Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

269×

body

valid

simplify54.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
30.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite14.0ms

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

Counts

2 → 50

Calls

2 calls:

3.0ms	(- (* x.im y.re) (* x.re y.im))
10.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series121.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(- (* x.im y.re) (* x.re y.im))
85.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

56 → 56

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	97	1020
1	268	919
2	879	841
3	2897	837
done	5000	835

prune170.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot y.re y.im))
0.2b	(* (/ 1 (hypot y.re y.im)) (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im)))
0.7b	(- (* y.re x.im) (* y.im x.re))
15.8b	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im))

rewrite34.0ms

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:

2.0ms	(/ 1 (hypot y.re y.im))
17.0ms	(* (/ 1 (hypot y.re y.im)) (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im)))
3.0ms	(- (* y.re x.im) (* y.im x.re))
7.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im))

series382.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 1 (hypot y.re y.im))
181.0ms	(* (/ 1 (hypot y.re y.im)) (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im)))
40.0ms	(- (* y.re x.im) (* y.im x.re))
107.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im))

simplify1.3s

Counts

151 → 151

Iterations

Useful iterations: 2 (219.0ms)

Iter	Nodes	Cost
0	176	2462
1	487	2264
2	1517	1997
done	5001	1997

prune373.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot y.re y.im))
0.2b	(* (/ 1 (hypot y.re y.im)) (- (/ x.im (/ (hypot y.re y.im) y.re)) (/ (* y.im x.re) (hypot y.re y.im))))
2.6b	(/ x.im (/ (hypot y.re y.im) y.re))
9.8b	(/ (* y.im x.re) (hypot y.re y.im))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

1289×	`times-frac`
746×	`add-sqr-sqrt`
733×	`*-un-lft-identity`
730×	`add-cube-cbrt`
616×	`prod-diff`
310×	`distribute-rgt-in` `distribute-lft-in`
152×	`div-inv`
27×	`add-exp-log`
21×	`add-cbrt-cube`
19×	`associate-/r*`
15×	`associate-/r/`
13×	`associate-l`
9×	`div-exp`
7×	`pow1` `cbrt-undiv` `associate-r` `associate-/l*`
5×	`prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `frac-2neg` `associate-*r/` `clear-num` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
2×	`sub-neg` `rec-exp` `flip3--` `1-exp` `frac-sub` `flip--`
1×	`pow-flip` `pow-prod-down` `associate-l/` `-commutative` `distribute-lft-out--` `inv-pow`

Counts

4 → 795

Calls

4 calls:

2.0ms	(/ 1 (hypot y.re y.im))
170.0ms	(* (/ 1 (hypot y.re y.im)) (- (/ x.im (/ (hypot y.re y.im) y.re)) (/ (* y.im x.re) (hypot y.re y.im))))
5.0ms	(/ x.im (/ (hypot y.re y.im) y.re))
3.0ms	(/ (* y.im x.re) (hypot y.re y.im))

series514.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ 1 (hypot y.re y.im))
305.0ms	(* (/ 1 (hypot y.re y.im)) (- (/ x.im (/ (hypot y.re y.im) y.re)) (/ (* y.im x.re) (hypot y.re y.im))))
70.0ms	(/ x.im (/ (hypot y.re y.im) y.re))
86.0ms	(/ (* y.im x.re) (hypot y.re y.im))

simplify3.0s

Counts

807 → 807

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	1267	50699
1	3242	41717
done	5000	38901

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ x.im (/ (hypot y.re y.im) y.re)) (/ y.im (/ (hypot y.re y.im) x.re)))
0.1b	(/ (- (/ x.im (/ (hypot y.re y.im) y.re)) (/ y.im (/ (hypot y.re y.im) x.re))) (hypot y.re y.im))
2.6b	(/ x.im (/ (hypot y.re y.im) y.re))
8.2b	(/ y.im (/ (hypot y.re y.im) x.re))

rewrite857.0ms

Algorithm

rewrite-expression-head

Rules

6248×	`times-frac`
3416×	`add-sqr-sqrt`
3336×	`*-un-lft-identity`
3236×	`add-cube-cbrt`
1936×	`prod-diff`
377×	`div-inv`
91×	`associate-/r/`
45×	`difference-of-squares`
44×	`fma-neg`
30×	`distribute-lft-out--`
29×	`associate-/r*`
24×	`associate-/l*`
16×	`add-exp-log` `add-cbrt-cube`
7×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num` `associate-/l/`
2×	`flip3--` `frac-sub` `flip--`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 2247

Calls

4 calls:

144.0ms	(- (/ x.im (/ (hypot y.re y.im) y.re)) (/ y.im (/ (hypot y.re y.im) x.re)))
409.0ms	(/ (- (/ x.im (/ (hypot y.re y.im) y.re)) (/ y.im (/ (hypot y.re y.im) x.re))) (hypot y.re y.im))
5.0ms	(/ x.im (/ (hypot y.re y.im) y.re))
5.0ms	(/ y.im (/ (hypot y.re y.im) x.re))

series809.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(- (/ x.im (/ (hypot y.re y.im) y.re)) (/ y.im (/ (hypot y.re y.im) x.re)))
235.0ms	(/ (- (/ x.im (/ (hypot y.re y.im) y.re)) (/ y.im (/ (hypot y.re y.im) x.re))) (hypot y.re y.im))
286.0ms	(/ x.im (/ (hypot y.re y.im) y.re))
97.0ms	(/ y.im (/ (hypot y.re y.im) x.re))

simplify1.1s

Counts

2259 → 2259

Iterations

Useful iterations: done (918.0ms)

Iter	Nodes	Cost
0	2571	165116
done	5000	151866

prune10.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes136.0ms

Accuracy

0% (1.0b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 1.0b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	24	94
1	34	92
2	38	92
3	40	92
done	40	92

end0.0ms

sample515.0ms

Algorithm

intervals

Results

303.0ms

8475×

body

valid