Details

sample31.0ms

Algorithm

intervals

Results

12.0ms

278×

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: 28.5b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
27.8b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

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)))

series40.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (* 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)))

simplify96.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	251	464
1	938	427
2	3490	426
3	5002	426

prune92.0ms

Filtered

39 candidates to 50 candidates (-28.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	43	7	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	7	51

Merged error: 27.6b

Counts

51 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
18.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.7b	(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)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
43.0ms	(/ (- (* 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 (23.0ms)

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

prune122.0ms

Filtered

75 candidates to 98 candidates (-30.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	95	10	105

Merged error: 22.9b

Counts

105 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
18.9b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
30.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite20.0ms

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

Counts

4 → 85

Calls

4 calls:

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

series44.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
23.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify66.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	264	887
1	808	842
2	2343	837
3	5001	837

prune116.0ms

Filtered

74 candidates to 97 candidates (-31.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	97	10	107

Merged error: 22.9b

Counts

107 → 10

localize11.0ms

Local error

Found 3 expressions with local error:

0.6b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
1.1b	(- (* x.im y.re) (* x.re y.im))
27.4b	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
55×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `pow-flip` `flip3-+` `diff-log` `flip-+` `inv-pow`

Counts

3 → 127

Calls

3 calls:

9.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
3.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

series56.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
10.0ms	(- (* x.im y.re) (* x.re y.im))
18.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	478	1746
1	2150	1597
2	5002	1509

prune81.0ms

Filtered

75 candidates to 136 candidates (-81.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	136	10	146

Merged error: 22.9b

Counts

146 → 10

regimes362.0ms

Accuracy

-12.8% (3.6b remaining)

Error of 26.6b against oracle of 23.0b and baseline of 26.2b

bsearch51.0ms

Steps

Iters	Range		Point
11	2.0007175661403905e+66	2.104971704307965e+86	1.7617882023142252e+86
9	-9.058200306615924e+29	-5.010716216231439e+23	-8.929632650564872e+29

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	24
1	29	24
2	29	24

end0.0ms

sample690.0ms

Algorithm

intervals

Results

381.0ms

8476×

body

valid

Details

sample31.0ms

simplify9.0ms

prune4.0ms

localize9.0ms

rewrite12.0ms

series40.0ms

simplify96.0ms

prune92.0ms

localize14.0ms

rewrite21.0ms

series65.0ms

simplify94.0ms

prune122.0ms

localize13.0ms

rewrite20.0ms

series44.0ms

simplify66.0ms

prune116.0ms

localize11.0ms

rewrite25.0ms

series56.0ms

simplify55.0ms

prune81.0ms

regimes362.0ms

bsearch51.0ms

simplify2.0ms

end0.0ms

sample690.0ms

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