Details

sample27.0ms

Algorithm

intervals

Results

11.0ms

270×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	68	15
1	68	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: 25.7b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.4b	(- (* x.im y.re) (* x.re y.im))
25.1b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite17.0ms

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:

3.0ms	(+ (* 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))
27.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify31.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5289	981

prune101.0ms

Filtered

49 candidates to 64 candidates (-30.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	55	9	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	9	65

Merged error: 19.3b

Counts

65 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

6.5b	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
7.9b	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
9.0b	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))
10.4b	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))

rewrite32.0ms

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:

7.0ms	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))
9.0ms	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify47.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5333	1682

prune149.0ms

Filtered

104 candidates to 138 candidates (-32.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	133	5	138
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	139	8	147

Merged error: 19.3b

Counts

147 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

7.9b	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
9.0b	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))
29.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
15×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`sqrt-prod`
4×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 93

Calls

4 calls:

6.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))
5.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4986	1169
1	4986	1169

prune141.0ms

Filtered

82 candidates to 105 candidates (-28.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	105	8	113

Merged error: 19.3b

Counts

113 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

6.5b	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
10.4b	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))
29.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
15×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`sqrt-prod`
4×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 93

Calls

4 calls:

9.0ms	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
18.0ms	(* y.re (/ x.im (+ (* 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)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

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))))
5.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4945	1169
1	4945	1169

prune91.0ms

Filtered

82 candidates to 105 candidates (-28.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	105	8	113

Merged error: 19.3b

Counts

113 → 8

regimes509.0ms

Accuracy

49.9% (1.5b remaining)

Error of 23.8b against oracle of 22.2b and baseline of 25.3b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	95
1	34	95

end0.0ms

sample770.0ms

Algorithm

intervals

Results

378.0ms

8502×

body

valid

Details

sample27.0ms

simplify3.0ms

prune3.0ms

localize13.0ms

rewrite17.0ms

series41.0ms

simplify31.0ms

prune101.0ms

localize10.0ms

rewrite32.0ms

series50.0ms

simplify47.0ms

prune149.0ms

localize13.0ms

rewrite24.0ms

series38.0ms

simplify62.0ms

prune141.0ms

localize19.0ms

rewrite44.0ms

series39.0ms

simplify80.0ms

prune91.0ms

regimes509.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample770.0ms

Profiling