Details

sample61.0ms

Algorithm

intervals

Results

44.0ms

273×

body

valid

simplify85.0ms

Counts: 1 → 1

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize38.0ms

Local error

Found 2 expressions with local error:

24.7b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))
0.3b	(- (* x.im y.re) (* x.re y.im))

rewrite35.0ms

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:

Slowest

21.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))
13.0ms	(- (* x.im y.re) (* x.re y.im))

series184.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

123.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))
61.0ms	(- (* x.im y.re) (* x.re y.im))

simplify835.0ms

Counts: 56 → 56

prune944.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.2b

localize51.0ms

Local error

Found 4 expressions with local error:

28.8b	(sqrt (fma y.im y.im (* y.re y.re)))
28.8b	(sqrt (fma y.im y.im (* y.re y.re)))
15.2b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
0.3b	(- (* x.im y.re) (* x.re y.im))

rewrite60.0ms

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:

Slowest

41.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
13.0ms	(- (* x.im y.re) (* x.re y.im))
3.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

192.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
83.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
60.0ms	(- (* x.im y.re) (* x.re y.im))
52.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify881.0ms

Counts: 108 → 108

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.5b

localize55.0ms

Local error

Found 4 expressions with local error:

28.8b	(sqrt (fma y.im y.im (* y.re y.re)))
15.2b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
0.3b	(- (* x.im y.re) (* x.re y.im))
0.0b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 189

Calls

4 calls:

Slowest

18.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
16.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
8.0ms	(- (* x.im y.re) (* x.re y.im))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series557.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

264.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
152.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
76.0ms	(- (* x.im y.re) (* x.re y.im))
65.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify869.0ms

Counts: 201 → 201

prune3.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.9b

localize51.0ms

Local error

Found 4 expressions with local error:

15.3b	(/ (hypot y.im y.re) (- (* y.re x.im) (* y.im x.re)))
0.3b	(- (* y.re x.im) (* y.im x.re))
0.2b	(/ 1 (/ (hypot y.im y.re) (- (* y.re x.im) (* y.im x.re))))
0.0b	(/ (/ 1 (/ (hypot y.im y.re) (- (* y.re x.im) (* y.im x.re)))) (hypot y.im y.re))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

528×	`times-frac`
255×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
56×	`associate-/l*`
39×	`associate-/r/`
36×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
21×	`associate-/r*`
20×	`add-cbrt-cube`
18×	`flip3--` `flip--`
10×	`cbrt-undiv`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 363

Calls

4 calls:

Slowest

31.0ms	(/ 1 (/ (hypot y.im y.re) (- (* y.re x.im) (* y.im x.re))))
30.0ms	(/ (/ 1 (/ (hypot y.im y.re) (- (* y.re x.im) (* y.im x.re)))) (hypot y.im y.re))
24.0ms	(/ (hypot y.im y.re) (- (* y.re x.im) (* y.im x.re)))
23.0ms	(- (* y.re x.im) (* y.im x.re))

series785.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

306.0ms	(/ (/ 1 (/ (hypot y.im y.re) (- (* y.re x.im) (* y.im x.re)))) (hypot y.im y.re))
254.0ms	(/ 1 (/ (hypot y.im y.re) (- (* y.re x.im) (* y.im x.re))))
147.0ms	(/ (hypot y.im y.re) (- (* y.re x.im) (* y.im x.re)))
78.0ms	(- (* y.re x.im) (* y.im x.re))

simplify878.0ms

Counts: 375 → 375

prune6.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.1b

regimes505.0ms

Accuracy

27.5% (10.1b remaining)

Error of 12.6b against oracle of 2.5b and baseline of 16.4b

bsearch155.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.5s

8465×

body

valid