Details

sample56.0ms

Algorithm

intervals

Results

38.0ms

269×

body

valid

simplify67.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	80
5	80
4	76
3	56
2	40
1	21
0	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
24.0b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

rewrite52.0ms

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--` `insert-posit16` `log1p-expm1-u` `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

2 → 50

Calls

2 calls:

22.0ms	(- (* x.im y.re) (* x.re y.im))
29.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

series176.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (* x.im y.re) (* x.re y.im))
132.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

simplify599.0ms

Counts

56 → 56

Iterations

Iter	Nodes
3	2462
2	717
1	223
0	90

prune693.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
14.9b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
26.6b	(sqrt (fma y.im y.im (* y.re y.re)))
26.6b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite43.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `fma-udef` `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 → 96

Calls

4 calls:

15.0ms	(- (* x.im y.re) (* x.re y.im))
24.0ms	(/ (- (* x.im y.re) (* x.re 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)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (* x.im y.re) (* x.re y.im))
148.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
61.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
85.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify667.0ms

Counts

108 → 108

Iterations

Iter	Nodes
3	2132
2	760
1	270
0	117

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* y.re x.im) (* y.im x.re))
14.9b	(/ (- (* y.re x.im) (* y.im x.re)) (sqrt (fma y.im y.im (* y.re y.re))))
26.6b	(sqrt (fma y.im y.im (* y.re y.re)))
26.6b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite59.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `fma-udef` `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 → 96

Calls

4 calls:

14.0ms	(- (* y.re x.im) (* y.im x.re))
39.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (sqrt (fma y.im y.im (* y.re y.re))))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (* y.re x.im) (* y.im x.re))
140.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (sqrt (fma y.im y.im (* y.re y.re))))
75.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
47.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify681.0ms

Counts

108 → 108

Iterations

Iter	Nodes
3	2193
2	779
1	266
0	115

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.3b

localize18.0ms

Local error

Found 2 expressions with local error:

0.3b	(fma x.im y.re (- (* x.re y.im)))
24.0b	(/ (fma x.im y.re (- (* x.re 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.im y.re (- (* x.re y.im)))
10.0ms	(/ (fma x.im y.re (- (* x.re y.im))) (fma y.im y.im (* y.re y.re)))

series186.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(fma x.im y.re (- (* x.re y.im)))
129.0ms	(/ (fma x.im y.re (- (* x.re y.im))) (fma y.im y.im (* y.re y.re)))

simplify665.0ms

Counts

47 → 47

Iterations

Iter	Nodes
4	2274
3	690
2	244
1	111
0	68

prune551.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.3b

regimes394.0ms

Accuracy

-6.3% (2.9b remaining)

Error of 26.2b against oracle of 23.3b and baseline of 26.0b

bsearch49.0ms

Steps

Iters	Range		Point
7	2.4172616844736594e+42	2.204943531360865e+44	2.1596338989920688e+44

simplify5.0ms

Iterations

Iter	Nodes
2	18
1	18
0	16

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.2s

8527×

body

valid