Complex division, imag part

Percentage Accurate: 62.0% → 80.1%

Time: 11.4s

Alternatives: 8

Speedup: 1.8×

Specification

Math

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

FPCore

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

C

double code(double a, double b, double c, double d) {
	return ((b * c) - (a * 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 = ((b * c) - (a * d)) / ((c * c) + (d * d))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 62.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double a, double b, double c, double d) {
	return ((b * c) - (a * 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 = ((b * c) - (a * d)) / ((c * c) + (d * d))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 80.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{b}{c} - \frac{\frac{d}{c}}{\frac{c}{a}}\\ \mathbf{if}\;c \leq -6.2 \cdot 10^{+87}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 1.16 \cdot 10^{-122}:\\ \;\;\;\;\frac{b \cdot \frac{c}{d} - a}{d}\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+99}:\\ \;\;\;\;\frac{c \cdot b - d \cdot a}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (- (/ b c) (/ (/ d c) (/ c a)))))
   (if (<= c -6.2e+87)
     t_0
     (if (<= c 1.16e-122)
       (/ (- (* b (/ c d)) a) d)
       (if (<= c 1.15e+99) (/ (- (* c b) (* d a)) (+ (* c c) (* d d))) t_0)))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (b / c) - ((d / c) / (c / a));
	double tmp;
	if (c <= -6.2e+87) {
		tmp = t_0;
	} else if (c <= 1.16e-122) {
		tmp = ((b * (c / d)) - a) / d;
	} else if (c <= 1.15e+99) {
		tmp = ((c * b) - (d * a)) / ((c * c) + (d * d));
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (b / c) - ((d / c) / (c / a))
    if (c <= (-6.2d+87)) then
        tmp = t_0
    else if (c <= 1.16d-122) then
        tmp = ((b * (c / d)) - a) / d
    else if (c <= 1.15d+99) then
        tmp = ((c * b) - (d * a)) / ((c * c) + (d * d))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = (b / c) - ((d / c) / (c / a));
	double tmp;
	if (c <= -6.2e+87) {
		tmp = t_0;
	} else if (c <= 1.16e-122) {
		tmp = ((b * (c / d)) - a) / d;
	} else if (c <= 1.15e+99) {
		tmp = ((c * b) - (d * a)) / ((c * c) + (d * d));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (b / c) - ((d / c) / (c / a))
	tmp = 0
	if c <= -6.2e+87:
		tmp = t_0
	elif c <= 1.16e-122:
		tmp = ((b * (c / d)) - a) / d
	elif c <= 1.15e+99:
		tmp = ((c * b) - (d * a)) / ((c * c) + (d * d))
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(b / c) - Float64(Float64(d / c) / Float64(c / a)))
	tmp = 0.0
	if (c <= -6.2e+87)
		tmp = t_0;
	elseif (c <= 1.16e-122)
		tmp = Float64(Float64(Float64(b * Float64(c / d)) - a) / d);
	elseif (c <= 1.15e+99)
		tmp = Float64(Float64(Float64(c * b) - Float64(d * a)) / Float64(Float64(c * c) + Float64(d * d)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (b / c) - ((d / c) / (c / a));
	tmp = 0.0;
	if (c <= -6.2e+87)
		tmp = t_0;
	elseif (c <= 1.16e-122)
		tmp = ((b * (c / d)) - a) / d;
	elseif (c <= 1.15e+99)
		tmp = ((c * b) - (d * a)) / ((c * c) + (d * d));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(b / c), $MachinePrecision] - N[(N[(d / c), $MachinePrecision] / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.2e+87], t$95$0, If[LessEqual[c, 1.16e-122], N[(N[(N[(b * N[(c / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[c, 1.15e+99], N[(N[(N[(c * b), $MachinePrecision] - N[(d * a), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.1999999999999999e87 or 1.1500000000000001e99 < c

   1. Initial program 45.2%

      \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \]

   2. Taylor expanded in c around inf 77.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{a \cdot d}{{c}^{2}} + \frac{b}{c}} \]
   3. Step-by-step derivation

      1. +-commutative 77.4%

         \[\leadsto \color{blue}{\frac{b}{c} + -1 \cdot \frac{a \cdot d}{{c}^{2}}} \]

      2. mul-1-neg 77.4%

         \[\leadsto \frac{b}{c} + \color{blue}{\left(-\frac{a \cdot d}{{c}^{2}}\right)} \]

      3. unsub-neg 77.4%

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

      4. unpow2 77.4%

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

      5. times-frac 90.5%

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

   4. Simplified 90.5%

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

      1. *-commutative 90.5%

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

      2. clear-num 90.5%

         \[\leadsto \frac{b}{c} - \frac{d}{c} \cdot \color{blue}{\frac{1}{\frac{c}{a}}} \]

      3. un-div-inv 90.5%

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

   6. Applied egg-rr 90.5%

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

   if -6.1999999999999999e87 < c < 1.16000000000000001e-122

   1. Initial program 72.9%

      \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \]

