Details

sample22.0ms

Algorithm

intervals

Results

11.0ms

267×

body

valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	36	7
2	48	7
3	66	7
4	72	7
5	72	7

prune2.0ms

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: 26.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.0b	(- (* x.im y.re) (* x.re y.im))
25.4b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite19.0ms

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:

7.0ms	(+ (* 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)))

series151.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* y.re y.re) (* y.im y.im))
39.0ms	(- (* x.im y.re) (* x.re y.im))
84.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify38.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	292	541
1	1273	493
2	5001	491

prune166.0ms

Filtered

64 candidates to 50 candidates (78.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	56	8	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	8	65

Merged error: 25.3b

Counts

65 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.6b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*`
11×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`div-sub` `associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`flip3--` `flip--`

Counts

4 → 266

Calls

4 calls:

19.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
9.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
112.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
42.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify94.0ms

Algorithm

egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	745	5703
1	2888	5224
2	5001	5172

prune478.0ms

Filtered

278 candidates to 147 candidates (52.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	273	5	278
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	278	8	286

Merged error: 21.2b

Counts

286 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.0b	(- (/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im))) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
16.4b	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
19.2b	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt` `associate-/r/` `add-log-exp`
6×	`times-frac` `associate-/r*`
5×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `div-exp` `div-inv`
3×	`distribute-rgt-out--`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l*`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 76

Calls

4 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
13.0ms	(- (/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im))) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* y.re y.re) (* y.im y.im))
120.0ms	(- (/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im))) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
46.0ms	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
46.0ms	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	385	746
1	1875	664
2	5001	660

prune191.0ms

Filtered

88 candidates to 65 candidates (73.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	91	5	96

Merged error: 20.4b

Counts

96 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (/ x.re (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ y.im (sqrt (+ (* y.re y.re) (* y.im y.im)))))
16.4b	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
26.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
51×	`times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
30×	`sqrt-prod`
24×	`associate-r` `associate-l`
21×	`add-exp-log` `add-cbrt-cube`
9×	`unswap-sqr`
8×	`pow1` `sqrt-div`
6×	`cbrt-undiv` `div-exp` `associate-/r/`
5×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
4×	`add-log-exp`
3×	`associate-/r*` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l`

Counts

4 → 130

Calls

4 calls:

22.0ms	(* (/ x.re (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ y.im (sqrt (+ (* y.re y.re) (* y.im y.im)))))
6.0ms	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series167.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (/ x.re (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ y.im (sqrt (+ (* y.re y.re) (* y.im y.im)))))
46.0ms	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	576	1547
1	2594	1391
2	5001	1322

prune301.0ms

Filtered

142 candidates to 102 candidates (71.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	142	5	147

Merged error: 20.4b

Counts

147 → 5

regimes122.0ms

Accuracy

38.4% (1.7b remaining)

Error of 23.9b against oracle of 22.2b and baseline of 25.0b

bsearch52.0ms

Steps

Iters	Range		Point
9	4.930736435694452e+38	1.444517049223159e+44	1.3996110887003636e+39

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	28
1	31	28

end0.0ms

sample578.0ms

Algorithm

intervals

Results

364.0ms

8452×

body

valid

Details

sample22.0ms

simplify11.0ms

prune2.0ms

localize10.0ms

rewrite19.0ms

series151.0ms

simplify38.0ms

prune166.0ms

localize12.0ms

rewrite50.0ms

series277.0ms

simplify94.0ms

prune478.0ms

localize15.0ms

rewrite32.0ms

series239.0ms

simplify52.0ms

prune191.0ms

localize14.0ms

rewrite41.0ms

series167.0ms

simplify64.0ms

prune301.0ms

regimes122.0ms

bsearch52.0ms

simplify1.0ms

end0.0ms

sample578.0ms

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