Details

analyze1.2s

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 0.195169%

Guaranteed chance to sample good point: 79.736328%

sample29.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
1.0ms	19×	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

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: 26.4b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.2b	(- (* x.im y.re) (* x.re y.im))
25.8b	(/ (- (* 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:

4.0ms	(+ (* 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)))

series42.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* 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 (30.0ms)

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

prune128.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	53	11	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	11	65

Merged error: 25.6b

Counts

65 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
15.2b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b	(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)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
36.0ms	(/ (- (* 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

prune133.0ms

Filtered

75 candidates to 98 candidates (-30.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	93	5	98
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	97	12	109

Merged error: 23.6b

Counts

109 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.0b	(+ (* y.re y.re) (* y.im y.im))
17.3b	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
18.4b	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
6×	`times-frac` `associate-/r*`
4×	`pow1` `cbrt-undiv` `flip3-+` `div-exp` `associate-/r/` `flip-+`
2×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 68

Calls

4 calls:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(+ (* y.re y.re) (* y.im y.im))
6.0ms	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
5.0ms	(+ (* y.re y.re) (* y.im y.im))
16.0ms	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
14.0ms	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))

simplify39.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	309	530
1	1570	442
2	5001	438

prune126.0ms

Filtered

60 candidates to 80 candidates (-33.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	3	7	10
Picked	1	0	1
Done	1	0	1
Total	81	11	92

Merged error: 21.7b

Counts

92 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow y.re 2) (pow y.im 2))
3.0b	(/ x.re (/ (+ (pow y.re 2) (pow y.im 2)) y.im))
16.8b	(/ (+ (pow y.re 2) (pow y.im 2)) y.im)
18.4b	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

140×	`*-un-lft-identity`
135×	`times-frac`
72×	`add-sqr-sqrt` `add-cube-cbrt`
34×	`unpow-prod-down` `distribute-lft-out`
25×	`associate-/r*`
16×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
7×	`div-inv`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`pow1`
3×	`frac-2neg` `flip3-+` `clear-num` `associate-/r/` `flip-+`
2×	`associate-/l/`
1×	`+-commutative` `prod-exp` `sum-log` `cbrt-unprod`

Counts

4 → 167

Calls

4 calls:

7.0ms	(+ (pow y.re 2) (pow y.im 2))
12.0ms	(/ x.re (/ (+ (pow y.re 2) (pow y.im 2)) y.im))
9.0ms	(/ (+ (pow y.re 2) (pow y.im 2)) y.im)
6.0ms	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (pow y.re 2) (pow y.im 2))
14.0ms	(/ x.re (/ (+ (pow y.re 2) (pow y.im 2)) y.im))
8.0ms	(/ (+ (pow y.re 2) (pow y.im 2)) y.im)
15.0ms	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))

simplify69.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	611	1515
1	2660	1416
2	5002	1416

prune267.0ms

Filtered

116 candidates to 179 candidates (-54.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	175	4	179
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	180	10	190

Merged error: 16.4b

Counts

190 → 10

Details

analyze1.2s

sample29.0ms

simplify9.0ms

prune4.0ms

localize10.0ms

rewrite16.0ms

series42.0ms

simplify36.0ms

prune128.0ms

localize12.0ms

rewrite21.0ms

series57.0ms

simplify97.0ms

prune133.0ms

localize11.0ms

rewrite20.0ms

series41.0ms

simplify39.0ms

prune126.0ms

localize15.0ms

rewrite43.0ms

series43.0ms

simplify69.0ms

prune267.0ms

regimes378.0ms

bsearch1.0ms

Profiling