Details

sample38.0ms

Algorithm

intervals

Results

28.0ms

277×

body

valid

simplify14.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

14.0ms

(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.3b

localize20.0ms

Local error

Found 3 expressions with local error:

22.3b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
0.3b	(fma x.re y.re (* x.im y.im))
0.0b	(fma y.im y.im (* y.re y.re))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 52

Calls

3 calls:

Slowest

5.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
0.0ms	(fma x.re y.re (* x.im y.im))
0.0ms	(fma y.im y.im (* y.re y.re))

series201.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

99.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
51.0ms	(fma x.re y.re (* x.im y.im))
50.0ms	(fma y.im y.im (* y.re y.re))

simplify1.1s

Counts

34 → 61

Calls

34 calls:

Slowest

409.0ms	(/ (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (* (* (fma y.im y.im (* y.re y.re)) (fma y.im y.im (* y.re y.re))) (fma y.im y.im (* y.re y.re))))
65.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re)))))
43.0ms	(/ (cbrt (fma x.re y.re (* x.im y.im))) (sqrt (fma y.im y.im (* y.re y.re))))
42.0ms	(/ (sqrt (fma x.re y.re (* x.im y.im))) (sqrt (fma y.im y.im (* y.re y.re))))
41.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt (fma y.im y.im (* y.re y.re))))

prune762.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.9b

localize49.0ms

Local error

Found 4 expressions with local error:

27.9b	(sqrt (fma y.im y.im (* y.re y.re)))
27.9b	(sqrt (fma y.im y.im (* y.re y.re)))
13.5b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
0.3b	(fma x.re y.re (* x.im y.im))

rewrite16.0ms

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`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

Slowest

9.0ms	(/ (fma x.re y.re (* x.im y.im)) (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)))
0.0ms	(fma x.re y.re (* x.im y.im))

series347.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

145.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
78.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
63.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
61.0ms	(fma x.re y.re (* x.im y.im))

simplify1.8s

Counts

68 → 99

Calls

68 calls:

Slowest

227.0ms	(/ (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (* (* (sqrt (fma y.im y.im (* y.re y.re))) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re)))))
53.0ms	(/ (sqrt (fma x.re y.re (* x.im y.im))) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))
52.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (sqrt (fma y.im y.im (* y.re y.re)))) (cbrt (sqrt (fma y.im y.im (* y.re y.re))))))
48.0ms	(/ (sqrt (fma x.re y.re (* x.im y.im))) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))
48.0ms	(/ (sqrt (fma x.re y.re (* x.im y.im))) (* (cbrt (sqrt (fma y.im y.im (* y.re y.re)))) (cbrt (sqrt (fma y.im y.im (* y.re y.re))))))

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 20.5b

localize43.0ms

Local error

Found 4 expressions with local error:

27.9b	(sqrt (fma y.im y.im (* y.re y.re)))
27.9b	(sqrt (fma y.im y.im (* y.re y.re)))
14.1b	(cbrt (fma x.re y.re (* x.im y.im)))
14.1b	(cbrt (fma x.re y.re (* x.im y.im)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `fma-udef` `hypot-def`

Counts

4 → 62

Calls

4 calls:

Slowest

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	(cbrt (fma x.re y.re (* x.im y.im)))
1.0ms	(cbrt (fma x.re y.re (* x.im y.im)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

169.0ms	(cbrt (fma x.re y.re (* x.im y.im)))
126.0ms	(cbrt (fma x.re y.re (* x.im y.im)))
64.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
51.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.8s

Counts

28 → 74

Calls

28 calls:

Slowest

287.0ms	(exp (* -1/3 (+ (log (/ -1 y.re)) (log (/ -1 x.re)))))
284.0ms	(exp (* -1/3 (+ (log (/ -1 y.re)) (log (/ -1 x.re)))))
263.0ms	(exp (* -1/3 (+ (log (/ 1 x.re)) (log (/ 1 y.re)))))
260.0ms	(+ (exp (* 1/3 (+ (log y.im) (log x.im)))) (* 1/3 (* y.re (* (exp (* -1/3 (+ (* 2 (log y.im)) (* 2 (log x.im))))) x.re))))
256.0ms	(+ (exp (* 1/3 (+ (log y.im) (log x.im)))) (* 1/3 (* y.re (* (exp (* -1/3 (+ (* 2 (log y.im)) (* 2 (log x.im))))) x.re))))

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 20.5b

localize49.0ms

Local error

Found 4 expressions with local error:

22.3b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
22.3b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
22.3b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
11.2b	(cbrt (/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
35×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13×	`cbrt-prod`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r` `associate-/l`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`cbrt-div` `pow1/3`

Counts

4 → 115

Calls

4 calls:

Slowest

4.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
4.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
4.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
1.0ms	(cbrt (/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re))))

series658.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

293.0ms	(cbrt (/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re))))
143.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
119.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
104.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify4.7s

Counts

101 → 127

Calls

101 calls:

Slowest

523.0ms	(/ (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (* (* (fma y.im y.im (* y.re y.re)) (fma y.im y.im (* y.re y.re))) (fma y.im y.im (* y.re y.re))))
456.0ms	(/ (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (* (* (fma y.im y.im (* y.re y.re)) (fma y.im y.im (* y.re y.re))) (fma y.im y.im (* y.re y.re))))
397.0ms	(/ (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (* (* (fma y.im y.im (* y.re y.re)) (fma y.im y.im (* y.re y.re))) (fma y.im y.im (* y.re y.re))))
332.0ms	(exp (* 1/3 (- (log (/ -1 y.re)) (log (/ -1 x.re)))))
228.0ms	(exp (* 1/3 (- (log (/ 1 y.re)) (log (/ 1 x.re)))))

prune1.8s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 20.5b

regimes332.0ms

Accuracy

0% (2.5b remaining)

Error of 25.1b against oracle of 22.6b and baseline of 25.1b

bsearch3.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.4s

8463×

body

valid