   2. Taylor expanded in c around 0 78.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{d} + \frac{b \cdot c}{{d}^{2}}} \]
   3. Step-by-step derivation

      1. +-commutative 78.8%

         \[\leadsto \color{blue}{\frac{b \cdot c}{{d}^{2}} + -1 \cdot \frac{a}{d}} \]

      2. mul-1-neg 78.8%

         \[\leadsto \frac{b \cdot c}{{d}^{2}} + \color{blue}{\left(-\frac{a}{d}\right)} \]

      3. unsub-neg 78.8%

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

      4. unpow2 78.8%

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

      5. associate-/l* 78.9%

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

   4. Simplified 78.9%

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

      1. associate-/l* 78.8%

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

      2. times-frac 84.8%

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

      3. *-commutative 84.8%

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

      4. associate-*r/ 87.9%

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

      5. sub-div 88.8%

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

   6. Applied egg-rr 88.8%

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

   if 1.16000000000000001e-122 < c < 1.1500000000000001e99

   1. Initial program 72.1%

      \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+87}:\\ \;\;\;\;\frac{b}{c} - \frac{\frac{d}{c}}{\frac{c}{a}}\\ \mathbf{elif}\;c \leq 1.16 \cdot 10^{-122}:\\ \;\;\;\;\frac{b \cdot \frac{c}{d} - a}{d}\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+99}:\\ \;\;\;\;\frac{c \cdot b - d \cdot a}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} - \frac{\frac{d}{c}}{\frac{c}{a}}\\ \end{array} \]

Alternative 2: 72.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.96 \cdot 10^{+27} \lor \neg \left(d \leq 4.8 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - d \cdot \frac{a}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -1.96e+27) (not (<= d 4.8e+46)))
   (/ (- a) d)
   (/ (- b (* d (/ a c))) c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -1.96e+27) || !(d <= 4.8e+46)) {
		tmp = -a / d;
	} else {
		tmp = (b - (d * (a / c))) / 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 ((d <= (-1.96d+27)) .or. (.not. (d <= 4.8d+46))) then
        tmp = -a / d
    else
        tmp = (b - (d * (a / c))) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -1.96e+27) || !(d <= 4.8e+46)) {
		tmp = -a / d;
	} else {
		tmp = (b - (d * (a / c))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -1.96e+27) or not (d <= 4.8e+46):
		tmp = -a / d
	else:
		tmp = (b - (d * (a / c))) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -1.96e+27) || !(d <= 4.8e+46))
		tmp = Float64(Float64(-a) / d);
	else
		tmp = Float64(Float64(b - Float64(d * Float64(a / c))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -1.96e+27) || ~((d <= 4.8e+46)))
		tmp = -a / d;
	else
		tmp = (b - (d * (a / c))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -1.96e+27], N[Not[LessEqual[d, 4.8e+46]], $MachinePrecision]], N[((-a) / d), $MachinePrecision], N[(N[(b - N[(d * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d < -1.95999999999999989e27 or 4.80000000000000017e46 < d

   1. Initial program 51.1%

      \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \]

   2. Taylor expanded in c around 0 75.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{d}} \]
   3. Step-by-step derivation

      1. associate-*r/ 75.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot a}{d}} \]

      2. neg-mul-1 75.7%

         \[\leadsto \frac{\color{blue}{-a}}{d} \]

   4. Simplified 75.7%

      \[\leadsto \color{blue}{\frac{-a}{d}} \]

   if -1.95999999999999989e27 < d < 4.80000000000000017e46

   1. Initial program 73.6%

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

      1. clear-num 73.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot c + d \cdot d}{b \cdot c - a \cdot d}}} \]

      2. associate-/r/ 72.8%

         \[\leadsto \color{blue}{\frac{1}{c \cdot c + d \cdot d} \cdot \left(b \cdot c - a \cdot d\right)} \]

      3. frac-2neg 72.8%

         \[\leadsto \color{blue}{\frac{-1}{-\left(c \cdot c + d \cdot d\right)}} \cdot \left(b \cdot c - a \cdot d\right) \]

      4. frac-2neg 72.8%

         \[\leadsto \color{blue}{\frac{1}{c \cdot c + d \cdot d}} \cdot \left(b \cdot c - a \cdot d\right) \]

      5. fma-def 72.8%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{fma}\left(c, c, d \cdot d\right)}} \cdot \left(b \cdot c - a \cdot d\right) \]

   3. Applied egg-rr 72.8%

      \[\leadsto \color{blue}{\frac{1}{\mathsf{fma}\left(c, c, d \cdot d\right)} \cdot \left(b \cdot c - a \cdot d\right)} \]

   4. Taylor expanded in c around inf 69.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{a \cdot d}{{c}^{2}} + \frac{b}{c}} \]
   5. Step-by-step derivation

