Details

sample48.0ms

Algorithm

intervals

Results

21.0ms

265×

body

valid

simplify103.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	94
6	94
5	90
4	76
3	56
2	40
1	21
0	11

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* x.im y.re) (* x.re y.im))
23.4b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 50

Calls

2 calls:

7.0ms	(- (* x.im y.re) (* x.re y.im))
21.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series203.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(- (* x.im y.re) (* x.re y.im))
130.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify980.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
2	1224
1	278
0	97

prune471.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(/ 1 (hypot y.re y.im))
0.3b	(* (/ 1 (hypot y.re y.im)) (/ (fma (- y.im) x.re (* x.im y.re)) (hypot y.re y.im)))
16.1b	(/ (fma (- y.im) x.re (* x.im y.re)) (hypot y.re y.im))

rewrite48.0ms

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×	`clear-num` `frac-2neg`
1×	`frac-times` `hypot-udef` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 130

Calls

4 calls:

0.0ms	(hypot y.re y.im)
8.0ms	(/ 1 (hypot y.re y.im))
28.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma (- y.im) x.re (* x.im y.re)) (hypot y.re y.im)))
5.0ms	(/ (fma (- y.im) x.re (* x.im y.re)) (hypot y.re y.im))

series603.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(hypot y.re y.im)
93.0ms	(/ 1 (hypot y.re y.im))
274.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma (- y.im) x.re (* x.im y.re)) (hypot y.re y.im)))
161.0ms	(/ (fma (- y.im) x.re (* x.im y.re)) (hypot y.re y.im))

simplify2.1s

Counts

142 → 142

Iterations

Iter	Nodes
done	5001
2	2878
1	409
0	155

prune883.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(hypot y.re y.im)
0.0b	(/ (/ (fma x.re (- y.im) (* x.im y.re)) (hypot y.re y.im)) (hypot y.re y.im))
16.1b	(/ (fma x.re (- y.im) (* x.im y.re)) (hypot y.re y.im))

rewrite22.0ms

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`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef` `clear-num` `frac-2neg`
1×	`associate-/l/`

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot y.re y.im)
0.0ms	(hypot y.re y.im)
9.0ms	(/ (/ (fma x.re (- y.im) (* x.im y.re)) (hypot y.re y.im)) (hypot y.re y.im))
4.0ms	(/ (fma x.re (- y.im) (* x.im y.re)) (hypot y.re y.im))

series511.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(hypot y.re y.im)
71.0ms	(hypot y.re y.im)
178.0ms	(/ (/ (fma x.re (- y.im) (* x.im y.re)) (hypot y.re y.im)) (hypot y.re y.im))
182.0ms	(/ (fma x.re (- y.im) (* x.im y.re)) (hypot y.re y.im))

simplify891.0ms

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	1615
1	354
0	162

prune889.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(/ 1 (hypot y.re y.im))
0.0b	(/ (* (fma x.re (- y.im) (* x.im y.re)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
16.2b	(* (fma x.re (- y.im) (* x.im y.re)) (/ 1 (hypot y.re y.im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
29×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `times-frac`
22×	`add-cube-cbrt`
20×	`add-cbrt-cube`
13×	`associate-r`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r*`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-l` `div-inv` `unswap-sqr`
2×	`clear-num` `frac-2neg` `associate-*r/` `un-div-inv` `associate-/l/`
1×	`hypot-udef` `pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 110

Calls

4 calls:

0.0ms	(hypot y.re y.im)
4.0ms	(/ 1 (hypot y.re y.im))
11.0ms	(/ (* (fma x.re (- y.im) (* x.im y.re)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
12.0ms	(* (fma x.re (- y.im) (* x.im y.re)) (/ 1 (hypot y.re y.im)))

series566.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(hypot y.re y.im)
80.0ms	(/ 1 (hypot y.re y.im))
209.0ms	(/ (* (fma x.re (- y.im) (* x.im y.re)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
193.0ms	(* (fma x.re (- y.im) (* x.im y.re)) (/ 1 (hypot y.re y.im)))

simplify931.0ms

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	1837
1	309
0	133

prune575.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.7b

regimes508.0ms

Accuracy

29.9% (7.9b remaining)

Error of 13.7b against oracle of 5.8b and baseline of 17.1b

bsearch113.0ms

Steps

Iters	Range		Point
7	2.779174960643886e+83	1.7372164856765643e+85	6.220962021564848e+84
9	-1.4712480769989026e+218	-7.803139265274982e+212	-7.918258552369891e+212

simplify3.0ms

Iterations

Iter	Nodes
done	26
1	26
0	21

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.0s

8456×

body

valid