Details

sample61.0ms

Algorithm

intervals

Results

41.0ms

271×

body

valid

simplify103.0ms

Counts: 1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

localize27.0ms

Local error

Found 2 expressions with local error:

25.4b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))
0.9b	(- (* x.im y.re) (* x.re y.im))

rewrite30.0ms

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)))
8.0ms	(- (* x.im y.re) (* x.re y.im))

series153.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

104.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))
49.0ms	(- (* x.im y.re) (* x.re y.im))

simplify851.0ms

Counts: 56 → 56

prune679.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 24.9b

localize34.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (fma y.im y.im (* y.re y.re)))
27.7b	(sqrt (fma y.im y.im (* y.re y.re)))
15.9b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
0.9b	(- (* x.im y.re) (* x.re y.im))

rewrite27.0ms

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

16.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
7.0ms	(- (* x.im y.re) (* x.re y.im))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

161.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
75.0ms	(- (* x.im y.re) (* x.re y.im))
63.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
56.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify854.0ms

Counts: 108 → 108

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.7b

localize54.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (fma y.im y.im (* y.re y.re)))
27.7b	(sqrt (fma y.im y.im (* y.re y.re)))
27.7b	(sqrt (fma y.im y.im (* y.re y.re)))
12.1b	(/ (* x.im y.re) (sqrt (fma y.im y.im (* y.re y.re))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

15×	`sqrt-prod`
14×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r*` `times-frac`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef` `hypot-def`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 81

Calls

4 calls:

Slowest

9.0ms	(/ (* x.im y.re) (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)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

85.0ms	(/ (* x.im y.re) (sqrt (fma y.im y.im (* y.re y.re))))
79.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
71.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
61.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify5.3s

Counts: 93 → 93

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.2b

localize37.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (fma y.im y.im (* y.re y.re)))
27.7b	(sqrt (fma y.im y.im (* y.re y.re)))
27.7b	(sqrt (fma y.im y.im (* y.re y.re)))
9.2b	(/ (* x.re y.im) (sqrt (fma y.im y.im (* y.re y.re))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

15×	`sqrt-prod`
14×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r*` `times-frac`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef` `hypot-def`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 81

Calls

4 calls:

Slowest

9.0ms	(/ (* 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)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

90.0ms	(/ (* x.re y.im) (sqrt (fma y.im y.im (* y.re y.re))))
80.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
70.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
67.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify4.5s

Counts: 93 → 93

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.6b

regimes468.0ms

Accuracy

0% (0.4b remaining)

Error of 22.8b against oracle of 22.4b and baseline of 22.8b

bsearch4.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

8487×

body

valid