      1. +-commutative 69.1%

         \[\leadsto \color{blue}{\frac{b}{c} + -1 \cdot \frac{a \cdot d}{{c}^{2}}} \]

      2. mul-1-neg 69.1%

         \[\leadsto \frac{b}{c} + \color{blue}{\left(-\frac{a \cdot d}{{c}^{2}}\right)} \]

      3. *-commutative 69.1%

         \[\leadsto \frac{b}{c} + \left(-\frac{\color{blue}{d \cdot a}}{{c}^{2}}\right) \]

      4. unpow2 69.1%

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

      5. times-frac 73.3%

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

      6. *-commutative 73.3%

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

      7. sub-neg 73.3%

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

      8. associate-*r/ 73.9%

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

      9. *-commutative 73.9%

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

      10. div-sub 75.4%

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

   6. Simplified 75.4%

      \[\leadsto \color{blue}{\frac{b - d \cdot \frac{a}{c}}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.96 \cdot 10^{+27} \lor \neg \left(d \leq 4.8 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - d \cdot \frac{a}{c}}{c}\\ \end{array} \]

Alternative 3: 76.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.25 \cdot 10^{+89} \lor \neg \left(c \leq 5.5 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{b - d \cdot \frac{a}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot \frac{b}{d} - a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -2.25e+89) (not (<= c 5.5e+57)))
   (/ (- b (* d (/ a c))) c)
   (/ (- (* c (/ b d)) a) d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.25e+89) || !(c <= 5.5e+57)) {
		tmp = (b - (d * (a / c))) / c;
	} else {
		tmp = ((c * (b / d)) - a) / 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 ((c <= (-2.25d+89)) .or. (.not. (c <= 5.5d+57))) then
        tmp = (b - (d * (a / c))) / c
    else
        tmp = ((c * (b / d)) - a) / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.25e+89) || !(c <= 5.5e+57)) {
		tmp = (b - (d * (a / c))) / c;
	} else {
		tmp = ((c * (b / d)) - a) / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -2.25e+89) or not (c <= 5.5e+57):
		tmp = (b - (d * (a / c))) / c
	else:
		tmp = ((c * (b / d)) - a) / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -2.25e+89) || !(c <= 5.5e+57))
		tmp = Float64(Float64(b - Float64(d * Float64(a / c))) / c);
	else
		tmp = Float64(Float64(Float64(c * Float64(b / d)) - a) / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -2.25e+89) || ~((c <= 5.5e+57)))
		tmp = (b - (d * (a / c))) / c;
	else
		tmp = ((c * (b / d)) - a) / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -2.25e+89], N[Not[LessEqual[c, 5.5e+57]], $MachinePrecision]], N[(N[(b - N[(d * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(c * N[(b / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.25e89 or 5.5000000000000002e57 < c

   1. Initial program 48.4%

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

      1. clear-num 48.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot c + d \cdot d}{b \cdot c - a \cdot d}}} \]

      2. associate-/r/ 48.4%

         \[\leadsto \color{blue}{\frac{1}{c \cdot c + d \cdot d} \cdot \left(b \cdot c - a \cdot d\right)} \]

      3. frac-2neg 48.4%

         \[\leadsto \color{blue}{\frac{-1}{-\left(c \cdot c + d \cdot d\right)}} \cdot \left(b \cdot c - a \cdot d\right) \]

      4. frac-2neg 48.4%

         \[\leadsto \color{blue}{\frac{1}{c \cdot c + d \cdot d}} \cdot \left(b \cdot c - a \cdot d\right) \]

      5. fma-def 48.4%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{fma}\left(c, c, d \cdot d\right)}} \cdot \left(b \cdot c - a \cdot d\right) \]

   3. Applied egg-rr 48.4%

      \[\leadsto \color{blue}{\frac{1}{\mathsf{fma}\left(c, c, d \cdot d\right)} \cdot \left(b \cdot c - a \cdot d\right)} \]

   4. Taylor expanded in c around inf 76.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{a \cdot d}{{c}^{2}} + \frac{b}{c}} \]
   5. Step-by-step derivation

      1. +-commutative 76.0%

         \[\leadsto \color{blue}{\frac{b}{c} + -1 \cdot \frac{a \cdot d}{{c}^{2}}} \]

      2. mul-1-neg 76.0%

         \[\leadsto \frac{b}{c} + \color{blue}{\left(-\frac{a \cdot d}{{c}^{2}}\right)} \]

      3. *-commutative 76.0%

         \[\leadsto \frac{b}{c} + \left(-\frac{\color{blue}{d \cdot a}}{{c}^{2}}\right) \]

      4. unpow2 76.0%

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

      5. times-frac 86.7%

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

      6. *-commutative 86.7%

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

      7. sub-neg 86.7%

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

      8. associate-*r/ 87.6%

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

      9. *-commutative 87.6%

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

      10. div-sub 87.6%

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

   6. Simplified 87.6%

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

   if -2.25e89 < c < 5.5000000000000002e57

   1. Initial program 72.6%

      \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \]

