Details

sample1.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 0.195169%

Guaranteed chance to sample good point: 0%

Results

11.0ms	256×	body	80	valid
1.0ms	21×	body	80	invalid

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: 28.2b

Counts

2 → 1

localize10.0ms

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)))

rewrite18.0ms

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))
11.0ms	(/ (- (* 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 (29.0ms)

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

prune114.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	55	9	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	10	65

Merged error: 27.5b

Counts

65 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.2b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
0.5b	(- (* x.im y.re) (* x.re y.im))
27.7b	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 138

Calls

4 calls:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
9.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
5.0ms	(- (* 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)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
25.0ms	(/ 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)))

simplify68.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	516	1823
1	2545	1661
2	5001	1575

prune123.0ms

Filtered

85 candidates to 150 candidates (-76.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	150	10	160

Merged error: 27.5b

Counts

160 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
17.1b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.8b	(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))
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)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
35.0ms	(/ (- (* 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

prune120.0ms

Filtered

75 candidates to 98 candidates (-30.7%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	96	12	108

Merged error: 25.4b

Counts

108 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (- (* x.im y.re) (* x.re y.im)))))
0.3b	(/ 1 (- (* x.im y.re) (* x.re y.im)))
0.5b	(- (* x.im y.re) (* x.re y.im))
27.9b	(* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (- (* x.im y.re) (* x.re y.im))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
29×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `times-frac`
22×	`add-cube-cbrt`
20×	`div-exp` `add-cbrt-cube`
16×	`prod-exp`
15×	`associate-r`
10×	`pow1` `rec-exp` `1-exp` `associate-/r/`
6×	`cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`frac-times` `flip3-+` `associate-l/` `associate-/r` `cbrt-unprod` `flip-+`
3×	`flip3--` `pow-flip` `associate-l` `flip--` `div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-*r/` `pow-prod-down` `clear-num` `un-div-inv` `inv-pow`
1×	`sub-neg` `diff-log` `*-commutative`

Counts

4 → 131

Calls

4 calls:

11.0ms	(/ 1 (* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (- (* x.im y.re) (* x.re y.im)))))
5.0ms	(/ 1 (- (* x.im y.re) (* x.re y.im)))
3.0ms	(- (* x.im y.re) (* x.re y.im))
11.0ms	(* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (- (* x.im y.re) (* x.re y.im))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1 (* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (- (* x.im y.re) (* x.re y.im)))))
11.0ms	(/ 1 (- (* x.im y.re) (* x.re y.im)))
10.0ms	(- (* x.im y.re) (* x.re y.im))
20.0ms	(* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (- (* x.im y.re) (* x.re y.im))))

simplify56.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	475	1236
1	2279	1037
2	5002	997

prune92.0ms

Filtered

77 candidates to 143 candidates (-85.7%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	8	8
Picked	0	1	1
Done	0	3	3
Total	143	12	155

Merged error: 25.4b

Counts

155 → 12

regimes489.0ms

Accuracy

6.9% (2.7b remaining)

Error of 26.5b against oracle of 23.8b and baseline of 26.7b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	20
1	24	20

end0.0ms

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 0.195169%

Guaranteed chance to sample good point: 0%

Results

374.0ms	8000×	body	80	valid
21.0ms	476×	body	80	invalid

Details

sample1.2s

simplify9.0ms

prune3.0ms

localize10.0ms

rewrite18.0ms

series41.0ms

simplify36.0ms

prune114.0ms

localize11.0ms

rewrite30.0ms

series58.0ms

simplify68.0ms

prune123.0ms

localize14.0ms

rewrite21.0ms

series57.0ms

simplify94.0ms

prune120.0ms

localize12.0ms

rewrite34.0ms

series66.0ms

simplify56.0ms

prune92.0ms

regimes489.0ms

bsearch2.0ms

simplify1.0ms

end0.0ms

sample1.8s

Profiling