Details

sample34.0ms

Algorithm

intervals

Results

16.0ms

267×

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

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: 28.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.0b	(- (* x.im y.re) (* x.re y.im))
28.3b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite18.0ms

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

series50.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ (* y.re y.re) (* y.im y.im))
12.0ms	(- (* x.im y.re) (* x.re y.im))
31.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify30.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5289	981

prune120.0ms

Filtered

49 candidates to 64 candidates (-30.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	53	11	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	11	65

Merged error: 23.5b

Counts

65 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

5.3b	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
7.4b	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
12.5b	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))
12.6b	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))

rewrite35.0ms

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:

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
16.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
14.0ms	(* 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))))

simplify42.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5333	1682

prune185.0ms

Filtered

104 candidates to 138 candidates (-32.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	133	5	138
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	138	11	149

Merged error: 23.5b

Counts

149 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

5.3b	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
12.5b	(* 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)))

rewrite26.0ms

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

series43.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
14.0ms	(* 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)))

simplify75.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4945	1169
1	4945	1169

prune142.0ms

Filtered

82 candidates to 105 candidates (-28.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	105	11	116

Merged error: 23.5b

Counts

116 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

7.4b	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
12.6b	(* 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)))

rewrite26.0ms

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

series44.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
15.0ms	(* y.im (/ x.re (+ (* 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)))

simplify54.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4986	1169
1	4986	1169

prune106.0ms

Filtered

82 candidates to 105 candidates (-28.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	106	10	116

Merged error: 23.5b

Counts

116 → 10

regimes484.0ms

Accuracy

46.4% (1.8b remaining)

Error of 24.0b against oracle of 22.2b and baseline of 25.5b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	97
1	38	97

end0.0ms

sample848.0ms

Algorithm

intervals

Results

410.0ms

8461×

body

valid

Details

sample34.0ms

simplify3.0ms

prune4.0ms

localize10.0ms

rewrite18.0ms

series50.0ms

simplify30.0ms

prune120.0ms

localize15.0ms

rewrite35.0ms

series64.0ms

simplify42.0ms

prune185.0ms

localize14.0ms

rewrite26.0ms

series43.0ms

simplify75.0ms

prune142.0ms

localize15.0ms

rewrite26.0ms

series44.0ms

simplify54.0ms

prune106.0ms

regimes484.0ms

bsearch1.0ms

simplify1.0ms

end0.0ms

sample848.0ms

Profiling