Details

sample27.0ms

Algorithm

intervals

Results

12.0ms

271×

body

valid

simplify9.0ms

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

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: 28.4b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.8b	(- (* x.im y.re) (* x.re y.im))
27.7b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite20.0ms

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

series41.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
10.0ms	(- (* x.im y.re) (* x.re y.im))
26.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify36.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (30.0ms)

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

prune111.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	57	7	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	8	65

Merged error: 27.6b

Counts

65 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* x.im y.re) (* x.re y.im))
17.2b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
27.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms

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:

5.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ (- (* 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)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
33.0ms	(/ (- (* x.im y.re) (* x.re 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)))

simplify94.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	304	910
1	990	857
2	3340	845
3	5003	845

prune126.0ms

Filtered

75 candidates to 98 candidates (-30.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	97	9	106

Merged error: 24.5b

Counts

106 → 9

localize205.0ms

Local error

Found 4 expressions with local error:

9.0b	(* (/ 1 (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
27.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

137×	`add-sqr-sqrt`
108×	`sqrt-prod`
99×	`times-frac`
57×	`*-un-lft-identity`
45×	`add-cube-cbrt`
33×	`associate-r` `associate-l`
28×	`unswap-sqr`
26×	`add-exp-log`
16×	`add-cbrt-cube`
14×	`sqrt-div`
9×	`pow1`
8×	`div-exp` `prod-exp`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`rec-exp` `1-exp` `div-inv`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 163

Calls

4 calls:

33.0ms	(* (/ 1 (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* 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)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series48.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (/ 1 (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(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

175 → 175

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	568	3021
1	2570	2733
2	5001	2579

prune168.0ms

Filtered

104 candidates to 175 candidates (-68.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	175	9	184

Merged error: 24.5b

Counts

184 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

9.1b	(cbrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
27.7b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
27.7b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
27.7b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

5.0ms	(cbrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series147.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(cbrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
26.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
26.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
28.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	380	1586
1	1348	1478
2	5001	1468

prune167.0ms

Filtered

109 candidates to 132 candidates (-21.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	132	9	141

Merged error: 24.5b

Counts

141 → 9

regimes505.0ms

Accuracy

25.5% (2.2b remaining)

Error of 24.9b against oracle of 22.7b and baseline of 25.7b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	20
1	25	20
2	25	20

end0.0ms

sample772.0ms

Algorithm

intervals

Results

394.0ms

8428×

body

valid

Details

sample27.0ms

simplify9.0ms

prune4.0ms

localize10.0ms

rewrite20.0ms

series41.0ms

simplify36.0ms

prune111.0ms

localize12.0ms

rewrite22.0ms

series54.0ms

simplify94.0ms

prune126.0ms

localize205.0ms

rewrite53.0ms

series48.0ms

simplify75.0ms

prune168.0ms

localize15.0ms

rewrite33.0ms

series147.0ms

simplify49.0ms

prune167.0ms

regimes505.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample772.0ms

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