Details

sample38.0ms

Algorithm

intervals

Results

26.0ms

273×

body

valid

simplify107.0ms

Counts: 1 → 1

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize37.0ms

Local error

Found 2 expressions with local error:

27.9b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))
1.1b	(- (* x.im y.re) (* x.re y.im))

rewrite57.0ms

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

40.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))
15.0ms	(- (* x.im y.re) (* x.re y.im))

series199.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

146.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))
53.0ms	(- (* x.im y.re) (* x.re y.im))

simplify855.0ms

Counts: 56 → 56

prune668.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 27.4b

localize42.0ms

Local error

Found 4 expressions with local error:

31.5b	(sqrt (fma y.im y.im (* y.re y.re)))
31.5b	(sqrt (fma y.im y.im (* y.re y.re)))
17.5b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
1.1b	(- (* x.im y.re) (* x.re y.im))

rewrite33.0ms

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

21.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
8.0ms	(- (* x.im y.re) (* x.re y.im))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

167.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
63.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
54.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
54.0ms	(- (* x.im y.re) (* x.re y.im))

simplify892.0ms

Counts: 108 → 108

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 26.3b

localize25.0ms

Local error

Found 4 expressions with local error:

31.5b	(sqrt (fma y.im y.im (* y.re y.re)))
17.5b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
1.1b	(- (* x.im y.re) (* x.re y.im))
0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))

rewrite51.0ms

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

17.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
15.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
14.0ms	(- (* x.im y.re) (* x.re y.im))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

270.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
123.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
48.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
45.0ms	(- (* x.im y.re) (* x.re y.im))

simplify905.0ms

Counts: 201 → 201

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize18.0ms

Local error

Found 3 expressions with local error:

17.5b	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re))
1.1b	(- (* y.re x.im) (* y.im x.re))
0.1b	(/ (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re)) (hypot y.im y.re))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/l*`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `div-sub` `insert-posit16` `log1p-expm1-u` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

3 → 124

Calls

3 calls:

Slowest

32.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re))
28.0ms	(/ (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re)) (hypot y.im y.re))
21.0ms	(- (* y.re x.im) (* y.im x.re))

series351.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

177.0ms	(/ (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re)) (hypot y.im y.re))
129.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re))
45.0ms	(- (* y.re x.im) (* y.im x.re))

simplify1.9s

Counts: 133 → 133

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

regimes366.0ms

Accuracy

33.2% (6.9b remaining)

Error of 12.8b against oracle of 5.9b and baseline of 16.2b

bsearch164.0ms

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.7s

8485×

body

valid