Details

sample28.0ms

Algorithm

intervals

Results

12.0ms

283×

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

prune3.0ms

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: 28.3b

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))
27.7b	(/ (- (* 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:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
7.0ms	(- (* 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)))

series42.0ms

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))
27.0ms	(/ (- (* 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

prune109.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

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: 27.5b

Counts

65 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
16.0b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

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)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
34.0ms	(/ (- (* 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)))

simplify97.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (25.0ms)

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

prune127.0ms

Filtered

75 candidates to 98 candidates (-30.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	94	12	106

Merged error: 25.0b

Counts

106 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

9.4b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
32×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
10×	`sqrt-div`
9×	`associate-/r*`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 101

Calls

4 calls:

10.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (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)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series96.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (- (* 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)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify93.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	366	1263
1	1122	1192
2	3502	1157
3	5002	1157

prune138.0ms

Filtered

83 candidates to 113 candidates (-36.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	113	12	125

Merged error: 25.0b

Counts

125 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

23.9b	(/ (- (* x.im y.re) (* x.re y.im)) (* (cbrt (+ (* y.re y.re) (* y.im y.im))) (cbrt (+ (* y.re y.re) (* y.im y.im)))))
31.4b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
31.4b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
31.4b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

13.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (* (cbrt (+ (* y.re y.re) (* y.im y.im))) (cbrt (+ (* y.re y.re) (* y.im y.im)))))
3.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (* (cbrt (+ (* y.re y.re) (* y.im y.im))) (cbrt (+ (* y.re y.re) (* y.im y.im)))))
22.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
20.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
21.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify105.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	428	1021
1	1324	937
2	4392	898
3	5001	871

prune88.0ms

Filtered

70 candidates to 83 candidates (-18.6%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	3	6	9
Picked	0	1	1
Done	0	2	2
Total	83	12	95

Merged error: 25.0b

Counts

95 → 12

regimes346.0ms

Accuracy

0% (3.0b remaining)

Error of 25.8b against oracle of 22.7b and baseline of 25.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	13
1	16	13

end0.0ms

sample729.0ms

Algorithm

intervals

Results

368.0ms

8492×

body

valid

Details

sample28.0ms

simplify9.0ms

prune3.0ms

localize9.0ms

rewrite19.0ms

series42.0ms

simplify36.0ms

prune109.0ms

localize12.0ms

rewrite23.0ms

series56.0ms

simplify97.0ms

prune127.0ms

localize20.0ms

rewrite24.0ms

series96.0ms

simplify93.0ms

prune138.0ms

localize14.0ms

rewrite24.0ms

series154.0ms

simplify105.0ms

prune88.0ms

regimes346.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample729.0ms

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