Details

sample30.0ms

Algorithm

intervals

Results

11.0ms

267×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 26.7b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.8b	(+ (* x.re y.re) (* x.im y.im))
26.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

3.0ms	(+ (* x.re y.re) (* x.im y.im))
12.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series37.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(+ (* x.re y.re) (* x.im y.im))
27.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify85.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	231	450
1	847	413
2	2837	412
3	5001	412

prune91.0ms

Filtered

48 candidates to 38 candidates (20.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	41	7	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	7	49

Merged error: 25.9b

Counts

49 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (* x.re y.re) (* x.im y.im))
16.8b	(/ (+ (* x.re y.re) (* x.im 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)))

rewrite20.0ms

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`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

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

series58.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (* x.re y.re) (* x.im y.im))
36.0ms	(/ (+ (* x.re y.re) (* x.im 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)))

simplify84.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2679	828
3	5002	828

prune128.0ms

Filtered

96 candidates to 74 candidates (22.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	93	10	103

Merged error: 23.4b

Counts

103 → 10

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
0.8b	(+ (* x.re y.re) (* x.im y.im))
26.1b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 86

Calls

3 calls:

5.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(+ (* x.re y.re) (* x.im y.im))
11.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series45.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(+ (* x.re y.re) (* x.im y.im))
29.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify49.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	352	774
1	1671	681
2	5002	653

prune106.0ms

Filtered

95 candidates to 59 candidates (37.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	95	10	105

Merged error: 23.4b

Counts

105 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (* x.re y.re) (* x.im y.im))
26.1b	(* (+ (* x.re y.re) (* x.im y.im)) (/ (/ 1 (sqrt (+ (* y.re y.re) (* y.im 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)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
173×	`add-sqr-sqrt`
150×	`associate-r`
141×	`sqrt-prod`
138×	`*-un-lft-identity`
134×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`sqrt-div`
14×	`associate-/r/`
13×	`add-cbrt-cube`
12×	`flip3-+` `flip-+` `unswap-sqr`
8×	`pow1` `div-inv`
6×	`div-exp` `add-log-exp`
5×	`prod-exp`
3×	`cbrt-undiv` `associate-l` `cbrt-unprod`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/`
1×	`+-commutative` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `sum-log` `-commutative`

Counts

4 → 228

Calls

4 calls:

3.0ms	(+ (* x.re y.re) (* x.im y.im))
41.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series49.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (* x.re y.re) (* x.im y.im))
27.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ (/ 1 (sqrt (+ (* y.re y.re) (* y.im 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)))

simplify54.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	975	3429
1	5001	2870

prune167.0ms

Filtered

240 candidates to 128 candidates (46.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	240	0	240
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	240	10	250

Merged error: 23.4b

Counts

250 → 10

regimes334.0ms

Accuracy

0% (2.6b remaining)

Error of 26.1b against oracle of 23.6b and baseline of 26.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13

end0.0ms

sample700.0ms

Algorithm

intervals

Results

365.0ms

8436×

body

valid

Details

sample30.0ms

simplify4.0ms

prune4.0ms

localize9.0ms

rewrite16.0ms

series37.0ms

simplify85.0ms

prune91.0ms

localize12.0ms

rewrite20.0ms

series58.0ms

simplify84.0ms

prune128.0ms

localize11.0ms

rewrite22.0ms

series45.0ms

simplify49.0ms

prune106.0ms

localize15.0ms

rewrite69.0ms

series49.0ms

simplify54.0ms

prune167.0ms

regimes334.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample700.0ms

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