Complex division, real part

Percentage Accurate: 61.1% → 79.9%

Time: 7.8s

Alternatives: 8

Speedup: 1.6×

Specification

Math

\[\begin{array}{l} \\ \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))

C

double code(double a, double b, double c, double d) {
	return ((a * c) + (b * d)) / ((c * c) + (d * d));
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    code = ((a * c) + (b * d)) / ((c * c) + (d * d))
end function

Java

public static double code(double a, double b, double c, double d) {
	return ((a * c) + (b * d)) / ((c * c) + (d * d));
}

Python

def code(a, b, c, d):
	return ((a * c) + (b * d)) / ((c * c) + (d * d))

Julia

function code(a, b, c, d)
	return Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)))
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
end

Wolfram

code[a_, b_, c_, d_] := N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 61.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))

C

double code(double a, double b, double c, double d) {
	return ((a * c) + (b * d)) / ((c * c) + (d * d));
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    code = ((a * c) + (b * d)) / ((c * c) + (d * d))
end function

Java

public static double code(double a, double b, double c, double d) {
	return ((a * c) + (b * d)) / ((c * c) + (d * d));
}

Python

def code(a, b, c, d):
	return ((a * c) + (b * d)) / ((c * c) + (d * d))

Julia

function code(a, b, c, d)
	return Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)))
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
end

Wolfram

code[a_, b_, c_, d_] := N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 79.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{fma}\left(d, \frac{b}{c}, a\right)}{c}\\ \mathbf{if}\;c \leq -3.2 \cdot 10^{+92}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(d, b, c \cdot a\right)}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+17}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (fma d (/ b c) a) c)))
   (if (<= c -3.2e+92)
     t_0
     (if (<= c -3.3e-14)
       (/ (fma d b (* c a)) (+ (* c c) (* d d)))
       (if (<= c 6e+17) (/ (fma a (/ c d) b) d) t_0)))))

C

double code(double a, double b, double c, double d) {
	double t_0 = fma(d, (b / c), a) / c;
	double tmp;
	if (c <= -3.2e+92) {
		tmp = t_0;
	} else if (c <= -3.3e-14) {
		tmp = fma(d, b, (c * a)) / ((c * c) + (d * d));
	} else if (c <= 6e+17) {
		tmp = fma(a, (c / d), b) / d;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = Float64(fma(d, Float64(b / c), a) / c)
	tmp = 0.0
	if (c <= -3.2e+92)
		tmp = t_0;
	elseif (c <= -3.3e-14)
		tmp = Float64(fma(d, b, Float64(c * a)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (c <= 6e+17)
		tmp = Float64(fma(a, Float64(c / d), b) / d);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(d * N[(b / c), $MachinePrecision] + a), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[c, -3.2e+92], t$95$0, If[LessEqual[c, -3.3e-14], N[(N[(d * b + N[(c * a), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6e+17], N[(N[(a * N[(c / d), $MachinePrecision] + b), $MachinePrecision] / d), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.20000000000000025e92 or 6e17 < c

   1. Initial program 41.5%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{a \cdot c + b \cdot d}}{c \cdot c + d \cdot d} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{b \cdot d + a \cdot c}}{c \cdot c + d \cdot d} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{b \cdot d} + a \cdot c}{c \cdot c + d \cdot d} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{d \cdot b} + a \cdot c}{c \cdot c + d \cdot d} \]

      5. lower-fma.f64 41.6

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(d, b, a \cdot c\right)}}{c \cdot c + d \cdot d} \]

   4. Applied rewrites 41.6%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(d, b, a \cdot c\right)}}{c \cdot c + d \cdot d} \]

   5. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{a + \frac{b \cdot d}{c}}{c}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a + \frac{b \cdot d}{c}}{c}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{b \cdot d}{c} + a}}{c} \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{d \cdot b}}{c} + a}{c} \]

      4. associate-/l* N/A

         \[\leadsto \frac{\color{blue}{d \cdot \frac{b}{c}} + a}{c} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(d, \frac{b}{c}, a\right)}}{c} \]

      6. lower-/.f64 86.4

         \[\leadsto \frac{\mathsf{fma}\left(d, \color{blue}{\frac{b}{c}}, a\right)}{c} \]