   2. Taylor expanded in c around 0 74.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{d} + \frac{b \cdot c}{{d}^{2}}} \]
   3. Step-by-step derivation

      1. +-commutative 74.2%

         \[\leadsto \color{blue}{\frac{b \cdot c}{{d}^{2}} + -1 \cdot \frac{a}{d}} \]

      2. mul-1-neg 74.2%

         \[\leadsto \frac{b \cdot c}{{d}^{2}} + \color{blue}{\left(-\frac{a}{d}\right)} \]

      3. unsub-neg 74.2%

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

      4. unpow2 74.2%

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

      5. associate-/l* 74.3%

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

   4. Simplified 74.3%

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

   5. Taylor expanded in b around 0 74.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{d} + \frac{b \cdot c}{{d}^{2}}} \]
   6. Step-by-step derivation

      1. mul-1-neg 74.2%

         \[\leadsto \color{blue}{\left(-\frac{a}{d}\right)} + \frac{b \cdot c}{{d}^{2}} \]

      2. distribute-frac-neg 74.2%

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

      3. +-commutative 74.2%

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

      4. *-commutative 74.2%

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

      5. unpow2 74.2%

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

      6. *-commutative 74.2%

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

      7. associate-/l* 74.3%

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

      8. distribute-frac-neg 74.3%

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

      9. sub-neg 74.3%

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

      10. associate-/l* 74.2%

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

      11. *-commutative 74.2%

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

      12. associate-/r* 80.8%

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

      13. associate-*r/ 79.0%

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

      14. div-sub 79.9%

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

   7. Simplified 79.9%

      \[\leadsto \color{blue}{\frac{c \cdot \frac{b}{d} - a}{d}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.25 \cdot 10^{+89} \lor \neg \left(c \leq 5.5 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{b - d \cdot \frac{a}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot \frac{b}{d} - a}{d}\\ \end{array} \]

Alternative 4: 77.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.85 \cdot 10^{+87} \lor \neg \left(c \leq 4.4 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{b - d \cdot \frac{a}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b \cdot \frac{c}{d} - a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -1.85e+87) (not (<= c 4.4e+57)))
   (/ (- b (* d (/ a c))) c)
   (/ (- (* b (/ c d)) a) d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -1.85e+87) || !(c <= 4.4e+57)) {
		tmp = (b - (d * (a / c))) / c;
	} else {
		tmp = ((b * (c / d)) - a) / 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 ((c <= (-1.85d+87)) .or. (.not. (c <= 4.4d+57))) then
        tmp = (b - (d * (a / c))) / c
    else
        tmp = ((b * (c / d)) - a) / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -1.85e+87) || !(c <= 4.4e+57)) {
		tmp = (b - (d * (a / c))) / c;
	} else {
		tmp = ((b * (c / d)) - a) / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -1.85e+87) or not (c <= 4.4e+57):
		tmp = (b - (d * (a / c))) / c
	else:
		tmp = ((b * (c / d)) - a) / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -1.85e+87) || !(c <= 4.4e+57))
		tmp = Float64(Float64(b - Float64(d * Float64(a / c))) / c);
	else
		tmp = Float64(Float64(Float64(b * Float64(c / d)) - a) / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -1.85e+87) || ~((c <= 4.4e+57)))
		tmp = (b - (d * (a / c))) / c;
	else
		tmp = ((b * (c / d)) - a) / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -1.85e+87], N[Not[LessEqual[c, 4.4e+57]], $MachinePrecision]], N[(N[(b - N[(d * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(b * N[(c / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.85000000000000001e87 or 4.4000000000000001e57 < c

   1. Initial program 48.4%

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

      1. clear-num 48.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot c + d \cdot d}{b \cdot c - a \cdot d}}} \]

      2. associate-/r/ 48.4%

         \[\leadsto \color{blue}{\frac{1}{c \cdot c + d \cdot d} \cdot \left(b \cdot c - a \cdot d\right)} \]

      3. frac-2neg 48.4%

         \[\leadsto \color{blue}{\frac{-1}{-\left(c \cdot c + d \cdot d\right)}} \cdot \left(b \cdot c - a \cdot d\right) \]

      4. frac-2neg 48.4%

         \[\leadsto \color{blue}{\frac{1}{c \cdot c + d \cdot d}} \cdot \left(b \cdot c - a \cdot d\right) \]

      5. fma-def 48.4%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{fma}\left(c, c, d \cdot d\right)}} \cdot \left(b \cdot c - a \cdot d\right) \]

   3. Applied egg-rr 48.4%

      \[\leadsto \color{blue}{\frac{1}{\mathsf{fma}\left(c, c, d \cdot d\right)} \cdot \left(b \cdot c - a \cdot d\right)} \]

   4. Taylor expanded in c around inf 76.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{a \cdot d}{{c}^{2}} + \frac{b}{c}} \]
   5. Step-by-step derivation

      1. +-commutative 76.0%

         \[\leadsto \color{blue}{\frac{b}{c} + -1 \cdot \frac{a \cdot d}{{c}^{2}}} \]

      2. mul-1-neg 76.0%

         \[\leadsto \frac{b}{c} + \color{blue}{\left(-\frac{a \cdot d}{{c}^{2}}\right)} \]

      3. *-commutative 76.0%

         \[\leadsto \frac{b}{c} + \left(-\frac{\color{blue}{d \cdot a}}{{c}^{2}}\right) \]

      4. unpow2 76.0%

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

      5. times-frac 86.7%

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

      6. *-commutative 86.7%

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

      7. sub-neg 86.7%

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

      8. associate-*r/ 87.6%

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

      9. *-commutative 87.6%

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

      10. div-sub 87.6%

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

   6. Simplified 87.6%

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

   if -1.85000000000000001e87 < c < 4.4000000000000001e57

   1. Initial program 72.6%

      \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \]

   2. Taylor expanded in c around 0 74.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{d} + \frac{b \cdot c}{{d}^{2}}} \]
   3. Step-by-step derivation

      1. +-commutative 74.2%

         \[\leadsto \color{blue}{\frac{b \cdot c}{{d}^{2}} + -1 \cdot \frac{a}{d}} \]

      2. mul-1-neg 74.2%

         \[\leadsto \frac{b \cdot c}{{d}^{2}} + \color{blue}{\left(-\frac{a}{d}\right)} \]

      3. unsub-neg 74.2%

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

      4. unpow2 74.2%

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

      5. associate-/l* 74.3%

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

   4. Simplified 74.3%

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

      1. associate-/l* 74.2%

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

      2. times-frac 79.0%

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

      3. *-commutative 79.0%

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

      4. associate-*r/ 81.4%

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

      5. sub-div 82.3%

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

   6. Applied egg-rr 82.3%

      \[\leadsto \color{blue}{\frac{\frac{c}{d} \cdot b - a}{d}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.85 \cdot 10^{+87} \lor \neg \left(c \leq 4.4 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{b - d \cdot \frac{a}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b \cdot \frac{c}{d} - a}{d}\\ \end{array} \]

Alternative 5: 77.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.25 \cdot 10^{+89}:\\ \;\;\;\;\frac{b}{c} - \frac{d}{c} \cdot \frac{a}{c}\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+56}:\\ \;\;\;\;\frac{b \cdot \frac{c}{d} - a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - d \cdot \frac{a}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -2.25e+89)
   (- (/ b c) (* (/ d c) (/ a c)))
   (if (<= c 3.8e+56) (/ (- (* b (/ c d)) a) d) (/ (- b (* d (/ a c))) c))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -2.25e+89) {
		tmp = (b / c) - ((d / c) * (a / c));
	} else if (c <= 3.8e+56) {
		tmp = ((b * (c / d)) - a) / d;
	} else {
		tmp = (b - (d * (a / c))) / 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 <= (-2.25d+89)) then
        tmp = (b / c) - ((d / c) * (a / c))
    else if (c <= 3.8d+56) then
        tmp = ((b * (c / d)) - a) / d
    else
        tmp = (b - (d * (a / c))) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -2.25e+89) {
		tmp = (b / c) - ((d / c) * (a / c));
	} else if (c <= 3.8e+56) {
		tmp = ((b * (c / d)) - a) / d;
	} else {
		tmp = (b - (d * (a / c))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -2.25e+89:
		tmp = (b / c) - ((d / c) * (a / c))
	elif c <= 3.8e+56:
		tmp = ((b * (c / d)) - a) / d
	else:
		tmp = (b - (d * (a / c))) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -2.25e+89)
		tmp = Float64(Float64(b / c) - Float64(Float64(d / c) * Float64(a / c)));
	elseif (c <= 3.8e+56)
		tmp = Float64(Float64(Float64(b * Float64(c / d)) - a) / d);
	else
		tmp = Float64(Float64(b - Float64(d * Float64(a / c))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -2.25e+89)
		tmp = (b / c) - ((d / c) * (a / c));
	elseif (c <= 3.8e+56)
		tmp = ((b * (c / d)) - a) / d;
	else
		tmp = (b - (d * (a / c))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -2.25e+89], N[(N[(b / c), $MachinePrecision] - N[(N[(d / c), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.8e+56], N[(N[(N[(b * N[(c / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision], N[(N[(b - N[(d * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.25e89

   1. Initial program 49.0%

      \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \]

   2. Taylor expanded in c around inf 75.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{a \cdot d}{{c}^{2}} + \frac{b}{c}} \]
   3. Step-by-step derivation

      1. +-commutative 75.8%

         \[\leadsto \color{blue}{\frac{b}{c} + -1 \cdot \frac{a \cdot d}{{c}^{2}}} \]

      2. mul-1-neg 75.8%

         \[\leadsto \frac{b}{c} + \color{blue}{\left(-\frac{a \cdot d}{{c}^{2}}\right)} \]

      3. unsub-neg 75.8%

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

      4. unpow2 75.8%

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

      5. times-frac 90.7%

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

   4. Simplified 90.7%

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

   if -2.25e89 < c < 3.79999999999999996e56

   1. Initial program 72.6%

      \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \]

   2. Taylor expanded in c around 0 74.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{d} + \frac{b \cdot c}{{d}^{2}}} \]
   3. Step-by-step derivation

      1. +-commutative 74.2%

         \[\leadsto \color{blue}{\frac{b \cdot c}{{d}^{2}} + -1 \cdot \frac{a}{d}} \]

      2. mul-1-neg 74.2%

         \[\leadsto \frac{b \cdot c}{{d}^{2}} + \color{blue}{\left(-\frac{a}{d}\right)} \]

      3. unsub-neg 74.2%

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

      4. unpow2 74.2%

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

      5. associate-/l* 74.3%

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

   4. Simplified 74.3%

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

      1. associate-/l* 74.2%

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

      2. times-frac 79.0%

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

      3. *-commutative 79.0%

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

      4. associate-*r/ 81.4%

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

      5. sub-div 82.3%

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

   6. Applied egg-rr 82.3%

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

   if 3.79999999999999996e56 < c

   1. Initial program 47.9%

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

      1. clear-num 47.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot c + d \cdot d}{b \cdot c - a \cdot d}}} \]

      2. associate-/r/ 47.9%

         \[\leadsto \color{blue}{\frac{1}{c \cdot c + d \cdot d} \cdot \left(b \cdot c - a \cdot d\right)} \]

      3. frac-2neg 47.9%

         \[\leadsto \color{blue}{\frac{-1}{-\left(c \cdot c + d \cdot d\right)}} \cdot \left(b \cdot c - a \cdot d\right) \]

      4. frac-2neg 47.9%

         \[\leadsto \color{blue}{\frac{1}{c \cdot c + d \cdot d}} \cdot \left(b \cdot c - a \cdot d\right) \]

      5. fma-def 47.9%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{fma}\left(c, c, d \cdot d\right)}} \cdot \left(b \cdot c - a \cdot d\right) \]

   3. Applied egg-rr 47.9%

      \[\leadsto \color{blue}{\frac{1}{\mathsf{fma}\left(c, c, d \cdot d\right)} \cdot \left(b \cdot c - a \cdot d\right)} \]

   4. Taylor expanded in c around inf 76.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{a \cdot d}{{c}^{2}} + \frac{b}{c}} \]
   5. Step-by-step derivation

      1. +-commutative 76.2%

         \[\leadsto \color{blue}{\frac{b}{c} + -1 \cdot \frac{a \cdot d}{{c}^{2}}} \]

      2. mul-1-neg 76.2%

         \[\leadsto \frac{b}{c} + \color{blue}{\left(-\frac{a \cdot d}{{c}^{2}}\right)} \]

      3. *-commutative 76.2%

         \[\leadsto \frac{b}{c} + \left(-\frac{\color{blue}{d \cdot a}}{{c}^{2}}\right) \]

      4. unpow2 76.2%

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

      5. times-frac 83.2%

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

      6. *-commutative 83.2%

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

      7. sub-neg 83.2%

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

      8. associate-*r/ 85.0%

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

      9. *-commutative 85.0%

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

      10. div-sub 84.9%

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

   6. Simplified 84.9%

      \[\leadsto \color{blue}{\frac{b - d \cdot \frac{a}{c}}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.25 \cdot 10^{+89}:\\ \;\;\;\;\frac{b}{c} - \frac{d}{c} \cdot \frac{a}{c}\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+56}:\\ \;\;\;\;\frac{b \cdot \frac{c}{d} - a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - d \cdot \frac{a}{c}}{c}\\ \end{array} \]

Alternative 6: 77.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{+87}:\\ \;\;\;\;\frac{b}{c} - \frac{\frac{d}{c}}{\frac{c}{a}}\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+56}:\\ \;\;\;\;\frac{b \cdot \frac{c}{d} - a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - d \cdot \frac{a}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -1.8e+87)
   (- (/ b c) (/ (/ d c) (/ c a)))
   (if (<= c 1.85e+56) (/ (- (* b (/ c d)) a) d) (/ (- b (* d (/ a c))) c))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -1.8e+87) {
		tmp = (b / c) - ((d / c) / (c / a));
	} else if (c <= 1.85e+56) {
		tmp = ((b * (c / d)) - a) / d;
	} else {
		tmp = (b - (d * (a / c))) / 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 <= (-1.8d+87)) then
        tmp = (b / c) - ((d / c) / (c / a))
    else if (c <= 1.85d+56) then
        tmp = ((b * (c / d)) - a) / d
    else
        tmp = (b - (d * (a / c))) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -1.8e+87) {
		tmp = (b / c) - ((d / c) / (c / a));
	} else if (c <= 1.85e+56) {
		tmp = ((b * (c / d)) - a) / d;
	} else {
		tmp = (b - (d * (a / c))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -1.8e+87:
		tmp = (b / c) - ((d / c) / (c / a))
	elif c <= 1.85e+56:
		tmp = ((b * (c / d)) - a) / d
	else:
		tmp = (b - (d * (a / c))) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -1.8e+87)
		tmp = Float64(Float64(b / c) - Float64(Float64(d / c) / Float64(c / a)));
	elseif (c <= 1.85e+56)
		tmp = Float64(Float64(Float64(b * Float64(c / d)) - a) / d);
	else
		tmp = Float64(Float64(b - Float64(d * Float64(a / c))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -1.8e+87)
		tmp = (b / c) - ((d / c) / (c / a));
	elseif (c <= 1.85e+56)
		tmp = ((b * (c / d)) - a) / d;
	else
		tmp = (b - (d * (a / c))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -1.8e+87], N[(N[(b / c), $MachinePrecision] - N[(N[(d / c), $MachinePrecision] / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.85e+56], N[(N[(N[(b * N[(c / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision], N[(N[(b - N[(d * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.79999999999999997e87

   1. Initial program 49.0%

      \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \]

   2. Taylor expanded in c around inf 75.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{a \cdot d}{{c}^{2}} + \frac{b}{c}} \]
   3. Step-by-step derivation

      1. +-commutative 75.8%

         \[\leadsto \color{blue}{\frac{b}{c} + -1 \cdot \frac{a \cdot d}{{c}^{2}}} \]

      2. mul-1-neg 75.8%

         \[\leadsto \frac{b}{c} + \color{blue}{\left(-\frac{a \cdot d}{{c}^{2}}\right)} \]

      3. unsub-neg 75.8%

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

      4. unpow2 75.8%

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

      5. times-frac 90.7%

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

   4. Simplified 90.7%

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

      1. *-commutative 90.7%

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

      2. clear-num 90.7%

         \[\leadsto \frac{b}{c} - \frac{d}{c} \cdot \color{blue}{\frac{1}{\frac{c}{a}}} \]

      3. un-div-inv 90.8%

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

   6. Applied egg-rr 90.8%

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

   if -1.79999999999999997e87 < c < 1.84999999999999998e56

   1. Initial program 72.6%

      \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \]

   2. Taylor expanded in c around 0 74.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{d} + \frac{b \cdot c}{{d}^{2}}} \]
   3. Step-by-step derivation

      1. +-commutative 74.2%

         \[\leadsto \color{blue}{\frac{b \cdot c}{{d}^{2}} + -1 \cdot \frac{a}{d}} \]

      2. mul-1-neg 74.2%

         \[\leadsto \frac{b \cdot c}{{d}^{2}} + \color{blue}{\left(-\frac{a}{d}\right)} \]

      3. unsub-neg 74.2%

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

      4. unpow2 74.2%

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

      5. associate-/l* 74.3%

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

   4. Simplified 74.3%

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

      1. associate-/l* 74.2%

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

      2. times-frac 79.0%

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

      3. *-commutative 79.0%

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

      4. associate-*r/ 81.4%

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

      5. sub-div 82.3%

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

   6. Applied egg-rr 82.3%

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

   if 1.84999999999999998e56 < c

   1. Initial program 47.9%

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

      1. clear-num 47.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot c + d \cdot d}{b \cdot c - a \cdot d}}} \]

      2. associate-/r/ 47.9%

         \[\leadsto \color{blue}{\frac{1}{c \cdot c + d \cdot d} \cdot \left(b \cdot c - a \cdot d\right)} \]

      3. frac-2neg 47.9%

         \[\leadsto \color{blue}{\frac{-1}{-\left(c \cdot c + d \cdot d\right)}} \cdot \left(b \cdot c - a \cdot d\right) \]

      4. frac-2neg 47.9%

         \[\leadsto \color{blue}{\frac{1}{c \cdot c + d \cdot d}} \cdot \left(b \cdot c - a \cdot d\right) \]

      5. fma-def 47.9%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{fma}\left(c, c, d \cdot d\right)}} \cdot \left(b \cdot c - a \cdot d\right) \]

   3. Applied egg-rr 47.9%

      \[\leadsto \color{blue}{\frac{1}{\mathsf{fma}\left(c, c, d \cdot d\right)} \cdot \left(b \cdot c - a \cdot d\right)} \]

   4. Taylor expanded in c around inf 76.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{a \cdot d}{{c}^{2}} + \frac{b}{c}} \]
   5. Step-by-step derivation

      1. +-commutative 76.2%

         \[\leadsto \color{blue}{\frac{b}{c} + -1 \cdot \frac{a \cdot d}{{c}^{2}}} \]

      2. mul-1-neg 76.2%

         \[\leadsto \frac{b}{c} + \color{blue}{\left(-\frac{a \cdot d}{{c}^{2}}\right)} \]

      3. *-commutative 76.2%

         \[\leadsto \frac{b}{c} + \left(-\frac{\color{blue}{d \cdot a}}{{c}^{2}}\right) \]

      4. unpow2 76.2%

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

      5. times-frac 83.2%

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

      6. *-commutative 83.2%

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

      7. sub-neg 83.2%

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

      8. associate-*r/ 85.0%

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

      9. *-commutative 85.0%

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

      10. div-sub 84.9%

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

   6. Simplified 84.9%

      \[\leadsto \color{blue}{\frac{b - d \cdot \frac{a}{c}}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{+87}:\\ \;\;\;\;\frac{b}{c} - \frac{\frac{d}{c}}{\frac{c}{a}}\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+56}:\\ \;\;\;\;\frac{b \cdot \frac{c}{d} - a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - d \cdot \frac{a}{c}}{c}\\ \end{array} \]

Alternative 7: 62.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+91}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;c \leq 10^{+57}:\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -3.8e+91) (/ b c) (if (<= c 1e+57) (/ (- a) d) (/ b c))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -3.8e+91) {
		tmp = b / c;
	} else if (c <= 1e+57) {
		tmp = -a / d;
	} else {
		tmp = b / 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 <= (-3.8d+91)) then
        tmp = b / c
    else if (c <= 1d+57) then
        tmp = -a / d
    else
        tmp = b / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -3.8e+91) {
		tmp = b / c;
	} else if (c <= 1e+57) {
		tmp = -a / d;
	} else {
		tmp = b / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -3.8e+91:
		tmp = b / c
	elif c <= 1e+57:
		tmp = -a / d
	else:
		tmp = b / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -3.8e+91)
		tmp = Float64(b / c);
	elseif (c <= 1e+57)
		tmp = Float64(Float64(-a) / d);
	else
		tmp = Float64(b / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -3.8e+91)
		tmp = b / c;
	elseif (c <= 1e+57)
		tmp = -a / d;
	else
		tmp = b / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -3.8e+91], N[(b / c), $MachinePrecision], If[LessEqual[c, 1e+57], N[((-a) / d), $MachinePrecision], N[(b / c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if c < -3.7999999999999998e91 or 1.00000000000000005e57 < c

   1. Initial program 47.3%

      \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \]

   2. Taylor expanded in c around inf 75.7%

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

   if -3.7999999999999998e91 < c < 1.00000000000000005e57

   1. Initial program 73.0%

      \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \]

   2. Taylor expanded in c around 0 67.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{d}} \]
   3. Step-by-step derivation

      1. associate-*r/ 67.5%

         \[\leadsto \color{blue}{\frac{-1 \cdot a}{d}} \]

      2. neg-mul-1 67.5%

         \[\leadsto \frac{\color{blue}{-a}}{d} \]

   4. Simplified 67.5%

      \[\leadsto \color{blue}{\frac{-a}{d}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+91}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;c \leq 10^{+57}:\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c}\\ \end{array} \]

Alternative 8: 43.3% accurate, 5.0× speedup

Math

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

FPCore

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

C

double code(double a, double b, double c, double d) {
	return b / 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 = b / c
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.4%

   \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \]

2. Taylor expanded in c around inf 39.6%

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

3. Final simplification 39.6%

   \[\leadsto \frac{b}{c} \]

Developer target: 99.3% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (< (fabs d) (fabs c))
   (/ (- b (* a (/ d c))) (+ c (* d (/ d c))))
   (/ (+ (- a) (* b (/ 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 = (b - (a * (d / c))) / (c + (d * (d / c)));
	} else {
		tmp = (-a + (b * (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 = (b - (a * (d / c))) / (c + (d * (d / c)))
    else
        tmp = (-a + (b * (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 = (b - (a * (d / c))) / (c + (d * (d / c)));
	} else {
		tmp = (-a + (b * (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 = (b - (a * (d / c))) / (c + (d * (d / c)))
	else:
		tmp = (-a + (b * (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(b - Float64(a * Float64(d / c))) / Float64(c + Float64(d * Float64(d / c))));
	else
		tmp = Float64(Float64(Float64(-a) + Float64(b * 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 = (b - (a * (d / c))) / (c + (d * (d / c)));
	else
		tmp = (-a + (b * (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[(b - N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c + N[(d * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-a) + N[(b * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(d + N[(c * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023297 
(FPCore (a b c d)
  :name "Complex division, imag part"
  :precision binary64

  :herbie-target
  (if (< (fabs d) (fabs c)) (/ (- b (* a (/ d c))) (+ c (* d (/ d c)))) (/ (+ (- a) (* b (/ c d))) (+ d (* c (/ c d)))))

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