1))
10.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
8.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series98.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(sqrt.f64 (+.f64 x 1))
17.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
66.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify48.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4979	1561
1	4979	1561

prune71.0ms

Filtered

57 candidates to 80 candidates (-40.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	3	81

Merged error: 0b

Counts

81 → 3

localize8.0ms

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))))

rewrite38.0ms

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))))

series143.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt.f64 (+.f64 x 1))
15.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
66.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
49.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify84.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4952	2495
1	4952	2495

prune102.0ms

Filtered

89 candidates to 134 candidates (-50.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	134	3	137

Merged error: 0b

Counts

137 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(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 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
0.7b	(/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite75.0ms

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

series329.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
133.0ms	(/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
77.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
79.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

simplify170.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4943	6828
1	4943	6828

prune286.0ms

Filtered

139 candidates to 247 candidates (-77.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	247	3	250

Merged error: 0b

Counts

250 → 3

localize8.0ms

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)))))

rewrite52.0ms

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))
10.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
10.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
21.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series192.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt.f64 (+.f64 x 1))
17.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
99.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
61.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

simplify75.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5231	3803

prune113.0ms

Filtered

99 candidates to 172 candidates (-73.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	172	3	175

Merged error: 0b

Counts

175 → 3

regimes11.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	15
1	13	15

end0.0ms

sample301.0ms

Algorithm

intervals

Results

212.0ms	7997×	body	80	valid
0.0ms	3×	body	1280	valid

Details

analyze6.0ms

sample21.0ms

simplify14.0ms

prune1.0ms

localize5.0ms

rewrite24.0ms

series98.0ms

simplify48.0ms

prune71.0ms

localize8.0ms

rewrite38.0ms

series143.0ms

simplify84.0ms

prune102.0ms

localize9.0ms

rewrite75.0ms

series329.0ms

simplify170.0ms

prune286.0ms

localize8.0ms

rewrite52.0ms

series192.0ms

simplify75.0ms

prune113.0ms

regimes11.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample301.0ms

Profiling