Details

sample38.0ms

Algorithm

intervals

Results

15.0ms

272×

body

valid

simplify115.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* x.im y.re) (* x.re y.im))
28.4b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

rewrite40.0ms

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

Counts

2 → 48

Calls

2 calls:

13.0ms	(- (* x.im y.re) (* x.re y.im))
25.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

series172.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(- (* x.im y.re) (* x.re y.im))
129.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

simplify2.6s

Counts

54 → 54

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	88	931
1	216	906
2	713	807
3	2539	807
done	5000	801

prune202.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 19.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(hypot y.re y.im)
0.2b	(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
18.7b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite92.0ms

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` `unswap-sqr`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`rec-exp` `hypot-udef` `1-exp` `associate-/l/`
1×	`frac-times` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `flip--`

Counts

4 → 110

Calls

4 calls:

0.0ms	(hypot y.re y.im)
0.0ms	(hypot y.re y.im)
57.0ms	(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
31.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series533.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(hypot y.re y.im)
71.0ms	(hypot y.re y.im)
245.0ms	(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
166.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify1.9s

Counts

122 → 122

Iterations

Useful iterations: 2 (217.0ms)

Iter	Nodes	Cost
0	152	2083
1	404	1941
2	1344	1691
done	5000	1691

prune484.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(hypot y.re y.im)
0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
18.7b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite93.0ms

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`
3×	`div-sub` `associate-/l/`
2×	`hypot-udef` `frac-2neg` `clear-num`
1×	`flip3--` `flip--`

Counts

4 → 125

Calls

4 calls:

1.0ms	(hypot y.re y.im)
1.0ms	(hypot y.re y.im)
39.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
43.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series470.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(hypot y.re y.im)
61.0ms	(hypot y.re y.im)
165.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
181.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify3.0s

Counts

137 → 137

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	175	2732
1	403	2661
2	1078	2474
3	3797	2420
done	5001	2354

prune714.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* y.re x.im) (hypot y.re y.im)) (* y.im (/ x.re (hypot y.re y.im))))
0.1b	(/ (- (/ (* y.re x.im) (hypot y.re y.im)) (* y.im (/ x.re (hypot y.re y.im)))) (hypot y.re y.im))
8.8b	(* y.im (/ x.re (hypot y.re y.im)))
11.4b	(/ (* y.re x.im) (hypot y.re y.im))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

28.0ms	(- (/ (* y.re x.im) (hypot y.re y.im)) (* y.im (/ x.re (hypot y.re y.im))))
53.0ms	(/ (- (/ (* y.re x.im) (hypot y.re y.im)) (* y.im (/ x.re (hypot y.re y.im)))) (hypot y.re y.im))
32.0ms	(* y.im (/ x.re (hypot y.re y.im)))
20.0ms	(/ (* y.re x.im) (hypot y.re y.im))

series799.0ms

Counts

4 → 12

Calls

4 calls:

260.0ms	(- (/ (* y.re x.im) (hypot y.re y.im)) (* y.im (/ x.re (hypot y.re y.im))))
331.0ms	(/ (- (/ (* y.re x.im) (hypot y.re y.im)) (* y.im (/ x.re (hypot y.re y.im)))) (hypot y.re y.im))
96.0ms	(* y.im (/ x.re (hypot y.re y.im)))
112.0ms	(/ (* y.re x.im) (hypot y.re y.im))

simplify1.5s

Counts

133 → 133

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	188	2282
1	461	2168
2	1443	1974
done	5001	1956

prune545.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes285.0ms

Accuracy

43.3% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 1.3b

bsearch76.0ms

Steps

Iters	Range		Point
8	1.3585133677703968e-39	2.3498384803082583e-36	1.529815048138218e-38
4	-2.6910019437958406e+40	-1.5126856462889343e+40	-1.541489361906309e+40

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	73
1	35	47
done	35	47

end0.0ms

sample879.0ms

Algorithm

intervals

Results

416.0ms

8509×

body

valid