Details

sample34.0ms

Algorithm

intervals

Results

16.0ms

272×

body

valid

simplify90.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(- (* x.im y.re) (* x.re y.im))
27.2b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

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

series191.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* y.re y.re) (* y.im y.im))
46.0ms	(- (* x.im y.re) (* x.re y.im))
116.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.0s

Counts

73 → 73

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	112	1202
1	314	1070
2	1053	961
3	3501	961
done	5000	960

prune241.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x.im y.re (- (* y.im x.re)))
0.3b	(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)))
16.6b	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
34×	`times-frac`
27×	`add-exp-log` `*-un-lft-identity`
25×	`add-cube-cbrt`
17×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
9×	`div-exp`
8×	`prod-exp`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`rec-exp` `1-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `fma-udef`

Counts

3 → 97

Calls

3 calls:

0.0ms	(fma x.im y.re (- (* y.im x.re)))
23.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)))
5.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

series494.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(fma x.im y.re (- (* y.im x.re)))
245.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)))
193.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

simplify3.6s

Counts

106 → 106

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	141	2025
1	335	1894
2	1076	1642
3	4217	1642
done	5002	1608

prune433.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x.im y.re (- (* y.im x.re)))
0.0b	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
16.6b	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

rewrite25.0ms

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:

1.0ms	(fma x.im y.re (- (* y.im x.re)))
11.0ms	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
5.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

series478.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(fma x.im y.re (- (* y.im x.re)))
182.0ms	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
223.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

simplify2.5s

Counts

120 → 120

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	162	2652
1	329	2592
2	742	2403
3	2537	2349
done	5000	2285

prune578.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x.im y.re (- (* y.im x.re)))
0.0b	(/ (* (fma x.im y.re (- (* y.im x.re))) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
16.7b	(* (fma x.im y.re (- (* y.im x.re))) (/ 1 (hypot y.re y.im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log`
20×	`add-sqr-sqrt`
17×	`add-cbrt-cube`
14×	`*-un-lft-identity` `times-frac`
13×	`add-cube-cbrt` `associate-r`
9×	`div-exp`
8×	`prod-exp`
5×	`pow1` `cbrt-undiv`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `associate-l` `associate-/r*` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`rec-exp` `1-exp` `associate-*r/` `un-div-inv` `div-inv` `associate-/l/`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `fma-udef` `associate-/l`

Counts

3 → 77

Calls

3 calls:

0.0ms	(fma x.im y.re (- (* y.im x.re)))
14.0ms	(/ (* (fma x.im y.re (- (* y.im x.re))) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
15.0ms	(* (fma x.im y.re (- (* y.im x.re))) (/ 1 (hypot y.re y.im)))

series566.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(fma x.im y.re (- (* y.im x.re)))
253.0ms	(/ (* (fma x.im y.re (- (* y.im x.re))) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
230.0ms	(* (fma x.im y.re (- (* y.im x.re))) (/ 1 (hypot y.re y.im)))

simplify3.7s

Counts

86 → 86

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	121	1449
1	274	1289
2	800	1059
3	3481	1045
done	5000	1044

prune322.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.1b

regimes270.0ms

Accuracy

36.4% (7.1b remaining)

Error of 12.6b against oracle of 5.5b and baseline of 16.7b

bsearch128.0ms

Steps

Iters	Range		Point
9	1.5814553296019978e+194	7.10860021261402e+199	1.6082228280465774e+194
7	-1.5687549986519656e+132	-4.3271727545254867e+130	-5.0891457798304875e+131

simplify18.0ms

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	24	46
1	35	40
2	37	34
3	41	34
done	41	34

end0.0ms

sample1.3s

Algorithm

intervals

Results

821.0ms

8480×

body

valid