Details

sample25.0ms

Algorithm

intervals

Results

10.0ms

277×

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: 25.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.4b	(+ (* x.re y.re) (* x.im y.im))
25.0b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite42.0ms

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:

10.0ms	(+ (* 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)))

series165.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(+ (* x.re y.re) (* x.im y.im))
110.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify95.0ms

Counts

53 → 53

Iterations

Useful iterations: 2 (33.0ms)

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

prune157.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.2b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
15.7b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite73.0ms

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` `hypot-udef` `associate-r/` `associate-l/` `*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 145

Calls

4 calls:

0.0ms	(hypot y.re y.im)
11.0ms	(/ 1 (* (hypot y.re y.im) 1))
48.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
8.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series407.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(hypot y.re y.im)
56.0ms	(/ 1 (* (hypot y.re y.im) 1))
185.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
120.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify43.0ms

Counts

157 → 157

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	493	1177
1	1635	880
2	5001	872
done	5001	872

prune276.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
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))
15.7b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite21.0ms

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×	`hypot-udef` `frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`associate-/l/`

Counts

4 → 99

Calls

4 calls:

0.0ms	(hypot y.re y.im)
0.0ms	(hypot y.re y.im)
13.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
5.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series335.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(hypot y.re y.im)
45.0ms	(hypot y.re y.im)
123.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
120.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify73.0ms

Counts

111 → 111

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	301	780
1	1076	689
2	3153	689
3	5001	681
done	5001	681

prune297.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot y.re y.im))
0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im))) 1))
0.5b	(* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
15.7b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
41×	`add-exp-log`
40×	`times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
29×	`add-cbrt-cube`
21×	`sqrt-prod`
20×	`pow1`
16×	`div-exp` `associate-/l*`
13×	`prod-exp`
10×	`cbrt-undiv`
9×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
7×	`cbrt-unprod`
6×	`associate-r` `associate-l`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `1-exp` `associate-/r*` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`frac-2neg` `clear-num`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `*-commutative` `associate-/l/`

Counts

4 → 151

Calls

4 calls:

4.0ms	(sqrt (hypot y.re y.im))
36.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im))) 1))
12.0ms	(* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
5.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series379.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(sqrt (hypot y.re y.im))
129.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im))) 1))
46.0ms	(* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
123.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify78.0ms

Counts

163 → 163

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	511	1120
1	2654	920
2	5001	906
done	5001	906

prune345.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.0b

regimes200.0ms

Accuracy

34.5% (7.2b remaining)

Error of 12.9b against oracle of 5.8b and baseline of 16.7b

bsearch79.0ms

Steps

Iters	Range		Point
9	4.059466205825632e+120	8.087440263561752e+125	7.737953068228605e+125
7	-1.214189681212846e+122	-2.3797206039891623e+120	-1.1960291801949296e+122

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

sample596.0ms

Algorithm

intervals

Results

283.0ms

8508×

body

valid