Details

analyze1.0ms

Algorithm

Search

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

sample33.0ms

Algorithm

intervals

Results

10.0ms	69×	body	640	valid
10.0ms	31×	body	1280	valid
5.0ms	130×	body	80	valid
1.0ms	14×	body	320	valid
1.0ms	12×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	265	11
1	265	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: 20.2b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1.0))
0.2b	(/.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
0.3b	(/.f64 1.0 (sqrt.f64 x))
3.1b	(-.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity_binary64`
73×	`add-sqr-sqrt_binary64`
69×	`times-frac_binary64`
50×	`sqrt-prod_binary64`
42×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64`
11×	`distribute-lft-out--_binary64`
9×	`difference-of-squares_binary64`
8×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64`
5×	`pow1_binary64`
4×	`div-inv_binary64` `sqrt-div_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 132

Calls

4 calls:

3.0ms	(sqrt.f64 (+.f64 x 1.0))
7.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
6.0ms	(/.f64 1.0 (sqrt.f64 x))
33.0ms	(-.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

series42.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sqrt.f64 (+.f64 x 1.0))
8.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
10.0ms	(/.f64 1.0 (sqrt.f64 x))
18.0ms	(-.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

simplify35.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5076	1839

prune180.0ms

Filtered

103 candidates to 144 candidates (-39.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	132	12	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	12	145

Merged error: 19.6b

Counts

145 → 12

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1.0 x))
0.2b	(/.f64 (.f64 1.0 (-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))
3.1b	(-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
23×	`sqrt-prod_binary64`
20×	`*-un-lft-identity_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1_binary64` `add-cube-cbrt_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `associate-r/_binary64` `associate-l*_binary64` `sqrt-div_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`cbrt-undiv_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `div-exp_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `distribute-lft-out--_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64` `*-commutative_binary64`

Counts

4 → 92

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 1.0 x))
21.0ms	(/.f64 (.f64 1.0 (-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))

series72.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(sqrt.f64 (+.f64 1.0 x))
42.0ms	(/.f64 (.f64 1.0 (-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))
14.0ms	(-.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))

simplify40.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5212	1577

prune122.0ms

Filtered

76 candidates to 104 candidates (-36.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	112	4	116

Merged error: 0.3b

Counts

116 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))
0.2b	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))
0.3b	(/.f64 (.f64 1.0 (/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64`
35×	`sqrt-prod_binary64`
32×	`distribute-lft-out_binary64`
29×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
28×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
9×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`pow1_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
7×	`associate-/r_binary64` `associate-r*_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
5×	`flip3-+_binary64` `associate-r/_binary64` `associate-/l_binary64` `flip-+_binary64`
4×	`associate-/r/_binary64` `unswap-sqr_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `associate-/l/_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`sqrt-unprod_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 125

Calls

4 calls:

8.0ms	(+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))
14.0ms	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))
25.0ms	(/.f64 (.f64 1.0 (/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))
13.0ms	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
8.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x)))
49.0ms	(/.f64 (.f64 1.0 (/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1.0 x))))

simplify61.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5516	2087

prune168.0ms

Filtered

90 candidates to 137 candidates (-52.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	129	8	137
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	131	10	141

Merged error: 0.0b

Counts

141 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1.0 (+.f64 (+.f64 1.0 x) (*.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
0.1b	(.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (+.f64 (+.f64 1.0 x) (.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))
0.3b	(*.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))
0.3b	(/.f64 1.0 (sqrt.f64 x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt_binary64`
67×	`times-frac_binary64`
55×	`*-un-lft-identity_binary64`
53×	`add-cube-cbrt_binary64`
34×	`sqrt-prod_binary64`
29×	`associate-l_binary64`
28×	`associate-r_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-/r/_binary64`
11×	`flip3-+_binary64` `flip-+_binary64` `associate-*l/_binary64`
10×	`associate-/r*_binary64` `pow1_binary64` `unswap-sqr_binary64` `sqrt-div_binary64`
8×	`distribute-lft-out_binary64` `frac-add_binary64`
6×	`cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `div-inv_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`associate-*r/_binary64` `sqrt-unprod_binary64` `frac-times_binary64`

Counts

4 → 179

Calls

4 calls:

9.0ms	(/.f64 1.0 (+.f64 (+.f64 1.0 x) (*.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
22.0ms	(.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (+.f64 (+.f64 1.0 x) (.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))
9.0ms	(*.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))
4.0ms	(/.f64 1.0 (sqrt.f64 x))

series56.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/.f64 1.0 (+.f64 (+.f64 1.0 x) (*.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
24.0ms	(.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (+.f64 (+.f64 1.0 x) (.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))
9.0ms	(*.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))
13.0ms	(/.f64 1.0 (sqrt.f64 x))

simplify48.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5018	3178

prune246.0ms

Filtered

149 candidates to 191 candidates (-28.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	186	5	191
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	192	9	201

Merged error: 0.0b

Counts

201 → 9

regimes45.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	18
1	14	18

end0.0ms

sample800.0ms

Algorithm

intervals

Results

263.0ms	1833×	body	640	valid
204.0ms	1140×	body	1280	valid
156.0ms	4101×	body	80	valid
63.0ms	610×	body	320	valid
22.0ms	316×	body	160	valid

Details

analyze1.0ms

sample33.0ms

simplify16.0ms

prune4.0ms

localize7.0ms

rewrite55.0ms

series42.0ms

simplify35.0ms

prune180.0ms

localize8.0ms

rewrite46.0ms

series72.0ms

simplify40.0ms

prune122.0ms

localize11.0ms

rewrite61.0ms

series79.0ms

simplify61.0ms

prune168.0ms

localize9.0ms

rewrite51.0ms

series56.0ms

simplify48.0ms

prune246.0ms

regimes45.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample800.0ms

Profiling