Details

sample38.0ms

Algorithm

intervals

Results

23.0ms

274×

body

valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	21
2	21
1	17
0	11

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.0b

localize50.0ms

Local error

Found 2 expressions with local error:

0.5b	(fma x.re y.re (* x.im y.im))
25.0b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite10.0ms

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`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

2 → 41

Calls

2 calls:

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

series217.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(fma x.re y.re (* x.im y.im))
166.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify1.3s

Counts

47 → 47

Iterations

Iter	Nodes
4	3206
3	937
2	297
1	105
0	67

prune484.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma x.re y.re (* x.im y.im))
16.3b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
30.1b	(sqrt (fma y.im y.im (* y.re y.re)))
30.1b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite9.0ms

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` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

0.0ms	(fma x.re y.re (* x.im y.im))
6.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(fma x.re y.re (* x.im y.im))
138.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
73.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
81.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify782.0ms

Counts

99 → 99

Iterations

Iter	Nodes
4	2543
3	824
2	293
1	142
0	93

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))))
0.5b	(fma x.re y.re (* x.im y.im))
16.3b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
30.1b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
57×	`times-frac`
43×	`*-un-lft-identity`
40×	`add-cube-cbrt`
28×	`add-exp-log`
27×	`sqrt-prod`
22×	`associate-r`
18×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp` `unswap-sqr`
8×	`prod-exp`
7×	`pow1`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `1-exp` `fma-udef`
1×	`frac-times` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `hypot-def`

Counts

4 → 141

Calls

4 calls:

25.0ms	(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))))
0.0ms	(fma x.re y.re (* x.im y.im))
10.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))))
53.0ms	(fma x.re y.re (* x.im y.im))
119.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
78.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify4.9s

Counts

153 → 153

Iterations

Iter	Nodes
3	4919
2	1343
1	449
0	182

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.im y.re)
0.1b	(/ (/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.5b	(fma x.re y.re (* y.im x.im))
16.3b	(/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re))

rewrite24.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`hypot-udef` `fma-udef` `associate-/l/`

Counts

4 → 125

Calls

4 calls:

0.0ms	(hypot y.im y.re)
15.0ms	(/ (/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.0ms	(fma x.re y.re (* y.im x.im))
5.0ms	(/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re))

series533.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(hypot y.im y.re)
178.0ms	(/ (/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re)) (hypot y.im y.re))
68.0ms	(fma x.re y.re (* y.im x.im))
209.0ms	(/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re))

simplify1.6s

Counts

137 → 137

Iterations

Iter	Nodes
3	3412
2	899
1	340
0	171

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

regimes433.0ms

Accuracy

32.6% (7.2b remaining)

Error of 13.1b against oracle of 5.9b and baseline of 16.6b

bsearch120.0ms

Steps

Iters	Range		Point
9	9.907196037723178e+208	3.8358264394853737e+217	1.0136212948540185e+209
8	-3.9150248283130293e+127	-1.4003686841431728e+125	-8.115404358127398e+126

simplify3.0ms

Iterations

Iter	Nodes
2	23
1	23
0	20

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.0s

8475×

body

valid