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

sample18.0ms

Algorithm

intervals

Results

12.0ms

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	(+.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))))

series28.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify30.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5024	990

prune57.0ms

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

166×	`*-un-lft-identity_binary64`
156×	`times-frac_binary64`
114×	`add-sqr-sqrt_binary64`
79×	`add-cube-cbrt_binary64`
69×	`distribute-lft-out_binary64`
38×	`sqrt-prod_binary64`
25×	`associate-/r*_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
9×	`associate-/l*_binary64`
8×	`div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `div-inv_binary64`
4×	`cbrt-undiv_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `inv-pow_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

4 → 183

Calls

4 calls:

6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(sqrt.f64 (+.f64 x 1))
9.0ms	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
13.0ms	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))

series39.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(sqrt.f64 (+.f64 x 1))
13.0ms	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
18.0ms	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))

simplify56.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5216	2715

prune93.0ms

Filtered

111 candidates to 195 candidates (-75.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	195	4	199

Merged error: 0b

Counts

199 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (+.f64 1 (/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x))))))
7.0b	(sqrt.f64 (+.f64 1 (pow.f64 x 3)))
7.3b	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x))))
11.3b	(sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity_binary64`
59×	`sqrt-prod_binary64`
54×	`times-frac_binary64`
47×	`add-sqr-sqrt_binary64`
45×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out_binary64`
10×	`associate-/r_binary64` `associate-/l_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
6×	`pow1_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64`
2×	`associate-/l/_binary64` `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`
1×	`sqrt-undiv_binary64`

Counts

4 → 136

Calls

4 calls:

27.0ms	(/.f64 x (+.f64 1 (/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x))))))
6.0ms	(sqrt.f64 (+.f64 1 (pow.f64 x 3)))
16.0ms	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x))))
7.0ms	(sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))

series34.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/.f64 x (+.f64 1 (/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x))))))
4.0ms	(sqrt.f64 (+.f64 1 (pow.f64 x 3)))
7.0ms	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x))))
3.0ms	(sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))

simplify89.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4938	3212
1	4938	3212

prune115.0ms

Filtered

97 candidates to 148 candidates (-52.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	148	4	152

Merged error: 0b

Counts

152 → 4

localize7.0ms

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)))))

rewrite50.0ms

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:

8.0ms	(+.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))))
21.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series53.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(sqrt.f64 (+.f64 x 1))
27.0ms	(/.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)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4945	2366
1	4945	2366

prune81.0ms

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

regimes225.0ms

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

sample346.0ms

Algorithm

intervals

Results

245.0ms	7996×	body	80	valid
1.0ms	4×	body	1280	valid

Details

analyze3.0ms

sample18.0ms

simplify5.0ms

prune1.0ms

localize5.0ms

rewrite20.0ms

series28.0ms

simplify30.0ms

prune57.0ms

localize6.0ms

rewrite41.0ms

series39.0ms

simplify56.0ms

prune93.0ms

localize12.0ms

rewrite61.0ms

series34.0ms

simplify89.0ms

prune115.0ms

localize7.0ms

rewrite50.0ms

series53.0ms

simplify72.0ms

prune81.0ms

regimes225.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample346.0ms

Profiling