Details

sample23.0ms

Algorithm

intervals

Results

11.0ms

268×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	7
1	21	7
2	21	7
done	21	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.9b	(+ (* x.re y.re) (* x.im y.im))
22.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite38.0ms

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×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 47

Calls

2 calls:

7.0ms	(+ (* x.re y.re) (* x.im y.im))
30.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series120.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(+ (* x.re y.re) (* x.im y.im))
83.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify98.0ms

Counts

53 → 53

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	244	458
1	872	411
2	3164	403
3	5001	403
done	5001	403

prune144.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.3b	(fma x.re y.re (* x.im y.im))
0.3b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
14.4b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-exp-log`
92×	`prod-exp`
63×	`div-exp`
50×	`add-cbrt-cube`
41×	`1-exp`
17×	`cbrt-unprod`
16×	`cbrt-undiv`
15×	`rec-exp`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
9×	`pow1`
7×	`associate-r` `associate-l`
6×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r*`
1×	`frac-times` `associate-r/` `associate-l/` `*-commutative` `fma-udef` `inv-pow` `unswap-sqr`

Counts

4 → 145

Calls

4 calls:

11.0ms	(/ 1 (* (hypot y.re y.im) 1))
0.0ms	(fma x.re y.re (* x.im y.im))
47.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
7.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series397.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ 1 (* (hypot y.re y.im) 1))
39.0ms	(fma x.re y.re (* x.im y.im))
184.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
119.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify45.0ms

Counts

157 → 157

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	486	1191
1	1654	892
2	5002	884
done	5002	884

prune277.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.3b	(fma x.re y.re (* x.im y.im))
14.4b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
23×	`add-exp-log`
18×	`add-cbrt-cube`
16×	`associate-/l*`
10×	`div-exp`
7×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `prod-exp` `associate-/r*` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`hypot-udef` `fma-udef` `associate-/l/`

Counts

4 → 99

Calls

4 calls:

0.0ms	(hypot y.re y.im)
16.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.0ms	(fma x.re y.re (* x.im y.im))
5.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series346.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(hypot y.re y.im)
128.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
42.0ms	(fma x.re y.re (* x.im y.im))
126.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify75.0ms

Counts

111 → 111

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	308	794
1	1149	701
2	3275	701
3	5001	693
done	5001	693

prune309.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im))) (* (hypot y.re y.im) 1))
0.3b	(fma x.re y.re (* x.im y.im))
6.5b	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))
8.0b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

892×	`times-frac`
402×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
384×	`sqrt-prod`
161×	`associate-/l*`
41×	`add-exp-log`
32×	`add-cbrt-cube`
24×	`div-inv`
22×	`div-exp`
16×	`cbrt-undiv`
13×	`associate-/r*`
6×	`prod-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
2×	`associate-/l/`
1×	`fma-udef`

Counts

4 → 529

Calls

4 calls:

49.0ms	(/ (/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im))) (* (hypot y.re y.im) 1))
0.0ms	(fma x.re y.re (* x.im y.im))
17.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))
6.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ (/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im))) (* (hypot y.re y.im) 1))
40.0ms	(fma x.re y.re (* x.im y.im))
122.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))
210.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))

simplify91.0ms

Counts

541 → 541

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1235	8471
1	5001	7489
done	5001	7489

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.9b

regimes198.0ms

Accuracy

37.6% (7.4b remaining)

Error of 13.3b against oracle of 5.8b and baseline of 17.8b

bsearch78.0ms

Steps

Iters	Range		Point
10	4.967236903674525e+142	1.041635744750388e+157	6.189704792038335e+149
9	-6.9696378083464e+173	-2.77444321090993e+167	-1.8229538050890444e+171

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	30	14
2	30	14
done	30	14

end0.0ms

sample564.0ms

Algorithm

intervals

Results

275.0ms

8487×

body

valid