Details

sample36.0ms

Algorithm

intervals

Results

26.0ms

272×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x.re y.re) (* x.im y.im))
0.0b	(+ (* y.re y.re) (* y.im y.im))
24.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
4×	`flip3-+` `flip-+`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l`
2×	`+-commutative` `sum-log` `fma-def` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 64

Calls

3 calls:

8.0ms	(+ (* x.re y.re) (* x.im y.im))
8.0ms	(+ (* y.re y.re) (* y.im y.im))
32.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series154.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(+ (* x.re y.re) (* x.im y.im))
29.0ms	(+ (* y.re y.re) (* y.im y.im))
81.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify797.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	2001
3	2001
2	1123
1	299
0	107

prune707.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`*-un-lft-identity` `add-cube-cbrt`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*` `flip3-+` `flip-+`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `hypot-def`

Counts

4 → 278

Calls

4 calls:

82.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
35.0ms	(/ (+ (* x.re y.re) (* x.im 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)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
161.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
51.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
51.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

290 → 290

Iterations

Iter	Nodes
done	2005
3	2005
2	1795
1	734
0	311

prune3.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 18.4b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.1b	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (hypot y.re y.im))
14.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
98×	`add-sqr-sqrt`
97×	`*-un-lft-identity` `add-cube-cbrt`
51×	`sqrt-prod`
27×	`associate-/l*`
12×	`sqrt-div`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
8×	`flip3-+` `flip-+`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `fma-def` `sqrt-pow1` `pow1/2` `hypot-def`

Counts

4 → 197

Calls

4 calls:

8.0ms	(+ (* y.re y.re) (* y.im y.im))
36.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (hypot y.re y.im))
65.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* y.re y.re) (* y.im y.im))
201.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (hypot y.re y.im))
145.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts

209 → 209

Iterations

Iter	Nodes
done	2002
3	2002
2	1639
1	719
0	279

prune3.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize47.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (hypot y.re y.im))
0.2b	(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
14.9b	(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
238×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
50×	`associate-/l*`
35×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
19×	`associate-/r*` `add-cbrt-cube`
10×	`cbrt-undiv`
5×	`associate-/r/`
4×	`pow1` `rec-exp` `1-exp`
3×	`expm1-log1p-u` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow-flip` `inv-pow` `associate-/l/`

Counts

3 → 312

Calls

3 calls:

19.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (hypot y.re y.im))
13.0ms	(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
9.0ms	(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

series605.0ms

Counts

3 → 9

Calls

3 calls:

281.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (hypot y.re y.im))
187.0ms	(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
137.0ms	(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

simplify1.6s

Counts

321 → 321

Iterations

Iter	Nodes
done	2001
2	2001
1	1255
0	455

prune4.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

regimes399.0ms

Accuracy

32.7% (7.2b remaining)

Error of 13.2b against oracle of 6.0b and baseline of 16.7b

bsearch124.0ms

Steps

Iters	Range		Point
8	3.5313364632274564e+117	2.2449574683780836e+120	1.938821746780901e+120
6	-1.2097032068419212e+74	-1.3022738874414276e+73	-6.99838818051005e+73

simplify7.0ms

Iterations

Iter	Nodes
done	24
1	24
0	20

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.3s

8489×

body

valid