   7. Applied rewrites 86.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(d, \frac{b}{c}, a\right)}{c}} \]

   if -3.20000000000000025e92 < c < -3.2999999999999998e-14

   1. Initial program 79.0%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{a \cdot c + b \cdot d}}{c \cdot c + d \cdot d} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{b \cdot d + a \cdot c}}{c \cdot c + d \cdot d} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{b \cdot d} + a \cdot c}{c \cdot c + d \cdot d} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{d \cdot b} + a \cdot c}{c \cdot c + d \cdot d} \]

      5. lower-fma.f64 79.1

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(d, b, a \cdot c\right)}}{c \cdot c + d \cdot d} \]

   4. Applied rewrites 79.1%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(d, b, a \cdot c\right)}}{c \cdot c + d \cdot d} \]

   if -3.2999999999999998e-14 < c < 6e17

   1. Initial program 61.0%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in d around inf

      \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{a \cdot c}{d} + b}}{d} \]

      3. associate-/l* N/A

         \[\leadsto \frac{\color{blue}{a \cdot \frac{c}{d}} + b}{d} \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}}{d} \]

      5. lower-/.f64 83.6

         \[\leadsto \frac{\mathsf{fma}\left(a, \color{blue}{\frac{c}{d}}, b\right)}{d} \]

   5. Applied rewrites 83.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{+92}:\\ \;\;\;\;\frac{\mathsf{fma}\left(d, \frac{b}{c}, a\right)}{c}\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(d, b, c \cdot a\right)}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+17}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(d, \frac{b}{c}, a\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{+81}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;c \leq -1.09 \cdot 10^{-13}:\\ \;\;\;\;\frac{\mathsf{fma}\left(d, b, c \cdot a\right)}{c \cdot c}\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+79}:\\ \;\;\;\;\frac{c \cdot a}{\mathsf{fma}\left(d, d, c \cdot c\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -3.2e+81)
   (/ a c)
   (if (<= c -1.09e-13)
     (/ (fma d b (* c a)) (* c c))
     (if (<= c 6.5e-25)
       (/ b d)
       (if (<= c 4.5e+79) (/ (* c a) (fma d d (* c c))) (/ a c))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -3.2e+81) {
		tmp = a / c;
	} else if (c <= -1.09e-13) {
		tmp = fma(d, b, (c * a)) / (c * c);
	} else if (c <= 6.5e-25) {
		tmp = b / d;
	} else if (c <= 4.5e+79) {
		tmp = (c * a) / fma(d, d, (c * c));
	} else {
		tmp = a / c;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -3.2e+81)
		tmp = Float64(a / c);
	elseif (c <= -1.09e-13)
		tmp = Float64(fma(d, b, Float64(c * a)) / Float64(c * c));
	elseif (c <= 6.5e-25)
		tmp = Float64(b / d);
	elseif (c <= 4.5e+79)
		tmp = Float64(Float64(c * a) / fma(d, d, Float64(c * c)));
	else
		tmp = Float64(a / c);
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -3.2e+81], N[(a / c), $MachinePrecision], If[LessEqual[c, -1.09e-13], N[(N[(d * b + N[(c * a), $MachinePrecision]), $MachinePrecision] / N[(c * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.5e-25], N[(b / d), $MachinePrecision], If[LessEqual[c, 4.5e+79], N[(N[(c * a), $MachinePrecision] / N[(d * d + N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a / c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.2e81 or 4.49999999999999994e79 < c

   1. Initial program 36.0%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{a}{c}} \]
   4. Step-by-step derivation

      1. lower-/.f64 75.7

         \[\leadsto \color{blue}{\frac{a}{c}} \]

   5. Applied rewrites 75.7%

      \[\leadsto \color{blue}{\frac{a}{c}} \]

   if -3.2e81 < c < -1.09000000000000003e-13

   1. Initial program 83.1%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \frac{a \cdot c + b \cdot d}{\color{blue}{{c}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

         \[\leadsto \frac{a \cdot c + b \cdot d}{\color{blue}{c \cdot c}} \]

      2. lower-*.f64 72.0

         \[\leadsto \frac{a \cdot c + b \cdot d}{\color{blue}{c \cdot c}} \]

   5. Applied rewrites 72.0%

      \[\leadsto \frac{a \cdot c + b \cdot d}{\color{blue}{c \cdot c}} \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{a \cdot c + b \cdot d}}{c \cdot c} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{a \cdot c + \color{blue}{b \cdot d}}{c \cdot c} \]

      3. *-commutative N/A

         \[\leadsto \frac{a \cdot c + \color{blue}{d \cdot b}}{c \cdot c} \]

      4. +-commutative N/A

         \[\leadsto \frac{\color{blue}{d \cdot b + a \cdot c}}{c \cdot c} \]

      5. lift-fma.f64 72.0

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(d, b, a \cdot c\right)}}{c \cdot c} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(d, b, \color{blue}{a \cdot c}\right)}{c \cdot c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(d, b, \color{blue}{c \cdot a}\right)}{c \cdot c} \]

      8. lower-*.f64 72.0

         \[\leadsto \frac{\mathsf{fma}\left(d, b, \color{blue}{c \cdot a}\right)}{c \cdot c} \]

   7. Applied rewrites 72.0%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(d, b, c \cdot a\right)}}{c \cdot c} \]

   if -1.09000000000000003e-13 < c < 6.5e-25

   1. Initial program 60.1%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{b}{d}} \]
   4. Step-by-step derivation

      1. lower-/.f64 65.8

         \[\leadsto \color{blue}{\frac{b}{d}} \]

   5. Applied rewrites 65.8%

      \[\leadsto \color{blue}{\frac{b}{d}} \]

   if 6.5e-25 < c < 4.49999999999999994e79

   1. Initial program 80.7%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{a \cdot c}{{c}^{2} + {d}^{2}}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot c}{{c}^{2} + {d}^{2}}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{a \cdot c}}{{c}^{2} + {d}^{2}} \]

      3. +-commutative N/A

         \[\leadsto \frac{a \cdot c}{\color{blue}{{d}^{2} + {c}^{2}}} \]

      4. unpow2 N/A

         \[\leadsto \frac{a \cdot c}{\color{blue}{d \cdot d} + {c}^{2}} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{a \cdot c}{\color{blue}{\mathsf{fma}\left(d, d, {c}^{2}\right)}} \]

      6. unpow2 N/A

         \[\leadsto \frac{a \cdot c}{\mathsf{fma}\left(d, d, \color{blue}{c \cdot c}\right)} \]

      7. lower-*.f64 75.9

         \[\leadsto \frac{a \cdot c}{\mathsf{fma}\left(d, d, \color{blue}{c \cdot c}\right)} \]

   5. Applied rewrites 75.9%

      \[\leadsto \color{blue}{\frac{a \cdot c}{\mathsf{fma}\left(d, d, c \cdot c\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{+81}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;c \leq -1.09 \cdot 10^{-13}:\\ \;\;\;\;\frac{\mathsf{fma}\left(d, b, c \cdot a\right)}{c \cdot c}\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+79}:\\ \;\;\;\;\frac{c \cdot a}{\mathsf{fma}\left(d, d, c \cdot c\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{+81}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{\mathsf{fma}\left(d, b, c \cdot a\right)}{c \cdot c}\\ \mathbf{elif}\;c \leq 13500000:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -3.2e+81)
   (/ a c)
   (if (<= c -7.5e-10)
     (/ (fma d b (* c a)) (* c c))
     (if (<= c 13500000.0) (/ (fma a (/ c d) b) d) (/ a c)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -3.2e+81) {
		tmp = a / c;
	} else if (c <= -7.5e-10) {
		tmp = fma(d, b, (c * a)) / (c * c);
	} else if (c <= 13500000.0) {
		tmp = fma(a, (c / d), b) / d;
	} else {
		tmp = a / c;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -3.2e+81)
		tmp = Float64(a / c);
	elseif (c <= -7.5e-10)
		tmp = Float64(fma(d, b, Float64(c * a)) / Float64(c * c));
	elseif (c <= 13500000.0)
		tmp = Float64(fma(a, Float64(c / d), b) / d);
	else
		tmp = Float64(a / c);
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -3.2e+81], N[(a / c), $MachinePrecision], If[LessEqual[c, -7.5e-10], N[(N[(d * b + N[(c * a), $MachinePrecision]), $MachinePrecision] / N[(c * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 13500000.0], N[(N[(a * N[(c / d), $MachinePrecision] + b), $MachinePrecision] / d), $MachinePrecision], N[(a / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.2e81 or 1.35e7 < c

   1. Initial program 43.1%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{a}{c}} \]
   4. Step-by-step derivation

      1. lower-/.f64 73.4

         \[\leadsto \color{blue}{\frac{a}{c}} \]

   5. Applied rewrites 73.4%

      \[\leadsto \color{blue}{\frac{a}{c}} \]

   if -3.2e81 < c < -7.49999999999999995e-10

   1. Initial program 83.1%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \frac{a \cdot c + b \cdot d}{\color{blue}{{c}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

         \[\leadsto \frac{a \cdot c + b \cdot d}{\color{blue}{c \cdot c}} \]

      2. lower-*.f64 72.0

         \[\leadsto \frac{a \cdot c + b \cdot d}{\color{blue}{c \cdot c}} \]

   5. Applied rewrites 72.0%

      \[\leadsto \frac{a \cdot c + b \cdot d}{\color{blue}{c \cdot c}} \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{a \cdot c + b \cdot d}}{c \cdot c} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{a \cdot c + \color{blue}{b \cdot d}}{c \cdot c} \]

      3. *-commutative N/A

         \[\leadsto \frac{a \cdot c + \color{blue}{d \cdot b}}{c \cdot c} \]

      4. +-commutative N/A

         \[\leadsto \frac{\color{blue}{d \cdot b + a \cdot c}}{c \cdot c} \]

      5. lift-fma.f64 72.0

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(d, b, a \cdot c\right)}}{c \cdot c} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(d, b, \color{blue}{a \cdot c}\right)}{c \cdot c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(d, b, \color{blue}{c \cdot a}\right)}{c \cdot c} \]

      8. lower-*.f64 72.0

         \[\leadsto \frac{\mathsf{fma}\left(d, b, \color{blue}{c \cdot a}\right)}{c \cdot c} \]

   7. Applied rewrites 72.0%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(d, b, c \cdot a\right)}}{c \cdot c} \]

   if -7.49999999999999995e-10 < c < 1.35e7

   1. Initial program 60.4%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in d around inf

      \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{a \cdot c}{d} + b}}{d} \]

      3. associate-/l* N/A

         \[\leadsto \frac{\color{blue}{a \cdot \frac{c}{d}} + b}{d} \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}}{d} \]

      5. lower-/.f64 84.1

         \[\leadsto \frac{\mathsf{fma}\left(a, \color{blue}{\frac{c}{d}}, b\right)}{d} \]

   5. Applied rewrites 84.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 64.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.12 \cdot 10^{-13}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+79}:\\ \;\;\;\;\frac{c \cdot a}{\mathsf{fma}\left(d, d, c \cdot c\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -1.12e-13)
   (/ a c)
   (if (<= c 6.5e-25)
     (/ b d)
     (if (<= c 4.5e+79) (/ (* c a) (fma d d (* c c))) (/ a c)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -1.12e-13) {
		tmp = a / c;
	} else if (c <= 6.5e-25) {
		tmp = b / d;
	} else if (c <= 4.5e+79) {
		tmp = (c * a) / fma(d, d, (c * c));
	} else {
		tmp = a / c;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -1.12e-13)
		tmp = Float64(a / c);
	elseif (c <= 6.5e-25)
		tmp = Float64(b / d);
	elseif (c <= 4.5e+79)
		tmp = Float64(Float64(c * a) / fma(d, d, Float64(c * c)));
	else
		tmp = Float64(a / c);
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -1.12e-13], N[(a / c), $MachinePrecision], If[LessEqual[c, 6.5e-25], N[(b / d), $MachinePrecision], If[LessEqual[c, 4.5e+79], N[(N[(c * a), $MachinePrecision] / N[(d * d + N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.12e-13 or 4.49999999999999994e79 < c

   1. Initial program 47.6%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{a}{c}} \]
   4. Step-by-step derivation

      1. lower-/.f64 69.2

         \[\leadsto \color{blue}{\frac{a}{c}} \]

   5. Applied rewrites 69.2%

      \[\leadsto \color{blue}{\frac{a}{c}} \]

   if -1.12e-13 < c < 6.5e-25

   1. Initial program 60.1%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{b}{d}} \]
   4. Step-by-step derivation

      1. lower-/.f64 65.8

         \[\leadsto \color{blue}{\frac{b}{d}} \]

   5. Applied rewrites 65.8%

      \[\leadsto \color{blue}{\frac{b}{d}} \]

   if 6.5e-25 < c < 4.49999999999999994e79

   1. Initial program 80.7%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{a \cdot c}{{c}^{2} + {d}^{2}}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot c}{{c}^{2} + {d}^{2}}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{a \cdot c}}{{c}^{2} + {d}^{2}} \]

      3. +-commutative N/A

         \[\leadsto \frac{a \cdot c}{\color{blue}{{d}^{2} + {c}^{2}}} \]

      4. unpow2 N/A

         \[\leadsto \frac{a \cdot c}{\color{blue}{d \cdot d} + {c}^{2}} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{a \cdot c}{\color{blue}{\mathsf{fma}\left(d, d, {c}^{2}\right)}} \]

      6. unpow2 N/A

         \[\leadsto \frac{a \cdot c}{\mathsf{fma}\left(d, d, \color{blue}{c \cdot c}\right)} \]

      7. lower-*.f64 75.9

         \[\leadsto \frac{a \cdot c}{\mathsf{fma}\left(d, d, \color{blue}{c \cdot c}\right)} \]

   5. Applied rewrites 75.9%

      \[\leadsto \color{blue}{\frac{a \cdot c}{\mathsf{fma}\left(d, d, c \cdot c\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.12 \cdot 10^{-13}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+79}:\\ \;\;\;\;\frac{c \cdot a}{\mathsf{fma}\left(d, d, c \cdot c\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{fma}\left(d, \frac{b}{c}, a\right)}{c}\\ \mathbf{if}\;c \leq -7.5 \cdot 10^{-10}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+17}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (fma d (/ b c) a) c)))
   (if (<= c -7.5e-10) t_0 (if (<= c 6e+17) (/ (fma a (/ c d) b) d) t_0))))

C

double code(double a, double b, double c, double d) {
	double t_0 = fma(d, (b / c), a) / c;
	double tmp;
	if (c <= -7.5e-10) {
		tmp = t_0;
	} else if (c <= 6e+17) {
		tmp = fma(a, (c / d), b) / d;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = Float64(fma(d, Float64(b / c), a) / c)
	tmp = 0.0
	if (c <= -7.5e-10)
		tmp = t_0;
	elseif (c <= 6e+17)
		tmp = Float64(fma(a, Float64(c / d), b) / d);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(d * N[(b / c), $MachinePrecision] + a), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[c, -7.5e-10], t$95$0, If[LessEqual[c, 6e+17], N[(N[(a * N[(c / d), $MachinePrecision] + b), $MachinePrecision] / d), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if c < -7.49999999999999995e-10 or 6e17 < c

   1. Initial program 51.1%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{a \cdot c + b \cdot d}}{c \cdot c + d \cdot d} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{b \cdot d + a \cdot c}}{c \cdot c + d \cdot d} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{b \cdot d} + a \cdot c}{c \cdot c + d \cdot d} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{d \cdot b} + a \cdot c}{c \cdot c + d \cdot d} \]

      5. lower-fma.f64 51.2

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(d, b, a \cdot c\right)}}{c \cdot c + d \cdot d} \]

   4. Applied rewrites 51.2%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(d, b, a \cdot c\right)}}{c \cdot c + d \cdot d} \]

   5. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{a + \frac{b \cdot d}{c}}{c}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a + \frac{b \cdot d}{c}}{c}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{b \cdot d}{c} + a}}{c} \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{d \cdot b}}{c} + a}{c} \]

      4. associate-/l* N/A

         \[\leadsto \frac{\color{blue}{d \cdot \frac{b}{c}} + a}{c} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(d, \frac{b}{c}, a\right)}}{c} \]

      6. lower-/.f64 81.3

         \[\leadsto \frac{\mathsf{fma}\left(d, \color{blue}{\frac{b}{c}}, a\right)}{c} \]

   7. Applied rewrites 81.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(d, \frac{b}{c}, a\right)}{c}} \]

   if -7.49999999999999995e-10 < c < 6e17

   1. Initial program 61.0%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in d around inf

      \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{a \cdot c}{d} + b}}{d} \]

      3. associate-/l* N/A

         \[\leadsto \frac{\color{blue}{a \cdot \frac{c}{d}} + b}{d} \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}}{d} \]

      5. lower-/.f64 83.6

         \[\leadsto \frac{\mathsf{fma}\left(a, \color{blue}{\frac{c}{d}}, b\right)}{d} \]

   5. Applied rewrites 83.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 78.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{fma}\left(b, \frac{d}{c}, a\right)}{c}\\ \mathbf{if}\;c \leq -7.5 \cdot 10^{-10}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+17}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (fma b (/ d c) a) c)))
   (if (<= c -7.5e-10) t_0 (if (<= c 6e+17) (/ (fma a (/ c d) b) d) t_0))))

C

double code(double a, double b, double c, double d) {
	double t_0 = fma(b, (d / c), a) / c;
	double tmp;
	if (c <= -7.5e-10) {
		tmp = t_0;
	} else if (c <= 6e+17) {
		tmp = fma(a, (c / d), b) / d;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = Float64(fma(b, Float64(d / c), a) / c)
	tmp = 0.0
	if (c <= -7.5e-10)
		tmp = t_0;
	elseif (c <= 6e+17)
		tmp = Float64(fma(a, Float64(c / d), b) / d);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(b * N[(d / c), $MachinePrecision] + a), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[c, -7.5e-10], t$95$0, If[LessEqual[c, 6e+17], N[(N[(a * N[(c / d), $MachinePrecision] + b), $MachinePrecision] / d), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if c < -7.49999999999999995e-10 or 6e17 < c

   1. Initial program 51.1%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{a + \frac{b \cdot d}{c}}{c}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a + \frac{b \cdot d}{c}}{c}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{b \cdot d}{c} + a}}{c} \]

      3. associate-/l* N/A

         \[\leadsto \frac{\color{blue}{b \cdot \frac{d}{c}} + a}{c} \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(b, \frac{d}{c}, a\right)}}{c} \]

      5. lower-/.f64 80.5

         \[\leadsto \frac{\mathsf{fma}\left(b, \color{blue}{\frac{d}{c}}, a\right)}{c} \]

   5. Applied rewrites 80.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(b, \frac{d}{c}, a\right)}{c}} \]

   if -7.49999999999999995e-10 < c < 6e17

   1. Initial program 61.0%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in d around inf

      \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{a \cdot c}{d} + b}}{d} \]

      3. associate-/l* N/A

         \[\leadsto \frac{\color{blue}{a \cdot \frac{c}{d}} + b}{d} \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}}{d} \]

      5. lower-/.f64 83.6

         \[\leadsto \frac{\mathsf{fma}\left(a, \color{blue}{\frac{c}{d}}, b\right)}{d} \]

   5. Applied rewrites 83.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 63.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.12 \cdot 10^{-13}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;c \leq 3600000:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -1.12e-13) (/ a c) (if (<= c 3600000.0) (/ b d) (/ a c))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -1.12e-13) {
		tmp = a / c;
	} else if (c <= 3600000.0) {
		tmp = b / d;
	} else {
		tmp = a / c;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if (c <= (-1.12d-13)) then
        tmp = a / c
    else if (c <= 3600000.0d0) then
        tmp = b / d
    else
        tmp = a / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -1.12e-13) {
		tmp = a / c;
	} else if (c <= 3600000.0) {
		tmp = b / d;
	} else {
		tmp = a / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -1.12e-13:
		tmp = a / c
	elif c <= 3600000.0:
		tmp = b / d
	else:
		tmp = a / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -1.12e-13)
		tmp = Float64(a / c);
	elseif (c <= 3600000.0)
		tmp = Float64(b / d);
	else
		tmp = Float64(a / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -1.12e-13)
		tmp = a / c;
	elseif (c <= 3600000.0)
		tmp = b / d;
	else
		tmp = a / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -1.12e-13], N[(a / c), $MachinePrecision], If[LessEqual[c, 3600000.0], N[(b / d), $MachinePrecision], N[(a / c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if c < -1.12e-13 or 3.6e6 < c

   1. Initial program 52.3%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{a}{c}} \]
   4. Step-by-step derivation

      1. lower-/.f64 67.6

         \[\leadsto \color{blue}{\frac{a}{c}} \]

   5. Applied rewrites 67.6%

      \[\leadsto \color{blue}{\frac{a}{c}} \]

   if -1.12e-13 < c < 3.6e6

   1. Initial program 60.1%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{b}{d}} \]
   4. Step-by-step derivation

      1. lower-/.f64 64.9

         \[\leadsto \color{blue}{\frac{b}{d}} \]

   5. Applied rewrites 64.9%

      \[\leadsto \color{blue}{\frac{b}{d}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 42.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \frac{a}{c} \end{array} \]

FPCore

(FPCore (a b c d) :precision binary64 (/ a c))

C

double code(double a, double b, double c, double d) {
	return a / c;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    code = a / c
end function

Java

public static double code(double a, double b, double c, double d) {
	return a / c;
}

Python

def code(a, b, c, d):
	return a / c

Julia

function code(a, b, c, d)
	return Float64(a / c)
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = a / c;
end

Wolfram

code[a_, b_, c_, d_] := N[(a / c), $MachinePrecision]

Derivation

1. Initial program 56.2%

   \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
2. Add Preprocessing

3. Taylor expanded in c around inf

   \[\leadsto \color{blue}{\frac{a}{c}} \]
4. Step-by-step derivation

   1. lower-/.f64 42.5

      \[\leadsto \color{blue}{\frac{a}{c}} \]

5. Applied rewrites 42.5%

   \[\leadsto \color{blue}{\frac{a}{c}} \]
6. Add Preprocessing

Developer Target 1: 99.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left|d\right| < \left|c\right|:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c + d \cdot \frac{d}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d + c \cdot \frac{c}{d}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (< (fabs d) (fabs c))
   (/ (+ a (* b (/ d c))) (+ c (* d (/ d c))))
   (/ (+ b (* a (/ c d))) (+ d (* c (/ c d))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (fabs(d) < fabs(c)) {
		tmp = (a + (b * (d / c))) / (c + (d * (d / c)));
	} else {
		tmp = (b + (a * (c / d))) / (d + (c * (c / d)));
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if (abs(d) < abs(c)) then
        tmp = (a + (b * (d / c))) / (c + (d * (d / c)))
    else
        tmp = (b + (a * (c / d))) / (d + (c * (c / d)))
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (Math.abs(d) < Math.abs(c)) {
		tmp = (a + (b * (d / c))) / (c + (d * (d / c)));
	} else {
		tmp = (b + (a * (c / d))) / (d + (c * (c / d)));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if math.fabs(d) < math.fabs(c):
		tmp = (a + (b * (d / c))) / (c + (d * (d / c)))
	else:
		tmp = (b + (a * (c / d))) / (d + (c * (c / d)))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (abs(d) < abs(c))
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / Float64(c + Float64(d * Float64(d / c))));
	else
		tmp = Float64(Float64(b + Float64(a * Float64(c / d))) / Float64(d + Float64(c * Float64(c / d))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (abs(d) < abs(c))
		tmp = (a + (b * (d / c))) / (c + (d * (d / c)));
	else
		tmp = (b + (a * (c / d))) / (d + (c * (c / d)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Less[N[Abs[d], $MachinePrecision], N[Abs[c], $MachinePrecision]], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c + N[(d * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(d + N[(c * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024234 
(FPCore (a b c d)
  :name "Complex division, real part"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (fabs d) (fabs c)) (/ (+ a (* b (/ d c))) (+ c (* d (/ d c)))) (/ (+ b (* a (/ c d))) (+ d (* c (/ c d))))))

  (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))