Details

sample27.0ms

Algorithm

intervals

Results

12.0ms

271×

body

valid

simplify79.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	11	15
1	21	14
2	40	14
3	56	14
4	76	14
5	88	14
6	92	14
done	92	14

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize12.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
24.2b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

rewrite67.0ms

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` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `div-inv`

Counts

2 → 48

Calls

2 calls:

17.0ms	(- (* x.im y.re) (* x.re y.im))
47.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

series206.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (* x.im y.re) (* x.re y.im))
150.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

simplify2.9s

Counts

54 → 54

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	88	931
1	216	906
2	713	807
3	2539	807
done	5000	801

prune224.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot y.re y.im))
0.3b	(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.7b	(- (* x.im y.re) (* x.re y.im))
16.1b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r` `associate-/l` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `pow-flip` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 139

Calls

4 calls:

5.0ms	(/ 1 (hypot y.re y.im))
52.0ms	(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
8.0ms	(- (* x.im y.re) (* x.re y.im))
22.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series623.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ 1 (hypot y.re y.im))
264.0ms	(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
47.0ms	(- (* x.im y.re) (* x.re y.im))
239.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify2.0s

Counts

151 → 151

Iterations

Useful iterations: 2 (361.0ms)

Iter	Nodes	Cost
0	178	2462
1	470	2264
2	1552	1997
done	5000	1997

prune545.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.7b	(- (* x.im y.re) (* x.re y.im))
16.1b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `hypot-udef` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 131

Calls

4 calls:

0.0ms	(hypot y.re y.im)
23.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
19.0ms	(- (* x.im y.re) (* x.re y.im))
47.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series518.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(hypot y.re y.im)
186.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
72.0ms	(- (* x.im y.re) (* x.re y.im))
198.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify3.0s

Counts

143 → 143

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	194	2874
1	454	2796
2	1252	2600
3	4478	2545
done	5000	2542

prune573.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* y.re x.im) (hypot y.re y.im)) (* y.im (/ x.re (hypot y.re y.im))))
0.1b	(/ (- (/ (* y.re x.im) (hypot y.re y.im)) (* y.im (/ x.re (hypot y.re y.im)))) (hypot y.re y.im))
6.6b	(* y.im (/ x.re (hypot y.re y.im)))
11.1b	(/ (* y.re x.im) (hypot y.re y.im))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`times-frac`
26×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `add-cbrt-cube`
13×	`associate-r`
7×	`fma-neg` `prod-diff`
6×	`pow1` `associate-/r*` `add-log-exp`
5×	`associate-*r/` `div-inv`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `associate-/l/` `associate-/l*`
3×	`associate-l` `prod-exp` `cbrt-unprod`
2×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `diff-log` `div-sub` `pow-prod-down` `*-commutative`

Counts

4 → 121

Calls

4 calls:

24.0ms	(- (/ (* y.re x.im) (hypot y.re y.im)) (* y.im (/ x.re (hypot y.re y.im))))
70.0ms	(/ (- (/ (* y.re x.im) (hypot y.re y.im)) (* y.im (/ x.re (hypot y.re y.im)))) (hypot y.re y.im))
13.0ms	(* y.im (/ x.re (hypot y.re y.im)))
10.0ms	(/ (* y.re x.im) (hypot y.re y.im))

series736.0ms

Counts

4 → 12

Calls

4 calls:

253.0ms	(- (/ (* y.re x.im) (hypot y.re y.im)) (* y.im (/ x.re (hypot y.re y.im))))
287.0ms	(/ (- (/ (* y.re x.im) (hypot y.re y.im)) (* y.im (/ x.re (hypot y.re y.im)))) (hypot y.re y.im))
96.0ms	(* y.im (/ x.re (hypot y.re y.im)))
100.0ms	(/ (* y.re x.im) (hypot y.re y.im))

simplify1.5s

Counts

133 → 133

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	188	2282
1	461	2168
2	1443	1974
done	5001	1956

prune657.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes157.0ms

Accuracy

0% (1.2b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 1.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	13	21
1	18	19
done	18	19

end0.0ms

sample1.4s

Algorithm

intervals

Results

821.0ms

8497×

body

valid