Details

analyze3.0ms

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

sample11.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	11	12
1	11	12

prune6.0ms

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

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b	(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:

6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(sqrt.f64 (+.f64 x 1))
8.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series99.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
15.0ms	(sqrt.f64 (+.f64 x 1))
67.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify51.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4979	1561
1	4979	1561

prune65.0ms

Filtered

55 candidates to 80 candidates (-45.5%)

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

rewrite35.0ms

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:

6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(sqrt.f64 (+.f64 x 1))
8.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
14.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series137.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
13.0ms	(sqrt.f64 (+.f64 x 1))
49.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
61.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4952	2495
1	4952	2495

prune99.0ms

Filtered

81 candidates to 134 candidates (-65.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	135	3	138

Merged error: 0b

Counts

138 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

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:

6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(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)))))

series182.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
12.0ms	(sqrt.f64 (+.f64 x 1))
95.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
60.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

simplify79.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5231	3803

prune118.0ms

Filtered

98 candidates to 172 candidates (-75.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Merged error: 0b

Counts

175 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt_binary64`
95×	`*-un-lft-identity_binary64`
94×	`sqrt-prod_binary64`
68×	`pow1_binary64`
62×	`times-frac_binary64`
55×	`associate-r_binary64`
41×	`pow-prod-down_binary64` `add-cube-cbrt_binary64`
40×	`distribute-lft-out_binary64`
24×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
20×	`pow1/2_binary64` `sqrt-pow1_binary64`
16×	`unswap-sqr_binary64`
13×	`associate-l_binary64`
10×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`pow-prod-up_binary64`
7×	`associate-*r/_binary64` `sqrt-unprod_binary64`
6×	`associate-/r*_binary64` `associate-/r/_binary64` `pow-sqr_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `associate-/l_binary64` `div-inv_binary64` `flip-+_binary64` `-commutative_binary64`
2×	`pow-plus_binary64` `div-exp_binary64`
1×	`swap-sqr_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rem-square-sqrt_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `pow-flip_binary64` `frac-times_binary64` `pow2_binary64` `associate-*l/_binary64`

Counts

4 → 204

Calls

4 calls:

8.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
20.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
17.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
29.0ms	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))) (*.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))

series464.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
169.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
184.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
66.0ms	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))) (*.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))

simplify89.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5478	4950

prune216.0ms

Filtered

115 candidates to 216 candidates (-87.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	216	3	219

Merged error: 0b

Counts

219 → 3

regimes19.0ms

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	11	12
1	11	12

end0.0ms

sample301.0ms

Algorithm

intervals

Results

211.0ms	7996×	body	80	valid
1.0ms	4×	body	1280	valid

Details

analyze3.0ms

sample11.0ms

simplify13.0ms

prune6.0ms

localize6.0ms

rewrite20.0ms

series99.0ms

simplify51.0ms

prune65.0ms

localize6.0ms

rewrite35.0ms

series137.0ms

simplify87.0ms

prune99.0ms

localize9.0ms

rewrite45.0ms

series182.0ms

simplify79.0ms

prune118.0ms

localize10.0ms

rewrite83.0ms

series464.0ms

simplify89.0ms

prune216.0ms

regimes19.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample301.0ms

Profiling