Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

277×

body

valid

simplify10.0ms

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: 29.2b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
28.7b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

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)))

series154.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* y.re y.re) (* y.im y.im))
36.0ms	(- (* x.im y.re) (* x.re y.im))
86.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	292	541
1	1273	493
2	5002	491

prune157.0ms

Filtered

64 candidates to 50 candidates (78.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	58	6	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	6	65

Merged error: 28.5b

Counts

65 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
15.0b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite21.0ms

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

Counts

4 → 86

Calls

4 calls:

3.0ms	(- (* x.im y.re) (* x.re 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)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* x.im y.re) (* x.re y.im))
110.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify96.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	304	910
1	990	857
2	3354	845
3	5001	845

prune243.0ms

Filtered

98 candidates to 75 candidates (76.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	94	10	104

Merged error: 26.2b

Counts

104 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
0.6b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
28.5b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`flip3--` `flip3-+` `associate-l` `associate-/r` `flip--` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`+-commutative` `sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 98

Calls

4 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
5.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
11.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series193.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* y.re y.re) (* y.im y.im))
43.0ms	(- (* x.im y.re) (* x.re y.im))
37.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
85.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify55.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	384	857
1	1929	753
2	5002	724

prune204.0ms

Filtered

110 candidates to 69 candidates (62.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	110	10	120

Merged error: 26.2b

Counts

120 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

14.5b	(* (* (cbrt (- (* x.im y.re) (* x.re y.im))) (cbrt (- (* x.im y.re) (* x.re y.im)))) (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))
15.5b	(cbrt (- (* x.im y.re) (* x.re y.im)))
15.5b	(cbrt (- (* x.im y.re) (* x.re y.im)))
15.5b	(cbrt (- (* x.im y.re) (* x.re y.im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

23.0ms	(* (* (cbrt (- (* x.im y.re) (* x.re y.im))) (cbrt (- (* x.im y.re) (* x.re y.im)))) (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))
3.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
3.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
3.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (* (cbrt (- (* x.im y.re) (* x.re y.im))) (cbrt (- (* x.im y.re) (* x.re y.im)))) (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))
109.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
119.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
113.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))

simplify69.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	617	1928
1	2361	1739
2	5002	1650

prune324.0ms

Filtered

114 candidates to 91 candidates (79.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	114	10	124

Merged error: 26.2b

Counts

124 → 10

regimes320.0ms

Accuracy

0% (2.8b remaining)

Error of 26.4b against oracle of 23.6b and baseline of 26.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	13
1	16	13

end0.0ms

sample614.0ms

Algorithm

intervals

Results

362.0ms

8490×

body

valid

Details

sample23.0ms

simplify10.0ms

prune2.0ms

localize9.0ms

rewrite16.0ms

series154.0ms

simplify40.0ms

prune157.0ms

localize16.0ms

rewrite21.0ms

series219.0ms

simplify96.0ms

prune243.0ms

localize15.0ms

rewrite26.0ms

series193.0ms

simplify55.0ms

prune204.0ms

localize13.0ms

rewrite36.0ms

series425.0ms

simplify69.0ms

prune324.0ms

regimes320.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample614.0ms

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