Details

sample26.0ms

Algorithm

intervals

Results

11.0ms

266×

body

valid

simplify165.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (163.0ms)

Iter	Nodes	Cost
0	4841	15
1	4841	15

prune3.0ms

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: 25.1b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.2b	(- (* x.im y.re) (* x.re y.im))
24.7b	(/ (- (* 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 → 55

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)))

series44.0ms

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))
29.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5785	980

prune96.0ms

Filtered

49 candidates to 64 candidates (-30.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	56	8	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	9	65

Merged error: 21.9b

Counts

65 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* x.im y.re) (* x.re y.im))
16.0b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite21.0ms

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 → 86

Calls

4 calls:

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

series57.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (* x.im y.re) (* x.re y.im))
34.0ms	(/ (- (* 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)))

simplify47.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5760	1557

prune123.0ms

Filtered

77 candidates to 98 candidates (-27.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	98	9	107

Merged error: 21.9b

Counts

107 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

9.9b	(* y.im (/ x.re (sqrt (+ (* y.re y.re) (* y.im y.im)))))
31.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.0b	(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.im (/ x.re (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)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* y.im (/ x.re (sqrt (+ (* y.re y.re) (* y.im y.im)))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify36.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4989	1084
1	4989	1084

prune117.0ms

Filtered

75 candidates to 101 candidates (-34.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	101	9	110

Merged error: 21.9b

Counts

110 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

7.6b	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
8.3b	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
9.0b	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))
12.5b	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
30×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
6×	`associate-l` `associate-/r` `associate-/l`
4×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 126

Calls

4 calls:

5.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))
9.0ms	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))
15.0ms	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))

simplify60.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5147	1682

prune115.0ms

Filtered

104 candidates to 138 candidates (-32.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	1	4	5
Picked	1	0	1
Done	0	3	3
Total	138	9	147

Merged error: 21.9b

Counts

147 → 9

regimes412.0ms

Accuracy

0% (1.1b remaining)

Error of 24.1b against oracle of 23.0b and baseline of 24.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	36
1	53	36

end0.0ms

sample719.0ms

Algorithm

intervals

Results

357.0ms

8484×

body

valid

Details

sample26.0ms

simplify165.0ms

prune3.0ms

localize9.0ms

rewrite16.0ms

series44.0ms

simplify46.0ms

prune96.0ms

localize13.0ms

rewrite21.0ms

series57.0ms

simplify47.0ms

prune123.0ms

localize15.0ms

rewrite25.0ms

series32.0ms

simplify36.0ms

prune117.0ms

localize11.0ms

rewrite31.0ms

series55.0ms

simplify60.0ms

prune115.0ms

regimes412.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample719.0ms

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