Details

analyze600.0ms

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

12.0ms	256×	body	80	valid
1.0ms	19×	body	80	invalid

simplify165.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (163.0ms)

Iter	Nodes	Cost
0	4841	15
1	4841	15

prune4.0ms

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: 25.2b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.2b	(- (* x.im y.re) (* x.re y.im))
24.8b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 54

Calls

3 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series41.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
10.0ms	(- (* x.im y.re) (* x.re y.im))
26.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5785	976

prune99.0ms

Filtered

49 candidates to 63 candidates (-28.6%)

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: 20.8b

Counts

64 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
13.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 85

Calls

4 calls:

3.0ms	(- (* x.im y.re) (* x.re y.im))
9.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
37.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5760	1553

prune114.0ms

Filtered

77 candidates to 97 candidates (-26.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	97	7	104

Merged error: 20.8b

Counts

104 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

8.1b	(* y.re (/ x.im (sqrt (+ (* y.re y.re) (* y.im y.im)))))
26.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
19×	`sqrt-prod`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`sqrt-div`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `unswap-sqr`
2×	`prod-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

11.0ms	(* y.re (/ x.im (sqrt (+ (* y.re y.re) (* y.im y.im)))))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series34.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* y.re (/ x.im (sqrt (+ (* y.re y.re) (* y.im y.im)))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify39.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5040	1084

prune107.0ms

Filtered

75 candidates to 101 candidates (-34.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	101	7	108

Merged error: 20.8b

Counts

108 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

12.4b	(* (* (cbrt (- (* x.im y.re) (* x.re y.im))) (cbrt (- (* x.im y.re) (* x.re y.im)))) (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))
14.2b	(cbrt (- (* x.im y.re) (* x.re y.im)))
14.2b	(cbrt (- (* x.im y.re) (* x.re y.im)))
14.2b	(cbrt (- (* x.im y.re) (* x.re y.im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-div`
25×	`add-sqr-sqrt`
24×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
19×	`cbrt-prod`
16×	`add-exp-log` `frac-times`
15×	`flip3--` `flip--`
12×	`associate-*l/`
10×	`add-cbrt-cube`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod`
5×	`associate-*r/`
4×	`add-log-exp`
3×	`pow1/3` `pow-prod-down` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`flip3-+` `associate-l` `*-commutative` `flip-+` `div-inv`

Counts

4 → 102

Calls

4 calls:

22.0ms	(* (* (cbrt (- (* x.im y.re) (* x.re y.im))) (cbrt (- (* x.im y.re) (* x.re y.im)))) (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))
3.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
3.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
4.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))

series138.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (* (cbrt (- (* x.im y.re) (* x.re y.im))) (cbrt (- (* x.im y.re) (* x.re y.im)))) (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))
35.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
37.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
38.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4965	2743
1	4965	2743

prune117.0ms

Filtered

91 candidates to 114 candidates (-25.3%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	114	7	121

Merged error: 20.8b

Counts

121 → 7

regimes388.0ms

Accuracy

0% (1.2b remaining)

Error of 22.6b against oracle of 21.3b and baseline of 22.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	34
1	50	34

end0.0ms

sample589.0ms

Algorithm

intervals

Results

366.0ms	8000×	body	80	valid
22.0ms	489×	body	80	invalid

Details

analyze600.0ms

sample23.0ms

simplify165.0ms

prune4.0ms

localize13.0ms

rewrite16.0ms

series41.0ms

simplify47.0ms

prune99.0ms

localize12.0ms

rewrite22.0ms

series58.0ms

simplify50.0ms

prune114.0ms

localize14.0ms

rewrite25.0ms

series34.0ms

simplify39.0ms

prune107.0ms

localize14.0ms

rewrite36.0ms

series138.0ms

simplify59.0ms

prune117.0ms

regimes388.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample589.0ms

Profiling