Details

analyze1.0ms

Algorithm

Search

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

sample40.0ms

Algorithm

intervals

Results

22.0ms	93×	body	1280	valid
5.0ms	125×	body	80	valid
4.0ms	22×	body	640	valid
2.0ms	12×	body	320	valid
0.0ms	4×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	44	10
1	44	10

prune6.0ms

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: 15.9b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1/2 (hypot.f64 1 x))
2.1b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite14.0ms

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:

3.0ms	(/.f64 1/2 (hypot.f64 1 x))
10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series16.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/.f64 1/2 (hypot.f64 1 x))
11.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify272.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4833	557
1	4833	557

prune65.0ms

Filtered

34 candidates to 51 candidates (-50.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	3	52

Merged error: 15.4b

Counts

52 → 3

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 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
1.6b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r_binary64` `associate-/l_binary64`
4×	`pow1_binary64` `distribute-lft-out_binary64`
2×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `div-inv_binary64` `div-exp_binary64` `sqrt-prod_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 82

Calls

4 calls:

3.0ms	(/.f64 1/2 (hypot.f64 1 x))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
8.0ms	(+.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)))

series27.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/.f64 1/2 (hypot.f64 1 x))
5.0ms	(/.f64 1/2 (hypot.f64 1 x))
11.0ms	(+.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)))

simplify61.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5259	899

prune131.0ms

Filtered

67 candidates to 94 candidates (-40.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	89	5	94
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	92	5	97

Merged error: 15.1b

Counts

97 → 5

localize17.0ms

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 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.1b	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
1.6b	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

115×	`add-sqr-sqrt_binary64`
74×	`*-un-lft-identity_binary64`
70×	`times-frac_binary64`
36×	`difference-of-squares_binary64`
35×	`add-cube-cbrt_binary64`
25×	`unpow-prod-down_binary64` `cube-prod_binary64`
15×	`distribute-lft-out_binary64`
10×	`associate-/l*_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`sqr-pow_binary64`
6×	`distribute-lft-out--_binary64`
5×	`pow1_binary64`
4×	`associate-/r*_binary64`
3×	`pow-unpow_binary64` `div-inv_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-prod_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` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `unpow3_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

4 → 149

Calls

4 calls:

24.0ms	(/.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))))
10.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
5.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
12.0ms	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))

series107.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/.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))))
11.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
11.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
18.0ms	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))

simplify67.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5110	3684

prune272.0ms

Filtered

87 candidates to 161 candidates (-85.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	161	5	166

Merged error: 15.1b

Counts

166 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
0.1b	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
0.1b	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
1.5b	(-.f64 (.f64 1/8 1/8) (.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac_binary64`
49×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
39×	`unpow-prod-down_binary64` `cube-prod_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow-unpow_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `rem-cube-cbrt_binary64` `div-inv_binary64` `pow-exp_binary64`
3×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `cube-div_binary64` `div-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-squares_binary64` `flip--_binary64`

Counts

4 → 150

Calls

4 calls:

5.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
5.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
5.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
6.0ms	(-.f64 (.f64 1/8 1/8) (.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
11.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
11.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
25.0ms	(-.f64 (.f64 1/8 1/8) (.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)))

simplify53.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5289	1647

prune280.0ms

Filtered

78 candidates to 162 candidates (-107.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	161	6	167

Merged error: 15.0b

Counts

167 → 6

regimes89.0ms

Accuracy

0% (0.3b remaining)

Error of 14.6b against oracle of 14.3b and baseline of 14.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	66
1	53	66

end0.0ms

sample1.2s

Algorithm

intervals

Results

689.0ms	2822×	body	1280	valid
179.0ms	4095×	body	80	valid
123.0ms	599×	body	640	valid
41.0ms	307×	body	320	valid
16.0ms	177×	body	160	valid

Details

analyze1.0ms

sample40.0ms

simplify6.0ms

prune6.0ms

localize6.0ms

rewrite14.0ms

series16.0ms

simplify272.0ms

prune65.0ms

localize9.0ms

rewrite23.0ms

series27.0ms

simplify61.0ms

prune131.0ms

localize17.0ms

rewrite58.0ms

series107.0ms

simplify67.0ms

prune272.0ms

localize22.0ms

rewrite27.0ms

series58.0ms

simplify53.0ms

prune280.0ms

regimes89.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling