Average Error: 26.1 → 12.5
Time: 19.9s
Precision: 64
Internal Precision: 128
\[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
↓
\[\begin{array}{l} \mathbf{if}\;y.re \le -1.8506614466369815 \cdot 10^{+150}:\\ \;\;\;\;\frac{-x.re}{\sqrt{y.im^2 + y.re^2}^*}\\ \mathbf{elif}\;y.re \le 6.560820932670249 \cdot 10^{+185}:\\ \;\;\;\;\frac{\frac{1}{\frac{\sqrt{y.im^2 + y.re^2}^*}{(y.re \cdot x.re + \left(y.im \cdot x.im\right))_*}}}{\sqrt{y.im^2 + y.re^2}^*}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{\sqrt{y.im^2 + y.re^2}^*}\\ \end{array}\]

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

Derivation

  1. Split input into 3 regimes

  2. if y.re < -1.8506614466369815e+150

    1. Initial program 44.1

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]

    2. Simplified44.1

      \[\leadsto \color{blue}{\frac{(x.re \cdot y.re + \left(x.im \cdot y.im\right))_*}{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}}\]
    3. Using strategy rm

    4. Applied add-sqr-sqrt44.1

      \[\leadsto \frac{(x.re \cdot y.re + \left(x.im \cdot y.im\right))_*}{\color{blue}{\sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*} \cdot \sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}}}\]

    5. Applied *-un-lft-identity44.1

      \[\leadsto \frac{\color{blue}{1 \cdot (x.re \cdot y.re + \left(x.im \cdot y.im\right))_*}}{\sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*} \cdot \sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}}\]

    6. Applied times-frac44.1

      \[\leadsto \color{blue}{\frac{1}{\sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}} \cdot \frac{(x.re \cdot y.re + \left(x.im \cdot y.im\right))_*}{\sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}}}\]

    7. Simplified44.1

      \[\leadsto \color{blue}{\frac{1}{\sqrt{y.im^2 + y.re^2}^*}} \cdot \frac{(x.re \cdot y.re + \left(x.im \cdot y.im\right))_*}{\sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}}\]

    8. Simplified28.2

      \[\leadsto \frac{1}{\sqrt{y.im^2 + y.re^2}^*} \cdot \color{blue}{\frac{(y.im \cdot x.im + \left(x.re \cdot y.re\right))_*}{\sqrt{y.im^2 + y.re^2}^*}}\]
    9. Using strategy rm

    10. Applied associate-*l/28.1

      \[\leadsto \color{blue}{\frac{1 \cdot \frac{(y.im \cdot x.im + \left(x.re \cdot y.re\right))_*}{\sqrt{y.im^2 + y.re^2}^*}}{\sqrt{y.im^2 + y.re^2}^*}}\]

    11. Simplified28.1

      \[\leadsto \frac{\color{blue}{\frac{(y.re \cdot x.re + \left(x.im \cdot y.im\right))_*}{\sqrt{y.im^2 + y.re^2}^*}}}{\sqrt{y.im^2 + y.re^2}^*}\]

    12. Taylor expanded around -inf 13.3

      \[\leadsto \frac{\color{blue}{-1 \cdot x.re}}{\sqrt{y.im^2 + y.re^2}^*}\]

    13. Simplified13.3

      \[\leadsto \frac{\color{blue}{-x.re}}{\sqrt{y.im^2 + y.re^2}^*}\]

    if -1.8506614466369815e+150 < y.re < 6.560820932670249e+185

    1. Initial program 20.1

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]

    2. Simplified20.1

      \[\leadsto \color{blue}{\frac{(x.re \cdot y.re + \left(x.im \cdot y.im\right))_*}{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}}\]
    3. Using strategy rm

    4. Applied add-sqr-sqrt20.1

      \[\leadsto \frac{(x.re \cdot y.re + \left(x.im \cdot y.im\right))_*}{\color{blue}{\sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*} \cdot \sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}}}\]

    5. Applied *-un-lft-identity20.1

      \[\leadsto \frac{\color{blue}{1 \cdot (x.re \cdot y.re + \left(x.im \cdot y.im\right))_*}}{\sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*} \cdot \sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}}\]

    6. Applied times-frac20.2

      \[\leadsto \color{blue}{\frac{1}{\sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}} \cdot \frac{(x.re \cdot y.re + \left(x.im \cdot y.im\right))_*}{\sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}}}\]

    7. Simplified20.1

      \[\leadsto \color{blue}{\frac{1}{\sqrt{y.im^2 + y.re^2}^*}} \cdot \frac{(x.re \cdot y.re + \left(x.im \cdot y.im\right))_*}{\sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}}\]

    8. Simplified12.4

      \[\leadsto \frac{1}{\sqrt{y.im^2 + y.re^2}^*} \cdot \color{blue}{\frac{(y.im \cdot x.im + \left(x.re \cdot y.re\right))_*}{\sqrt{y.im^2 + y.re^2}^*}}\]
    9. Using strategy rm

    10. Applied associate-*l/12.2

      \[\leadsto \color{blue}{\frac{1 \cdot \frac{(y.im \cdot x.im + \left(x.re \cdot y.re\right))_*}{\sqrt{y.im^2 + y.re^2}^*}}{\sqrt{y.im^2 + y.re^2}^*}}\]

    11. Simplified12.2

      \[\leadsto \frac{\color{blue}{\frac{(y.re \cdot x.re + \left(x.im \cdot y.im\right))_*}{\sqrt{y.im^2 + y.re^2}^*}}}{\sqrt{y.im^2 + y.re^2}^*}\]
    12. Using strategy rm

    13. Applied clear-num12.3

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{\sqrt{y.im^2 + y.re^2}^*}{(y.re \cdot x.re + \left(x.im \cdot y.im\right))_*}}}}{\sqrt{y.im^2 + y.re^2}^*}\]

    if 6.560820932670249e+185 < y.re

    1. Initial program 44.6

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]

    2. Simplified44.6

      \[\leadsto \color{blue}{\frac{(x.re \cdot y.re + \left(x.im \cdot y.im\right))_*}{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}}\]
    3. Using strategy rm

    4. Applied add-sqr-sqrt44.6

      \[\leadsto \frac{(x.re \cdot y.re + \left(x.im \cdot y.im\right))_*}{\color{blue}{\sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*} \cdot \sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}}}\]

    5. Applied *-un-lft-identity44.6

      \[\leadsto \frac{\color{blue}{1 \cdot (x.re \cdot y.re + \left(x.im \cdot y.im\right))_*}}{\sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*} \cdot \sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}}\]

    6. Applied times-frac44.6

      \[\leadsto \color{blue}{\frac{1}{\sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}} \cdot \frac{(x.re \cdot y.re + \left(x.im \cdot y.im\right))_*}{\sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}}}\]

    7. Simplified44.6

      \[\leadsto \color{blue}{\frac{1}{\sqrt{y.im^2 + y.re^2}^*}} \cdot \frac{(x.re \cdot y.re + \left(x.im \cdot y.im\right))_*}{\sqrt{(y.im \cdot y.im + \left(y.re \cdot y.re\right))_*}}\]

    8. Simplified30.7

      \[\leadsto \frac{1}{\sqrt{y.im^2 + y.re^2}^*} \cdot \color{blue}{\frac{(y.im \cdot x.im + \left(x.re \cdot y.re\right))_*}{\sqrt{y.im^2 + y.re^2}^*}}\]
    9. Using strategy rm

    10. Applied associate-*l/30.7

      \[\leadsto \color{blue}{\frac{1 \cdot \frac{(y.im \cdot x.im + \left(x.re \cdot y.re\right))_*}{\sqrt{y.im^2 + y.re^2}^*}}{\sqrt{y.im^2 + y.re^2}^*}}\]

    11. Simplified30.7

      \[\leadsto \frac{\color{blue}{\frac{(y.re \cdot x.re + \left(x.im \cdot y.im\right))_*}{\sqrt{y.im^2 + y.re^2}^*}}}{\sqrt{y.im^2 + y.re^2}^*}\]
    12. Using strategy rm

    13. Applied clear-num30.7

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{\sqrt{y.im^2 + y.re^2}^*}{(y.re \cdot x.re + \left(x.im \cdot y.im\right))_*}}}}{\sqrt{y.im^2 + y.re^2}^*}\]

    14. Taylor expanded around 0 12.2

      \[\leadsto \frac{\color{blue}{x.re}}{\sqrt{y.im^2 + y.re^2}^*}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification12.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \le -1.8506614466369815 \cdot 10^{+150}:\\ \;\;\;\;\frac{-x.re}{\sqrt{y.im^2 + y.re^2}^*}\\ \mathbf{elif}\;y.re \le 6.560820932670249 \cdot 10^{+185}:\\ \;\;\;\;\frac{\frac{1}{\frac{\sqrt{y.im^2 + y.re^2}^*}{(y.re \cdot x.re + \left(y.im \cdot x.im\right))_*}}}{\sqrt{y.im^2 + y.re^2}^*}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{\sqrt{y.im^2 + y.re^2}^*}\\ \end{array}\]

Reproduce

herbie shell --seed 2019022 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_divideComplex, real part"
  (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))

Details

Time bar (total: 18.6s)Debug log

sample58.0ms

Algorithm
intervals
Results
42.0ms270×body80valid

simplify13.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
13.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize32.0ms

Local error

Found 3 expressions with local error:

26.8b
(/ (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))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
11×add-cube-cbrt
11×*-un-lft-identity
11×add-sqr-sqrt
9×times-frac
5×add-exp-log
5×add-cbrt-cube
3×add-log-exp
3×associate-/l*
3×log1p-expm1-u
3×associate-/r*
3×pow1
3×expm1-log1p-u
2×fma-udef
1×div-inv
1×div-exp
1×frac-2neg
1×clear-num
1×cbrt-undiv
Counts
3 → 49
Calls
3 calls:
Slowest
6.0ms
(/ (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))

series140.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
88.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
26.0ms
(fma y.im y.im (* y.re y.re))
26.0ms
(fma x.re y.re (* x.im y.im))

simplify527.0ms

Counts
34 → 58
Calls
34 calls:
Slowest
206.0ms
(/ (* (* (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))))
52.0ms
(/ (* (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)))))
20.0ms
(/ (* (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))))
19.0ms
(/ (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)))))
15.0ms
(/ (sqrt (fma x.re y.re (* x.im y.im))) (sqrt (fma y.im y.im (* y.re y.re))))

prune608.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.4b

localize20.0ms

Local error

Found 4 expressions with local error:

16.2b
(/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re))
0.5b
(fma y.im x.im (* x.re y.re))
0.2b
(* (/ 1 (hypot y.im y.re)) (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re)))
0.0b
(hypot y.im y.re)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cube-cbrt
20×*-un-lft-identity
20×add-sqr-sqrt
18×times-frac
16×add-exp-log
13×associate-*r*
11×add-cbrt-cube
6×pow1
4×add-log-exp
4×log1p-expm1-u
4×prod-exp
4×associate-*l*
4×expm1-log1p-u
3×associate-/l*
3×div-inv
3×div-exp
3×associate-/r*
2×cbrt-unprod
2×rec-exp
2×cbrt-undiv
1×fma-udef
1×*-commutative
1×associate-*r/
1×associate-*l/
1×pow-prod-down
1×frac-2neg
1×clear-num
1×hypot-udef
1×frac-times
Counts
4 → 86
Calls
4 calls:
Slowest
10.0ms
(* (/ 1 (hypot y.im y.re)) (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re)))
3.0ms
(/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re))
0.0ms
(hypot y.im y.re)
0.0ms
(fma y.im x.im (* x.re y.re))

series269.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(* (/ 1 (hypot y.im y.re)) (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re)))
63.0ms
(/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re))
36.0ms
(hypot y.im y.re)
35.0ms
(fma y.im x.im (* x.re y.re))

simplify1.9s

Counts
63 → 98
Calls
63 calls:
Slowest
579.0ms
(* (* (* (/ 1 (hypot y.im y.re)) (/ 1 (hypot y.im y.re))) (/ 1 (hypot y.im y.re))) (* (* (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re)) (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re))) (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re))))
210.0ms
(* (/ 1 (hypot y.im y.re)) (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re)))
162.0ms
(/ (* (* (fma y.im x.im (* x.re y.re)) (fma y.im x.im (* x.re y.re))) (fma y.im x.im (* x.re y.re))) (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re)))
157.0ms
(* (* (* (/ 1 (hypot y.im y.re)) (/ 1 (hypot y.im y.re))) (/ 1 (hypot y.im y.re))) (/ (* (* (fma y.im x.im (* x.re y.re)) (fma y.im x.im (* x.re y.re))) (fma y.im x.im (* x.re y.re))) (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re))))
107.0ms
(+ (log (/ 1 (hypot y.im y.re))) (log (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re))))

prune1.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.6b

localize15.0ms

Local error

Found 4 expressions with local error:

16.2b
(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))
0.3b
(fma y.re x.re (* x.im y.im))
0.1b
(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.0b
(hypot y.im y.re)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-cube-cbrt
54×*-un-lft-identity
54×add-sqr-sqrt
16×associate-/l*
11×add-exp-log
11×add-cbrt-cube
6×div-inv
6×associate-/r*
4×add-log-exp
4×log1p-expm1-u
4×div-exp
4×cbrt-undiv
4×pow1
4×expm1-log1p-u
2×frac-2neg
2×clear-num
1×associate-/l/
1×fma-udef
1×hypot-udef
Counts
4 → 121
Calls
4 calls:
Slowest
6.0ms
(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
4.0ms
(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))
0.0ms
(fma y.re x.re (* x.im y.im))
0.0ms
(hypot y.im y.re)

series228.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
100.0ms
(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
66.0ms
(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))
34.0ms
(hypot y.im y.re)
28.0ms
(fma y.re x.re (* x.im y.im))

simplify3.1s

Counts
135 → 133
Calls
135 calls:
Slowest
362.0ms
(/ (sqrt (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))) (sqrt (hypot y.im y.re)))
292.0ms
(/ (/ (* (* (fma y.re x.re (* x.im y.im)) (fma y.re x.re (* x.im y.im))) (fma y.re x.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) (hypot y.im y.re)) (hypot y.im y.re)))
209.0ms
(/ (* (* (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))) (/ (fma y.re x.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)))
177.0ms
(/ (/ (* (cbrt (fma y.re x.re (* x.im y.im))) (cbrt (fma y.re x.re (* x.im y.im)))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re)))) 1)
139.0ms
(/ (* (* (fma y.re x.re (* x.im y.im)) (fma y.re x.re (* x.im y.im))) (fma y.re x.re (* x.im y.im))) (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re)))

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.5b

localize15.0ms

Local error

Found 4 expressions with local error:

16.3b
(/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))
0.3b
(fma y.re x.re (* x.im y.im))
0.2b
(/ 1 (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im))))
0.1b
(/ (/ 1 (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))) (hypot y.im y.re))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
33×times-frac
29×add-cube-cbrt
29×*-un-lft-identity
29×add-sqr-sqrt
19×associate-/r*
16×add-exp-log
8×associate-/l*
8×div-inv
8×add-cbrt-cube
6×div-exp
5×associate-/r/
5×pow1
4×add-log-exp
4×log1p-expm1-u
4×rec-exp
4×expm1-log1p-u
3×frac-2neg
3×clear-num
2×cbrt-undiv
1×associate-/l/
1×inv-pow
1×pow-flip
1×fma-udef
Counts
4 → 109
Calls
4 calls:
Slowest
9.0ms
(/ (/ 1 (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))) (hypot y.im y.re))
7.0ms
(/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))
3.0ms
(/ 1 (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im))))
0.0ms
(fma y.re x.re (* x.im y.im))

series400.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(/ (/ 1 (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))) (hypot y.im y.re))
125.0ms
(/ 1 (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im))))
81.0ms
(/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))
40.0ms
(fma y.re x.re (* x.im y.im))

simplify5.0s

Counts
92 → 121
Calls
92 calls:
Slowest
406.0ms
(/ (/ 1 (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))) (cbrt (hypot y.im y.re)))
375.0ms
(/ (/ 1 (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))) (sqrt (hypot y.im y.re)))
340.0ms
(/ (/ 1 (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))) (cbrt (hypot y.im y.re)))
312.0ms
(/ (/ 1 (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))) (sqrt (hypot y.im y.re)))
271.0ms
(/ (/ 1 (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))) (hypot y.im y.re))

prune1.5s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 2.5b

regimes365.0ms

Accuracy

28.9% (10.0b remaining)

Error of 12.5b against oracle of 2.5b and baseline of 16.5b

bsearch133.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
1.1s8447×body80valid