Details

analyze7.0ms

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

sample13.0ms

Algorithm

intervals

Results

8.0ms	255×	body	128	valid
0.0ms	1×	body	2048	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	12
1	9	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))))

rewrite25.0ms

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))
7.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
10.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series186.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(sqrt.f64 (+.f64 x 1))
32.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
126.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify68.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4949	1549
1	4949	1549

prune67.0ms

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))))

rewrite46.0ms

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`
14×	`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` `flip-+_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `rec-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` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 120

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
7.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
17.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
9.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series276.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt.f64 (+.f64 x 1))
34.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
124.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
90.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify78.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4956	2465
1	4956	2465

prune105.0ms

Filtered

89 candidates to 132 candidates (-48.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	132	3	135

Merged error: 0b

Counts

135 → 3

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)))))

rewrite64.0ms

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:

4.0ms	(sqrt.f64 (+.f64 x 1))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
10.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
27.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series372.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt.f64 (+.f64 x 1))
32.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
192.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
119.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4974	3818
1	4974	3818

prune121.0ms

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

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)
0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
34.0b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

142×	`*-un-lft-identity_binary64`
91×	`add-sqr-sqrt_binary64`
90×	`times-frac_binary64`
68×	`distribute-lft-out_binary64`
57×	`add-cube-cbrt_binary64`
54×	`cbrt-prod_binary64`
48×	`unpow-prod-down_binary64` `cube-prod_binary64`
34×	`sqrt-prod_binary64`
10×	`associate-/r/_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `add-log-exp_binary64` `flip-+_binary64`
5×	`pow1_binary64` `div-inv_binary64`
3×	`pow-unpow_binary64` `associate-/l*_binary64`
2×	`cbrt-undiv_binary64` `sqr-pow_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `rem-cbrt-cube_binary64` `pow1/3_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 187

Calls

4 calls:

10.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
13.0ms	(pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)
9.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
14.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))

series529.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
261.0ms	(pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)
117.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
123.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))

simplify97.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4976	4814
1	4976	4814

prune122.0ms

Filtered

90 candidates to 199 candidates (-121.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	199	3	202

Merged error: 0b

Counts

202 → 3

regimes21.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	11	15

end0.0ms

sample314.0ms

Algorithm

intervals

Results

222.0ms	7996×	body	128	valid
1.0ms	4×	body	2048	valid

Details

analyze7.0ms

sample13.0ms

simplify8.0ms

prune1.0ms

localize5.0ms

rewrite25.0ms

series186.0ms

simplify68.0ms

prune67.0ms

localize8.0ms

rewrite46.0ms

series276.0ms

simplify78.0ms

prune105.0ms

localize7.0ms

rewrite64.0ms

series372.0ms

simplify63.0ms

prune121.0ms

localize8.0ms

rewrite67.0ms

series529.0ms

simplify97.0ms

prune122.0ms

regimes21.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample314.0ms

Profiling