Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

275×

body

valid

simplify48.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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: 22.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (* x.im y.re) (* x.re y.im))
22.3b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite14.0ms

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

Counts

2 → 50

Calls

2 calls:

3.0ms	(- (* x.im y.re) (* x.re y.im))
10.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series123.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(- (* x.im y.re) (* x.re y.im))
87.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.3s

Counts

56 → 56

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	97	1020
1	270	919
2	964	841
3	3550	837
done	5000	835

prune174.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.3b	(- (* y.re x.im) (* y.im x.re))
0.3b	(* (/ 1 (hypot y.re y.im)) (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im)))
12.0b	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
34×	`times-frac`
28×	`add-exp-log` `*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
9×	`div-exp`
8×	`prod-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `hypot-udef` `frac-2neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 116

Calls

4 calls:

0.0ms	(hypot y.re y.im)
3.0ms	(- (* y.re x.im) (* y.im x.re))
20.0ms	(* (/ 1 (hypot y.re y.im)) (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im)))
7.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im))

series381.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot y.re y.im)
40.0ms	(- (* y.re x.im) (* y.im x.re))
187.0ms	(* (/ 1 (hypot y.re y.im)) (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im)))
106.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im))

simplify822.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (169.0ms)

Iter	Nodes	Cost
0	169	2225
1	490	2088
2	1861	1817
done	5000	1817

prune363.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.1b	(/ (/ (fma y.re x.im (- (* x.re y.im))) (hypot y.re y.im)) (hypot y.re y.im))
0.3b	(fma y.re x.im (- (* x.re y.im)))
12.0b	(/ (fma y.re x.im (- (* x.re y.im))) (hypot y.re y.im))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

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

series306.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot y.re y.im)
110.0ms	(/ (/ (fma y.re x.im (- (* x.re y.im))) (hypot y.re y.im)) (hypot y.re y.im))
46.0ms	(fma y.re x.im (- (* x.re y.im)))
103.0ms	(/ (fma y.re x.im (- (* x.re y.im))) (hypot y.re y.im))

simplify2.1s

Counts

133 → 133

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	169	2712
1	351	2650
2	1176	2455
3	4020	2401
done	5001	2399

prune468.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot y.re y.im) (fma y.re x.im (- (* x.re y.im))))) (hypot y.re y.im))
0.1b	(/ 1 (/ (hypot y.re y.im) (fma y.re x.im (- (* x.re y.im)))))
0.3b	(fma y.re x.im (- (* x.re y.im)))
12.1b	(/ (hypot y.re y.im) (fma y.re x.im (- (* x.re y.im))))

rewrite47.0ms

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.re y.im) (fma y.re x.im (- (* x.re y.im))))) (hypot y.re y.im))
6.0ms	(/ 1 (/ (hypot y.re y.im) (fma y.re x.im (- (* x.re y.im)))))
0.0ms	(fma y.re x.im (- (* x.re y.im)))
2.0ms	(/ (hypot y.re y.im) (fma y.re x.im (- (* x.re y.im))))

series455.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma y.re x.im (- (* x.re y.im))))) (hypot y.re y.im))
124.0ms	(/ 1 (/ (hypot y.re y.im) (fma y.re x.im (- (* x.re y.im)))))
44.0ms	(fma y.re x.im (- (* x.re y.im)))
96.0ms	(/ (hypot y.re y.im) (fma y.re x.im (- (* x.re y.im))))

simplify3.0s

Counts

331 → 331

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	460	9298
1	1097	8458
2	3780	7632
done	5001	7626

prune680.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.9b

regimes197.0ms

Accuracy

35.1% (7.0b remaining)

Error of 12.6b against oracle of 5.7b and baseline of 16.4b

bsearch82.0ms

Steps

Iters	Range		Point
6	4.497054947537868e+154	5.359771339659149e+155	5.3202544266061094e+154
9	-9.04709806302392e+124	-4.4188440889263735e+116	-2.7774429101464625e+124

simplify9.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	27	60
1	38	54
2	41	54
3	44	54
4	48	54
5	50	54
done	50	54

end0.0ms

sample505.0ms

Algorithm

intervals

Results

295.0ms

8478×

body

valid