Details

sample22.0ms

Algorithm

intervals

Results

9.0ms

268×

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 24.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.0b	(+ (* x.re y.re) (* x.im y.im))
23.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

208×	`*-un-lft-identity`
85×	`distribute-lft-out`
76×	`associate-l`
56×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`swap-sqr`
8×	`associate-/r*`
7×	`associate-/l*` `add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow1`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 118

Calls

3 calls:

16.0ms	(+ (* y.re y.re) (* y.im y.im))
16.0ms	(+ (* x.re y.re) (* x.im y.im))
32.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series148.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* y.re y.re) (* y.im y.im))
32.0ms	(+ (* x.re y.re) (* x.im y.im))
86.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify132.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (120.0ms)

Iter	Nodes	Cost
0	272	1069
1	1142	1024
2	4550	1021
3	5002	1020

prune146.0ms

Filtered

127 candidates to 51 candidates (40.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	116	11	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	11	128

Merged error: 23.3b

Counts

128 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

3825×	`*-un-lft-identity`
1914×	`times-frac`
1475×	`distribute-lft-out`
1432×	`sqrt-prod`
1296×	`associate-l`
519×	`add-sqr-sqrt`
517×	`add-cube-cbrt`
358×	`swap-sqr`
97×	`associate-/l*`
33×	`associate-/r*`
32×	`sqrt-div`
28×	`associate-/r/`
27×	`associate-/l/`
18×	`flip3-+` `flip-+`
14×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 1197

Calls

4 calls:

83.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
36.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
116.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify249.0ms

Algorithm

egg-herbie

Counts

1209 → 1209

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	824	20608
1	2372	19996
2	5002	19963

prune472.0ms

Filtered

1209 candidates to 157 candidates (13.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	1201	8	1209
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	1209	11	1220

Merged error: 21.7b

Counts

1220 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
14.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

1291×	`*-un-lft-identity`
507×	`sqrt-prod`
478×	`distribute-lft-out`
473×	`associate-/r*`
455×	`associate-l`
391×	`frac-times`
252×	`add-sqr-sqrt`
210×	`associate-/l*`
209×	`times-frac`
204×	`add-cube-cbrt`
124×	`swap-sqr`
83×	`associate-r`
44×	`clear-num`
43×	`frac-2neg`
38×	`associate-/l/`
28×	`add-exp-log`
24×	`flip3-+` `flip-+`
23×	`associate-*r/`
18×	`add-cbrt-cube`
17×	`associate-*l/`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r/` `un-div-inv`
5×	`cbrt-undiv`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 746

Calls

4 calls:

124.0ms	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
33.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
19.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
114.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
47.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify143.0ms

Algorithm

egg-herbie

Counts

758 → 758

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1433	9817
1	5001	9336

prune549.0ms

Filtered

758 candidates to 175 candidates (23.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	755	3	758
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	757	12	769

Merged error: 21.7b

Counts

769 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (* (cbrt 1) (cbrt 1)) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (cbrt 1)))
14.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite3.0s

Algorithm

rewrite-expression-head

Rules

34958×	`*-un-lft-identity`
30180×	`times-frac`
18207×	`add-sqr-sqrt`
13105×	`sqrt-prod`
11898×	`associate-l`
10705×	`distribute-lft-out`
10593×	`cbrt-prod`
8407×	`add-cube-cbrt`
6319×	`associate-r`
5751×	`unswap-sqr`
4075×	`swap-sqr`
355×	`*-commutative`
239×	`div-inv`
195×	`associate-/l*`
166×	`associate-/r/`
150×	`sqrt-div`
128×	`add-cbrt-cube`
98×	`associate-/r*`
77×	`flip3-+` `flip-+`
71×	`cbrt-undiv`
54×	`cbrt-unprod`
47×	`add-exp-log`
35×	`associate-/l/`
23×	`associate-*r/`
20×	`div-exp`
12×	`prod-exp`
6×	`pow1` `un-div-inv`
5×	`clear-num`
4×	`frac-2neg` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 12040

Calls

4 calls:

402.0ms	(/ (* (* (cbrt 1) (cbrt 1)) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (cbrt 1)))
40.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
20.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
20.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (* (* (cbrt 1) (cbrt 1)) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (cbrt 1)))
123.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
52.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify4.2s

Algorithm

egg-herbie

Counts

12052 → 12052

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	5002	403882

prune6.5s

Filtered

12052 candidates to 1303 candidates (10.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	12047	5	12052
Fresh	5	5	10
Picked	0	1	1
Done	0	1	1
Total	12052	12	12064

Merged error: 21.7b

Counts

12064 → 12

regimes195.0ms

Accuracy

0% (2.7b remaining)

Error of 25.5b against oracle of 22.8b and baseline of 25.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	19
1	25	19

end0.0ms

sample514.0ms

Algorithm

intervals

Results

300.0ms

8505×

body

valid