Details

sample29.0ms

Algorithm

intervals

Results

19.0ms

267×

body

valid

simplify41.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	80
5	80
4	76
3	56
2	40
1	21
0	11

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
25.0b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `fma-def` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

3 → 67

Calls

3 calls:

8.0ms	(+ (* y.re y.re) (* y.im y.im))
8.0ms	(- (* x.im y.re) (* x.re y.im))
23.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series176.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* y.re y.re) (* y.im y.im))
53.0ms	(- (* x.im y.re) (* x.re y.im))
94.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.2s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	4547
2	1176
1	327
0	114

prune296.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
16.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

4 → 102

Calls

4 calls:

8.0ms	(- (* x.im y.re) (* x.re y.im))
23.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* x.im y.re) (* x.re y.im))
124.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
45.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.3s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
3	2876
2	991
1	339
0	134

prune681.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
0.5b	(- (* x.im y.re) (* x.re y.im))
16.8b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
91×	`add-sqr-sqrt`
90×	`*-un-lft-identity` `add-cube-cbrt`
45×	`sqrt-prod`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `sqrt-div` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `hypot-def`

Counts

4 → 187

Calls

4 calls:

29.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.0ms	(- (* x.im y.re) (* x.re y.im))
25.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
58.0ms	(- (* x.im y.re) (* x.re y.im))
152.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.6s

Counts

199 → 199

Iterations

Iter	Nodes
done	5000
2	1993
1	713
0	275

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 15.1b

localize18.0ms

Local error

Found 4 expressions with local error:

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))
0.5b	(- (* x.im y.re) (* x.re y.im))
16.8b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`hypot-udef` `sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 135

Calls

4 calls:

0.0ms	(hypot y.re y.im)
18.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
8.0ms	(- (* x.im y.re) (* x.re y.im))
23.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series483.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(hypot y.re y.im)
195.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
67.0ms	(- (* x.im y.re) (* x.re y.im))
136.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify1.5s

Counts

147 → 147

Iterations

Iter	Nodes
done	5000
2	1480
1	474
0	198

prune807.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.0b

regimes373.0ms

Accuracy

33.2% (6.8b remaining)

Error of 12.6b against oracle of 5.8b and baseline of 16.0b

bsearch113.0ms

Steps

Iters	Range		Point
7	1.409584849115433e+155	4.2303463527079064e+156	1.512622379546738e+155
9	-8.57095689264558e+115	-1.514065729698029e+108	-7.729339549361261e+115

simplify6.0ms

Iterations

Iter	Nodes
done	22
1	22
0	19

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8448×

body

valid