Details

Time bar (total: 1.6m)

sample32.0ms

Algorithm
intervals
Results
22.0ms274×body80valid

simplify16.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
16.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.6b

localize17.0ms

Local error

Found 2 expressions with local error:

25.6b
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
0.0b
(fma x.re y.re (* x.im y.im))

rewrite5.0ms

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
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
2 → 41
Calls
2 calls:
Slowest
4.0ms
(/ (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))

series187.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
123.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
64.0ms
(fma x.re y.re (* x.im y.im))

simplify1.2s

Counts
31 → 47
Calls
31 calls:
Slowest
458.0ms
(/ (* (* (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))))
75.0ms
(/ (* (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)))))
50.0ms
(- (log (fma x.re y.re (* x.im y.im))) (log (fma y.im y.im (* y.re y.re))))
46.0ms
(/ (sqrt (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)))))
38.0ms
(/ (* (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))))

prune580.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.1b

localize31.0ms

Local error

Found 4 expressions with local error:

29.7b
(sqrt (fma y.im y.im (* y.re y.re)))
29.7b
(sqrt (fma y.im y.im (* y.re y.re)))
16.1b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
0.0b
(/ (/ (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))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×*-un-lft-identity add-cube-cbrt
150×sqrt-prod
25×associate-/l*
12×associate-/r*
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 fma-udef hypot-def
1×associate-/l/
Counts
4 → 254
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)))) (sqrt (fma y.im y.im (* y.re y.re))))
4.0ms
(/ (fma x.re y.re (* x.im 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)))

series470.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
194.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
115.0ms
(/ (/ (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))))
85.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
76.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify17.1s

Counts
364 → 266
Calls
364 calls:
Slowest
360.0ms
(/ (* (* (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))) (/ (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)))) (sqrt (fma y.im y.im (* y.re y.re)))))
264.0ms
(/ (* (* (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)))))
214.0ms
(/ (/ (* (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)))))) (* (cbrt (sqrt (fma y.im y.im (* y.re y.re)))) (cbrt (sqrt (fma y.im y.im (* y.re y.re))))))
212.0ms
(/ (/ (* (* (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))))) (* (* (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)))))
200.0ms
(/ (/ (* (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)))))) (sqrt (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re))))))

prune3.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.5b

localize34.0ms

Local error

Found 3 expressions with local error:

16.1b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
0.0b
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.0b
(fma x.re y.re (* x.im y.im))

rewrite21.0ms

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
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×fma-udef associate-/l/
Counts
3 → 114
Calls
3 calls:
Slowest
12.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
7.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
0.0ms
(fma x.re y.re (* x.im y.im))

series404.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
177.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
174.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
53.0ms
(fma x.re y.re (* x.im y.im))

simplify5.4s

Counts
132 → 123
Calls
132 calls:
Slowest
420.0ms
(/ (* (* (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))) (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re)))
277.0ms
(/ (* (* (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))) (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re)))
177.0ms
(/ (/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re)))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re))))
176.0ms
(/ (/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt (hypot y.im y.re))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re))))
154.0ms
(/ (/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re)))) (sqrt (hypot y.im y.re)))

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.9b

localize32.0ms

Local error

Found 4 expressions with local error:

16.1b
(/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))
0.2b
(/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im))))
0.0b
(/ (/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))) (hypot y.im y.re))
0.0b
(fma x.re y.re (* x.im y.im))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
239×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
50×associate-/l*
36×add-exp-log
23×div-inv
22×div-exp
20×add-cbrt-cube
19×associate-/r*
10×cbrt-undiv
5×pow1 associate-/r/
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×fma-udef pow-flip inv-pow associate-/l/
Counts
4 → 323
Calls
4 calls:
Slowest
27.0ms
(/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im))))
20.0ms
(/ (/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))) (hypot y.im y.re))
9.0ms
(/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))
0.0ms
(fma x.re y.re (* x.im y.im))

series745.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
268.0ms
(/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im))))
267.0ms
(/ (/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))) (hypot y.im y.re))
154.0ms
(/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))
56.0ms
(fma x.re y.re (* x.im y.im))

simplify56.5s

Counts
457 → 335
Calls
457 calls:
Slowest
672.0ms
(/ (* (* 1 1) 1) (/ (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re)) (* (* (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)))))
637.0ms
(/ (/ (* (* 1 1) 1) (* (* (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im))) (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))) (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im))))) (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re)))
591.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re))) (sqrt (fma x.re y.re (* x.im y.im))))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re))))
578.0ms
(/ (/ (sqrt 1) (/ (hypot y.im y.re) (cbrt (fma x.re y.re (* x.im y.im))))) (cbrt (hypot y.im y.re)))
513.0ms
(/ (/ (sqrt 1) (/ (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re))) (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))))) (sqrt (hypot y.im y.re)))

prune4.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.5b

regimes431.0ms

Accuracy

25% (10.8b remaining)

Error of 13.1b against oracle of 2.3b and baseline of 16.7b

bsearch141.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.5s8459×body80valid