Details

sample4.2s

Algorithm

intervals

Results

4.0s	946×	body	10240	exit
71.0ms	256×	body	80	valid

simplify4.3s

Counts: 1 → 1

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize70.0ms

Local error

Found 4 expressions with local error:

28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
24.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
0.3b	(* (atan2 x.im x.re) y.im)

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

Slowest

32.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
15.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(* (atan2 x.im x.re) y.im)

series370.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

196.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
90.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms	(* (atan2 x.im x.re) y.im)

simplify1.0s

Counts: 72 → 72

prune1.3s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize61.0ms

Local error

Found 4 expressions with local error:

28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b	(* (atan2 x.im x.re) y.im)
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.0b	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`pow1`
9×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-r` `add-log-exp`
4×	`insert-posit16`
3×	`log-pow` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

4 → 70

Calls

4 calls:

Slowest

23.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
19.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms	(* (atan2 x.im x.re) y.im)

series368.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

155.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
124.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
66.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms	(* (atan2 x.im x.re) y.im)

simplify882.0ms

Counts: 82 → 82

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (atan2 x.im x.re) y.im)
0.3b	(* (log (- x.re)) y.re)
0.0b	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`pow1`
7×	`-un-lft-identity` `add-cbrt-cube` `associate-l*` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
5×	`add-log-exp`
3×	`insert-posit16`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `log-pow` `flip--`

Counts

3 → 52

Calls

3 calls:

Slowest

11.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
7.0ms	(* (log (- x.re)) y.re)

series295.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

146.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
123.0ms	(* (log (- x.re)) y.re)
26.0ms	(* (atan2 x.im x.re) y.im)

simplify2.0s

Counts: 61 → 61

prune739.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize76.0ms

Local error

Found 4 expressions with local error:

60.0b	(posit16->real (real->posit16 (- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))))
0.3b	(* (atan2 x.im x.re) y.im)
0.3b	(* (log (- x.re)) y.re)
0.0b	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`pow1`
8×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
7×	`associate-l`
6×	`associate-r` `add-log-exp`
4×	`insert-posit16`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `log-pow` `remove-posit16` `flip--`

Counts

4 → 61

Calls

4 calls:

Slowest

20.0ms	(* (log (- x.re)) y.re)
15.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
11.0ms	(* (atan2 x.im x.re) y.im)
1.0ms	(posit16->real (real->posit16 (- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))))

series435.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

186.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
148.0ms	(posit16->real (real->posit16 (- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))))
77.0ms	(* (log (- x.re)) y.re)
24.0ms	(* (atan2 x.im x.re) y.im)

simplify2.0s

Counts: 73 → 73

prune1.9s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

regimes343.0ms

Accuracy

97% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 7.4b

bsearch2.1s

end0.0ms

sample2.1m

Algorithm

intervals

Results

2.0m	30271×	body	10240	exit
3.9s	8000×	body	80	valid