Details

sample21.0ms

Algorithm

intervals

Results

11.0ms

268×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	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: 30.3b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x.re y.re) (* x.im y.im))
29.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite13.0ms

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×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 42

Calls

2 calls:

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

series107.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(+ (* x.re y.re) (* x.im y.im))
77.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify81.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	231	450
1	847	413
2	2837	412
3	5001	412

prune143.0ms

Filtered

48 candidates to 38 candidates (79.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	38	10	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	10	49

Merged error: 29.5b

Counts

49 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
33.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite66.0ms

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

Counts

4 → 264

Calls

4 calls:

21.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
17.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
5.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
106.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
33.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify90.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	714	5680
1	2516	5201
2	5001	5144

prune587.0ms

Filtered

276 candidates to 145 candidates (52.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	269	7	276
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	273	13	286

Merged error: 28.3b

Counts

286 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

13.8b	(* (/ 1 (* (cbrt (+ (* y.re y.re) (* y.im y.im))) (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (+ (* x.re y.re) (* x.im y.im)) (cbrt (+ (* y.re y.re) (* y.im y.im)))))
34.4b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
34.4b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
34.4b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
43×	`add-sqr-sqrt`
33×	`times-frac`
25×	`*-un-lft-identity`
24×	`associate-r`
22×	`add-cube-cbrt`
21×	`cbrt-prod`
20×	`cbrt-div` `prod-exp`
18×	`add-cbrt-cube`
15×	`div-exp` `associate-l`
10×	`flip3-+` `associate-/r/` `flip-+`
9×	`unswap-sqr`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1`
5×	`frac-times`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`pow1/3` `associate-r/` `associate-l/`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 119

Calls

4 calls:

36.0ms	(* (/ 1 (* (cbrt (+ (* y.re y.re) (* y.im y.im))) (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (+ (* x.re y.re) (* x.im y.im)) (cbrt (+ (* y.re y.re) (* y.im y.im)))))
4.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (/ 1 (* (cbrt (+ (* y.re y.re) (* y.im y.im))) (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (+ (* x.re y.re) (* x.im y.im)) (cbrt (+ (* y.re y.re) (* y.im y.im)))))
91.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
93.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
96.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify85.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	614	2237
1	3263	1929
2	5001	1759

prune386.0ms

Filtered

131 candidates to 93 candidates (71.0%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	131	13	144

Merged error: 28.3b

Counts

144 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

33.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.4b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
34.4b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
91.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
94.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	141	444
1	440	420
2	1471	416
3	5001	414

prune330.0ms

Filtered

68 candidates to 60 candidates (88.2%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	68	13	81

Merged error: 28.3b

Counts

81 → 13

regimes211.0ms

Accuracy

0% (2.8b remaining)

Error of 26.3b against oracle of 23.4b and baseline of 26.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13

end0.0ms

sample570.0ms

Algorithm

intervals

Results

356.0ms

8455×

body

valid

Details

sample21.0ms

simplify4.0ms

prune2.0ms

localize9.0ms

rewrite13.0ms

series107.0ms

simplify81.0ms

prune143.0ms

localize12.0ms

rewrite66.0ms

series249.0ms

simplify90.0ms

prune587.0ms

localize16.0ms

rewrite53.0ms

series422.0ms

simplify85.0ms

prune386.0ms

localize22.0ms

rewrite19.0ms

series258.0ms

simplify51.0ms

prune330.0ms

regimes211.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample570.0ms

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