Details

sample20.0ms

Algorithm

intervals

Results

10.0ms

277×

body

valid

simplify45.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.re y.re (* y.im y.im))
0.8b	(- (* x.im y.re) (* x.re y.im))
26.6b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma y.re y.re (* y.im y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

series155.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(fma y.re y.re (* y.im y.im))
34.0ms	(- (* x.im y.re) (* x.re y.im))
85.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

simplify1.5s

Counts

67 → 67

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	97	1039
1	224	1011
2	784	892
3	3587	892
done	5000	890

prune202.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot y.im y.re))
0.2b	(* (/ 1 (hypot y.im y.re)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re)))
0.5b	(fma x.im y.re (- (* y.im x.re)))
15.5b	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re))

rewrite23.0ms

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` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 130

Calls

4 calls:

2.0ms	(/ 1 (hypot y.im y.re))
14.0ms	(* (/ 1 (hypot y.im y.re)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re)))
0.0ms	(fma x.im y.re (- (* y.im x.re)))
2.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re))

series415.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 1 (hypot y.im y.re))
179.0ms	(* (/ 1 (hypot y.im y.re)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re)))
47.0ms	(fma x.im y.re (- (* y.im x.re)))
135.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re))

simplify2.3s

Counts

142 → 142

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	155	2322
1	379	2140
2	1136	1874
3	4681	1874
done	5000	1873

prune351.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re)) (hypot y.im y.re))
0.5b	(fma x.im y.re (- (* y.im x.re)))
15.5b	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`fma-udef` `associate-/l/`

Counts

3 → 111

Calls

3 calls:

6.0ms	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re)) (hypot y.im y.re))
0.0ms	(fma x.im y.re (- (* y.im x.re)))
2.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re))

series314.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re)) (hypot y.im y.re))
44.0ms	(fma x.im y.re (- (* y.im x.re)))
136.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re))

simplify1.4s

Counts

120 → 120

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	162	2652
1	335	2592
2	901	2403
3	3177	2349
done	5001	2347

prune341.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re))))) (hypot y.im y.re))
0.3b	(/ 1 (/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re)))))
0.5b	(fma x.im y.re (- (* y.im x.re)))
15.5b	(/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 319

Calls

4 calls:

16.0ms	(/ (/ 1 (/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re))))) (hypot y.im y.re))
5.0ms	(/ 1 (/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re)))))
0.0ms	(fma x.im y.re (- (* y.im x.re)))
2.0ms	(/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re))))

series477.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ (/ 1 (/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re))))) (hypot y.im y.re))
161.0ms	(/ 1 (/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re)))))
43.0ms	(fma x.im y.re (- (* y.im x.re)))
95.0ms	(/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re))))

simplify1.5s

Counts

331 → 331

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	459	9296
1	1079	8209
2	2504	7631
done	5001	7589

prune584.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.6b

regimes170.0ms

Accuracy

29.3% (10.4b remaining)

Error of 12.9b against oracle of 2.5b and baseline of 17.2b

bsearch85.0ms

Steps

Iters	Range		Point
9	1.7730613794721092e+90	2.146195974309642e+97	9.660964437171677e+96
10	-9.740554122961985e+194	-6.1643187501909224e+178	-3.8916390277007425e+179

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	34
1	24	34
2	26	34
done	26	34

end0.0ms

sample531.0ms

Algorithm

intervals

Results

311.0ms

8494×

body

valid