Details

analyze530.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

sample23.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
1.0ms	19×	body	80	invalid

simplify312.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (303.0ms)

Iter	Nodes	Cost
0	5128	30

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: 26.6b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.7b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
26.0b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/r_binary64` `pow1_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 54

Calls

3 calls:

4.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
9.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series166.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
41.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
105.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify91.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5717	1814

prune84.0ms

Filtered

51 candidates to 63 candidates (-23.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	7	64

Merged error: 25.8b

Counts

64 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
16.5b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
31.1b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
31.1b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
28×	`sqrt-prod_binary64`
25×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
10×	`distribute-lft-out_binary64` `unpow-prod-down_binary64`
8×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 95

Calls

4 calls:

4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
14.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
133.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
22.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
23.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5186	3239

prune105.0ms

Filtered

78 candidates to 107 candidates (-37.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	104	10	114

Merged error: 23.3b

Counts

114 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
16.5b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
31.1b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
31.1b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
30×	`sqrt-prod_binary64`
25×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out_binary64` `unpow-prod-down_binary64`
8×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 97

Calls

4 calls:

4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
14.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
11.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
137.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
26.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify99.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4917	3269
1	4917	3269

prune131.0ms

Filtered

77 candidates to 109 candidates (-41.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	109	10	119

Merged error: 23.3b

Counts

119 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
2.7b	(exp.f64 (log.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
26.0b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (exp.f64 (log.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
32.3b	(log.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64`
30×	`log-prod_binary64`
25×	`exp-sum_binary64`
24×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64`
12×	`distribute-lft-out_binary64` `unpow-prod-down_binary64`
8×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `log-div_binary64`
4×	`exp-diff_binary64` `exp-prod_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `log-pow_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 98

Calls

4 calls:

4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
9.0ms	(exp.f64 (log.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
15.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (exp.f64 (log.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
8.0ms	(log.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

series195.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
20.0ms	(exp.f64 (log.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
99.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (exp.f64 (log.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
32.0ms	(log.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify113.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5749	3155

prune78.0ms

Filtered

69 candidates to 110 candidates (-59.4%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	108	12	120

Merged error: 23.3b

Counts

120 → 12

regimes127.0ms

Accuracy

26.2% (2.3b remaining)

Error of 25.2b against oracle of 22.9b and baseline of 26.0b

bsearch1.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	105
1	64	105

end0.0ms

sample577.0ms

Algorithm

intervals

Results

348.0ms	8000×	body	80	valid
20.0ms	477×	body	80	invalid

Details

analyze530.0ms

sample23.0ms

simplify312.0ms

prune1.0ms

localize10.0ms

rewrite18.0ms

series166.0ms

simplify91.0ms

prune84.0ms

localize18.0ms

rewrite34.0ms

series220.0ms

simplify80.0ms

prune105.0ms

localize15.0ms

rewrite39.0ms

series227.0ms

simplify99.0ms

prune131.0ms

localize15.0ms

rewrite39.0ms

series195.0ms

simplify113.0ms

prune78.0ms

regimes127.0ms

bsearch1.0ms

simplify4.0ms

end0.0ms

sample577.0ms

Profiling