Details

sample22.0ms

Algorithm

intervals

Results

11.0ms

270×

body

valid

simplify11.0ms

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: 29.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(- (* x.im y.re) (* x.re y.im))
28.6b	(/ (- (* 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)))

series146.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* y.re y.re) (* y.im y.im))
37.0ms	(- (* x.im y.re) (* x.re y.im))
83.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify38.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (31.0ms)

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

prune144.0ms

Filtered

64 candidates to 50 candidates (78.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	6	65

Merged error: 28.3b

Counts

65 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
16.7b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.5b	(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)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* x.im y.re) (* x.re y.im))
104.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify96.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (25.0ms)

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

prune222.0ms

Filtered

98 candidates to 75 candidates (76.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	95	9	104

Merged error: 26.5b

Counts

104 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

14.7b	(* (/ 1 (* (cbrt (+ (* y.re y.re) (* y.im y.im))) (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re y.im)) (cbrt (+ (* y.re y.re) (* y.im y.im)))))
32.5b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
32.5b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
32.5b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite42.0ms

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:

27.0ms	(* (/ 1 (* (cbrt (+ (* y.re y.re) (* y.im y.im))) (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re 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)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (/ 1 (* (cbrt (+ (* y.re y.re) (* y.im y.im))) (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re y.im)) (cbrt (+ (* y.re y.re) (* y.im y.im)))))
88.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
88.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
89.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	600	2237
1	2807	1929
2	5001	1759

prune304.0ms

Filtered

131 candidates to 92 candidates (70.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	131	9	140

Merged error: 26.5b

Counts

140 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

16.7b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.6b	(cbrt (pow (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) 3))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-prod` `times-frac`
50×	`add-sqr-sqrt`
48×	`add-cube-cbrt` `*-un-lft-identity`
36×	`sqrt-prod`
24×	`unpow-prod-down` `cube-prod`
10×	`sqrt-div`
6×	`pow1` `add-exp-log` `associate-/r*` `associate-/r/` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`cbrt-undiv` `cube-div` `cube-mult` `cbrt-div` `flip3--` `frac-2neg` `pow1/3` `unpow3` `div-sub` `div-exp` `clear-num` `flip--` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

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)))
10.0ms	(cbrt (pow (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) 3))

series301.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
33.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
129.0ms	(cbrt (pow (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) 3))

simplify66.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	576	1911
1	2375	1849
2	5003	1739

prune296.0ms

Filtered

150 candidates to 87 candidates (58.0%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	150	9	159

Merged error: 26.5b

Counts

159 → 9

regimes176.0ms

Accuracy

27.3% (2.1b remaining)

Error of 26.1b against oracle of 24.0b and baseline of 26.9b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	26
1	27	26
2	27	26

end0.0ms

sample566.0ms

Algorithm

intervals

Results

353.0ms

8460×

body

valid

Details

sample22.0ms

simplify11.0ms

prune2.0ms

localize10.0ms

rewrite16.0ms

series146.0ms

simplify38.0ms

prune144.0ms

localize12.0ms

rewrite21.0ms

series207.0ms

simplify96.0ms

prune222.0ms

localize14.0ms

rewrite42.0ms

series402.0ms

simplify80.0ms

prune304.0ms

localize15.0ms

rewrite31.0ms

series301.0ms

simplify66.0ms

prune296.0ms

regimes176.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample566.0ms

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