Details

analyze2.0ms

Algorithm

Search

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

sample37.0ms

Algorithm

intervals

Results

18.0ms	71×	body	2048	valid
6.0ms	30×	body	1024	valid
5.0ms	129×	body	128	valid
2.0ms	16×	body	512	valid
1.0ms	10×	body	256	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	45	15
1	45	15

prune3.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 14.9b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1/2 (hypot.f64 1 x))
1.4b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `sqrt-prod_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64`
2×	`pow1_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64`

Counts

2 → 45

Calls

2 calls:

7.0ms	(/.f64 1/2 (hypot.f64 1 x))
10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series155.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/.f64 1/2 (hypot.f64 1 x))
117.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify75.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4918	846
1	4918	846

prune44.0ms

Filtered

34 candidates to 51 candidates (-50.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	2	52

Merged error: 14.4b

Counts

52 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.9b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt_binary64`
85×	`*-un-lft-identity_binary64`
62×	`times-frac_binary64`
34×	`add-cube-cbrt_binary64`
28×	`distribute-lft-out_binary64`
16×	`difference-of-squares_binary64`
14×	`sqrt-prod_binary64`
12×	`associate-/r_binary64` `associate-/l_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`distribute-lft-out--_binary64`
6×	`add-log-exp_binary64`
4×	`pow1_binary64`
3×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `flip-+_binary64`

Counts

4 → 133

Calls

4 calls:

3.0ms	(/.f64 1/2 (hypot.f64 1 x))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
22.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/.f64 1/2 (hypot.f64 1 x))
38.0ms	(/.f64 1/2 (hypot.f64 1 x))
294.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
69.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify95.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4875	3758
1	4875	3758

prune181.0ms

Filtered

92 candidates to 145 candidates (-57.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	144	3	147

Merged error: 14.1b

Counts

147 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
0.0b	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
0.1b	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
0.9b	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-sqr-sqrt_binary64`
86×	`*-un-lft-identity_binary64`
82×	`times-frac_binary64`
44×	`add-cube-cbrt_binary64`
36×	`difference-of-squares_binary64`
25×	`unpow-prod-down_binary64` `cube-prod_binary64`
15×	`distribute-lft-out_binary64`
14×	`associate-/l*_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`associate-/r*_binary64` `sqr-pow_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
5×	`pow1_binary64`
4×	`associate-/l/_binary64` `div-inv_binary64`
3×	`pow-unpow_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `diff-log_binary64` `pow-pow_binary64` `cube-div_binary64` `div-sub_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 168

Calls

4 calls:

31.0ms	(/.f64 (-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
9.0ms	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
5.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
13.0ms	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))

series914.0ms

Counts

4 → 12

Calls

4 calls:

568.0ms	(/.f64 (-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
114.0ms	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
93.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
139.0ms	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))

simplify100.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5357	6100

prune333.0ms

Filtered

100 candidates to 180 candidates (-80.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	178	2	180
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	180	3	183

Merged error: 14.1b

Counts

183 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
0.1b	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
1.2b	(log.f64 (exp.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)))
31.0b	(-.f64 1/8 (log.f64 (exp.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
48×	`times-frac_binary64`
47×	`add-sqr-sqrt_binary64`
45×	`add-cube-cbrt_binary64`
34×	`log-pow_binary64`
32×	`exp-prod_binary64`
26×	`unpow-prod-down_binary64` `cube-prod_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`log-prod_binary64`
5×	`add-log-exp_binary64` `div-inv_binary64`
4×	`distribute-lft-out_binary64` `associate-/l*_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `associate--r+_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `rem-cube-cbrt_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `cube-div_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 140

Calls

4 calls:

9.0ms	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
6.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
11.0ms	(log.f64 (exp.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)))
23.0ms	(-.f64 1/8 (log.f64 (exp.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))))

series801.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
96.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
280.0ms	(log.f64 (exp.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)))
305.0ms	(-.f64 1/8 (log.f64 (exp.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))))

simplify56.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5003	2402

prune244.0ms

Filtered

87 candidates to 152 candidates (-74.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	152	3	155

Merged error: 14.1b

Counts

155 → 3

regimes25.0ms

Accuracy

0% (0.3b remaining)

Error of 14.8b against oracle of 14.5b and baseline of 14.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	55
1	36	55

end0.0ms

sample1.1s

Algorithm

intervals

Results

541.0ms	2141×	body	2048	valid
199.0ms	1031×	body	1024	valid
174.0ms	4128×	body	128	valid
61.0ms	454×	body	512	valid
20.0ms	246×	body	256	valid

Details

analyze2.0ms

sample37.0ms

simplify9.0ms

prune3.0ms

localize6.0ms

rewrite20.0ms

series155.0ms

simplify75.0ms

prune44.0ms

localize9.0ms

rewrite50.0ms

series440.0ms

simplify95.0ms

prune181.0ms

localize16.0ms

rewrite82.0ms

series914.0ms

simplify100.0ms

prune333.0ms

localize19.0ms

rewrite67.0ms

series801.0ms

simplify56.0ms

prune244.0ms

regimes25.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling