Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.8% → 93.2%

Time: 17.1s

Alternatives: 19

Speedup: 1.5×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
}

Python

def code(x, y, z, t, a, b):
	return ((x * y) + (z * (t - a))) / (y + (z * (b - y)))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
}

Python

def code(x, y, z, t, a, b):
	return ((x * y) + (z * (t - a))) / (y + (z * (b - y)))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 93.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00166 \lor \neg \left(z \leq 4100000000000\right):\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.00166) (not (<= z 4100000000000.0)))
   (+ (* (/ y (- b y)) (/ x z)) (/ (- t a) (- b y)))
   (/ (+ (* y x) (* z (- t a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.00166) || !(z <= 4100000000000.0)) {
		tmp = ((y / (b - y)) * (x / z)) + ((t - a) / (b - y));
	} else {
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-0.00166d0)) .or. (.not. (z <= 4100000000000.0d0))) then
        tmp = ((y / (b - y)) * (x / z)) + ((t - a) / (b - y))
    else
        tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.00166) || !(z <= 4100000000000.0)) {
		tmp = ((y / (b - y)) * (x / z)) + ((t - a) / (b - y));
	} else {
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.00166) or not (z <= 4100000000000.0):
		tmp = ((y / (b - y)) * (x / z)) + ((t - a) / (b - y))
	else:
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.00166) || !(z <= 4100000000000.0))
		tmp = Float64(Float64(Float64(y / Float64(b - y)) * Float64(x / z)) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.00166) || ~((z <= 4100000000000.0)))
		tmp = ((y / (b - y)) * (x / z)) + ((t - a) / (b - y));
	else
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.00166], N[Not[LessEqual[z, 4100000000000.0]], $MachinePrecision]], N[(N[(N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.00166 or 4.1e12 < z

   1. Initial program 35.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around -inf 58.5%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. +-commutative 58.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]

      2. associate--l+ 58.5%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   4. Simplified 90.9%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]

   5. Taylor expanded in x around inf 82.5%

      \[\leadsto \color{blue}{\frac{y \cdot x}{\left(b - y\right) \cdot z}} + \frac{t - a}{b - y} \]
   6. Step-by-step derivation

      1. times-frac 99.1%

         \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]

   7. Simplified 99.1%

      \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]

   if -0.00166 < z < 4.1e12

   1. Initial program 91.2%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00166 \lor \neg \left(z \leq 4100000000000\right):\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 2: 78.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ t_3 := \frac{y}{b - y} \cdot \frac{x}{z} + t_1\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{-45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-99}:\\ \;\;\;\;t_1 + \frac{y}{z} \cdot \frac{x}{b}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (/ (+ (* y x) (* z (- t a))) y))
        (t_3 (+ (* (/ y (- b y)) (/ x z)) t_1)))
   (if (<= z -7.5e-45)
     t_3
     (if (<= z -1.5e-67)
       t_2
       (if (<= z -1.85e-99)
         (+ t_1 (* (/ y z) (/ x b)))
         (if (<= z 2.3e-102) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((y * x) + (z * (t - a))) / y;
	double t_3 = ((y / (b - y)) * (x / z)) + t_1;
	double tmp;
	if (z <= -7.5e-45) {
		tmp = t_3;
	} else if (z <= -1.5e-67) {
		tmp = t_2;
	} else if (z <= -1.85e-99) {
		tmp = t_1 + ((y / z) * (x / b));
	} else if (z <= 2.3e-102) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = ((y * x) + (z * (t - a))) / y
    t_3 = ((y / (b - y)) * (x / z)) + t_1
    if (z <= (-7.5d-45)) then
        tmp = t_3
    else if (z <= (-1.5d-67)) then
        tmp = t_2
    else if (z <= (-1.85d-99)) then
        tmp = t_1 + ((y / z) * (x / b))
    else if (z <= 2.3d-102) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((y * x) + (z * (t - a))) / y;
	double t_3 = ((y / (b - y)) * (x / z)) + t_1;
	double tmp;
	if (z <= -7.5e-45) {
		tmp = t_3;
	} else if (z <= -1.5e-67) {
		tmp = t_2;
	} else if (z <= -1.85e-99) {
		tmp = t_1 + ((y / z) * (x / b));
	} else if (z <= 2.3e-102) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((y * x) + (z * (t - a))) / y
	t_3 = ((y / (b - y)) * (x / z)) + t_1
	tmp = 0
	if z <= -7.5e-45:
		tmp = t_3
	elif z <= -1.5e-67:
		tmp = t_2
	elif z <= -1.85e-99:
		tmp = t_1 + ((y / z) * (x / b))
	elif z <= 2.3e-102:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / y)
	t_3 = Float64(Float64(Float64(y / Float64(b - y)) * Float64(x / z)) + t_1)
	tmp = 0.0
	if (z <= -7.5e-45)
		tmp = t_3;
	elseif (z <= -1.5e-67)
		tmp = t_2;
	elseif (z <= -1.85e-99)
		tmp = Float64(t_1 + Float64(Float64(y / z) * Float64(x / b)));
	elseif (z <= 2.3e-102)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((y * x) + (z * (t - a))) / y;
	t_3 = ((y / (b - y)) * (x / z)) + t_1;
	tmp = 0.0;
	if (z <= -7.5e-45)
		tmp = t_3;
	elseif (z <= -1.5e-67)
		tmp = t_2;
	elseif (z <= -1.85e-99)
		tmp = t_1 + ((y / z) * (x / b));
	elseif (z <= 2.3e-102)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[z, -7.5e-45], t$95$3, If[LessEqual[z, -1.5e-67], t$95$2, If[LessEqual[z, -1.85e-99], N[(t$95$1 + N[(N[(y / z), $MachinePrecision] * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e-102], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5000000000000006e-45 or 2.29999999999999987e-102 < z

   1. Initial program 47.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around -inf 57.5%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. +-commutative 57.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]

      2. associate--l+ 57.5%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   4. Simplified 83.9%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]

   5. Taylor expanded in x around inf 79.2%

      \[\leadsto \color{blue}{\frac{y \cdot x}{\left(b - y\right) \cdot z}} + \frac{t - a}{b - y} \]
   6. Step-by-step derivation

      1. times-frac 92.1%

         \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]

   7. Simplified 92.1%

      \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]

   if -7.5000000000000006e-45 < z < -1.50000000000000016e-67 or -1.85e-99 < z < 2.29999999999999987e-102

   1. Initial program 90.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 72.5%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y}} \]

   if -1.50000000000000016e-67 < z < -1.85e-99

   1. Initial program 76.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around -inf 59.8%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. +-commutative 59.8%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]

      2. associate--l+ 59.8%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   4. Simplified 69.4%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]

   5. Taylor expanded in b around inf 61.4%

      \[\leadsto \color{blue}{\frac{y \cdot x}{b \cdot z}} + \frac{t - a}{b - y} \]
   6. Step-by-step derivation

      1. *-commutative 61.4%

         \[\leadsto \frac{y \cdot x}{\color{blue}{z \cdot b}} + \frac{t - a}{b - y} \]

      2. times-frac 69.2%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot \frac{x}{b}} + \frac{t - a}{b - y} \]

   7. Simplified 69.2%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot \frac{x}{b}} + \frac{t - a}{b - y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-99}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-102}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 3: 66.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+86}:\\ \;\;\;\;\frac{t}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.54 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-99}:\\ \;\;\;\;\frac{\left(t - a\right) + \frac{y}{\frac{z}{x}}}{b}\\ \mathbf{elif}\;z \leq 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (/ (+ (* y x) (* z (- t a))) y)))
   (if (<= z -7e+162)
     t_1
     (if (<= z -1.06e+86)
       (- (/ t (- b y)) (/ x z))
       (if (<= z -1.54e-27)
         t_1
         (if (<= z -9.2e-68)
           t_2
           (if (<= z -4.6e-99)
             (/ (+ (- t a) (/ y (/ z x))) b)
             (if (<= z 1e-102) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((y * x) + (z * (t - a))) / y;
	double tmp;
	if (z <= -7e+162) {
		tmp = t_1;
	} else if (z <= -1.06e+86) {
		tmp = (t / (b - y)) - (x / z);
	} else if (z <= -1.54e-27) {
		tmp = t_1;
	} else if (z <= -9.2e-68) {
		tmp = t_2;
	} else if (z <= -4.6e-99) {
		tmp = ((t - a) + (y / (z / x))) / b;
	} else if (z <= 1e-102) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = ((y * x) + (z * (t - a))) / y
    if (z <= (-7d+162)) then
        tmp = t_1
    else if (z <= (-1.06d+86)) then
        tmp = (t / (b - y)) - (x / z)
    else if (z <= (-1.54d-27)) then
        tmp = t_1
    else if (z <= (-9.2d-68)) then
        tmp = t_2
    else if (z <= (-4.6d-99)) then
        tmp = ((t - a) + (y / (z / x))) / b
    else if (z <= 1d-102) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((y * x) + (z * (t - a))) / y;
	double tmp;
	if (z <= -7e+162) {
		tmp = t_1;
	} else if (z <= -1.06e+86) {
		tmp = (t / (b - y)) - (x / z);
	} else if (z <= -1.54e-27) {
		tmp = t_1;
	} else if (z <= -9.2e-68) {
		tmp = t_2;
	} else if (z <= -4.6e-99) {
		tmp = ((t - a) + (y / (z / x))) / b;
	} else if (z <= 1e-102) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((y * x) + (z * (t - a))) / y
	tmp = 0
	if z <= -7e+162:
		tmp = t_1
	elif z <= -1.06e+86:
		tmp = (t / (b - y)) - (x / z)
	elif z <= -1.54e-27:
		tmp = t_1
	elif z <= -9.2e-68:
		tmp = t_2
	elif z <= -4.6e-99:
		tmp = ((t - a) + (y / (z / x))) / b
	elif z <= 1e-102:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / y)
	tmp = 0.0
	if (z <= -7e+162)
		tmp = t_1;
	elseif (z <= -1.06e+86)
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(x / z));
	elseif (z <= -1.54e-27)
		tmp = t_1;
	elseif (z <= -9.2e-68)
		tmp = t_2;
	elseif (z <= -4.6e-99)
		tmp = Float64(Float64(Float64(t - a) + Float64(y / Float64(z / x))) / b);
	elseif (z <= 1e-102)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((y * x) + (z * (t - a))) / y;
	tmp = 0.0;
	if (z <= -7e+162)
		tmp = t_1;
	elseif (z <= -1.06e+86)
		tmp = (t / (b - y)) - (x / z);
	elseif (z <= -1.54e-27)
		tmp = t_1;
	elseif (z <= -9.2e-68)
		tmp = t_2;
	elseif (z <= -4.6e-99)
		tmp = ((t - a) + (y / (z / x))) / b;
	elseif (z <= 1e-102)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -7e+162], t$95$1, If[LessEqual[z, -1.06e+86], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.54e-27], t$95$1, If[LessEqual[z, -9.2e-68], t$95$2, If[LessEqual[z, -4.6e-99], N[(N[(N[(t - a), $MachinePrecision] + N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 1e-102], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.00000000000000036e162 or -1.06e86 < z < -1.54e-27 or 9.99999999999999933e-103 < z

   1. Initial program 49.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 77.9%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -7.00000000000000036e162 < z < -1.06e86

   1. Initial program 32.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around -inf 21.6%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. +-commutative 21.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]

      2. associate--l+ 21.6%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   4. Simplified 84.1%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]

   5. Taylor expanded in y around inf 95.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]
   6. Step-by-step derivation

      1. associate-*r/ 95.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z}} + \frac{t - a}{b - y} \]

      2. mul-1-neg 95.0%

         \[\leadsto \frac{\color{blue}{-x}}{z} + \frac{t - a}{b - y} \]

   7. Simplified 95.0%

      \[\leadsto \color{blue}{\frac{-x}{z}} + \frac{t - a}{b - y} \]

   8. Taylor expanded in a around 0 95.0%

      \[\leadsto \color{blue}{\frac{t}{b - y} + -1 \cdot \frac{x}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 95.0%

         \[\leadsto \frac{t}{b - y} + \color{blue}{\left(-\frac{x}{z}\right)} \]

      2. unsub-neg 95.0%

         \[\leadsto \color{blue}{\frac{t}{b - y} - \frac{x}{z}} \]

   10. Simplified 95.0%

       \[\leadsto \color{blue}{\frac{t}{b - y} - \frac{x}{z}} \]

   if -1.54e-27 < z < -9.19999999999999987e-68 or -4.5999999999999997e-99 < z < 9.99999999999999933e-103

   1. Initial program 90.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 71.8%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y}} \]

   if -9.19999999999999987e-68 < z < -4.5999999999999997e-99

   1. Initial program 82.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around -inf 64.7%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. +-commutative 64.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]

      2. associate--l+ 64.7%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   4. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]

   5. Taylor expanded in x around inf 66.9%

      \[\leadsto \color{blue}{\frac{y \cdot x}{\left(b - y\right) \cdot z}} + \frac{t - a}{b - y} \]
   6. Step-by-step derivation

      1. times-frac 53.9%

         \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]

   7. Simplified 53.9%

      \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]
   8. Step-by-step derivation

      1. clear-num 53.7%

         \[\leadsto \frac{y}{b - y} \cdot \frac{x}{z} + \color{blue}{\frac{1}{\frac{b - y}{t - a}}} \]

      2. inv-pow 53.7%

         \[\leadsto \frac{y}{b - y} \cdot \frac{x}{z} + \color{blue}{{\left(\frac{b - y}{t - a}\right)}^{-1}} \]

   9. Applied egg-rr 53.7%

      \[\leadsto \frac{y}{b - y} \cdot \frac{x}{z} + \color{blue}{{\left(\frac{b - y}{t - a}\right)}^{-1}} \]
   10. Step-by-step derivation

       1. unpow-1 53.7%

          \[\leadsto \frac{y}{b - y} \cdot \frac{x}{z} + \color{blue}{\frac{1}{\frac{b - y}{t - a}}} \]

   11. Simplified 53.7%

       \[\leadsto \frac{y}{b - y} \cdot \frac{x}{z} + \color{blue}{\frac{1}{\frac{b - y}{t - a}}} \]

   12. Taylor expanded in b around inf 64.8%

       \[\leadsto \color{blue}{\frac{\left(\frac{y \cdot x}{z} + t\right) - a}{b}} \]
   13. Step-by-step derivation

       1. associate--l+ 64.8%

          \[\leadsto \frac{\color{blue}{\frac{y \cdot x}{z} + \left(t - a\right)}}{b} \]

       2. associate-/l* 63.7%

          \[\leadsto \frac{\color{blue}{\frac{y}{\frac{z}{x}}} + \left(t - a\right)}{b} \]

   14. Simplified 63.7%

       \[\leadsto \color{blue}{\frac{\frac{y}{\frac{z}{x}} + \left(t - a\right)}{b}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+162}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+86}:\\ \;\;\;\;\frac{t}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.54 \cdot 10^{-27}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-68}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-99}:\\ \;\;\;\;\frac{\left(t - a\right) + \frac{y}{\frac{z}{x}}}{b}\\ \mathbf{elif}\;z \leq 10^{-102}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 66.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+85}:\\ \;\;\;\;\frac{t}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-99}:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (/ (+ (* y x) (* z (- t a))) y)))
   (if (<= z -7e+162)
     t_1
     (if (<= z -1.25e+85)
       (- (/ t (- b y)) (/ x z))
       (if (<= z -2.25e-27)
         t_1
         (if (<= z -2.05e-67)
           t_2
           (if (<= z -8.2e-99)
             (/ (- (+ t (/ (* y x) z)) a) b)
             (if (<= z 2.8e-102) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((y * x) + (z * (t - a))) / y;
	double tmp;
	if (z <= -7e+162) {
		tmp = t_1;
	} else if (z <= -1.25e+85) {
		tmp = (t / (b - y)) - (x / z);
	} else if (z <= -2.25e-27) {
		tmp = t_1;
	} else if (z <= -2.05e-67) {
		tmp = t_2;
	} else if (z <= -8.2e-99) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else if (z <= 2.8e-102) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = ((y * x) + (z * (t - a))) / y
    if (z <= (-7d+162)) then
        tmp = t_1
    else if (z <= (-1.25d+85)) then
        tmp = (t / (b - y)) - (x / z)
    else if (z <= (-2.25d-27)) then
        tmp = t_1
    else if (z <= (-2.05d-67)) then
        tmp = t_2
    else if (z <= (-8.2d-99)) then
        tmp = ((t + ((y * x) / z)) - a) / b
    else if (z <= 2.8d-102) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((y * x) + (z * (t - a))) / y;
	double tmp;
	if (z <= -7e+162) {
		tmp = t_1;
	} else if (z <= -1.25e+85) {
		tmp = (t / (b - y)) - (x / z);
	} else if (z <= -2.25e-27) {
		tmp = t_1;
	} else if (z <= -2.05e-67) {
		tmp = t_2;
	} else if (z <= -8.2e-99) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else if (z <= 2.8e-102) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((y * x) + (z * (t - a))) / y
	tmp = 0
	if z <= -7e+162:
		tmp = t_1
	elif z <= -1.25e+85:
		tmp = (t / (b - y)) - (x / z)
	elif z <= -2.25e-27:
		tmp = t_1
	elif z <= -2.05e-67:
		tmp = t_2
	elif z <= -8.2e-99:
		tmp = ((t + ((y * x) / z)) - a) / b
	elif z <= 2.8e-102:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / y)
	tmp = 0.0
	if (z <= -7e+162)
		tmp = t_1;
	elseif (z <= -1.25e+85)
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(x / z));
	elseif (z <= -2.25e-27)
		tmp = t_1;
	elseif (z <= -2.05e-67)
		tmp = t_2;
	elseif (z <= -8.2e-99)
		tmp = Float64(Float64(Float64(t + Float64(Float64(y * x) / z)) - a) / b);
	elseif (z <= 2.8e-102)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((y * x) + (z * (t - a))) / y;
	tmp = 0.0;
	if (z <= -7e+162)
		tmp = t_1;
	elseif (z <= -1.25e+85)
		tmp = (t / (b - y)) - (x / z);
	elseif (z <= -2.25e-27)
		tmp = t_1;
	elseif (z <= -2.05e-67)
		tmp = t_2;
	elseif (z <= -8.2e-99)
		tmp = ((t + ((y * x) / z)) - a) / b;
	elseif (z <= 2.8e-102)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -7e+162], t$95$1, If[LessEqual[z, -1.25e+85], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.25e-27], t$95$1, If[LessEqual[z, -2.05e-67], t$95$2, If[LessEqual[z, -8.2e-99], N[(N[(N[(t + N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 2.8e-102], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.00000000000000036e162 or -1.25e85 < z < -2.2500000000000001e-27 or 2.80000000000000013e-102 < z

   1. Initial program 49.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 77.9%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -7.00000000000000036e162 < z < -1.25e85

   1. Initial program 32.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around -inf 21.6%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. +-commutative 21.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]

      2. associate--l+ 21.6%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   4. Simplified 84.1%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]

   5. Taylor expanded in y around inf 95.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]
   6. Step-by-step derivation

      1. associate-*r/ 95.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z}} + \frac{t - a}{b - y} \]

      2. mul-1-neg 95.0%

         \[\leadsto \frac{\color{blue}{-x}}{z} + \frac{t - a}{b - y} \]

   7. Simplified 95.0%

      \[\leadsto \color{blue}{\frac{-x}{z}} + \frac{t - a}{b - y} \]

   8. Taylor expanded in a around 0 95.0%

      \[\leadsto \color{blue}{\frac{t}{b - y} + -1 \cdot \frac{x}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 95.0%

         \[\leadsto \frac{t}{b - y} + \color{blue}{\left(-\frac{x}{z}\right)} \]

      2. unsub-neg 95.0%

         \[\leadsto \color{blue}{\frac{t}{b - y} - \frac{x}{z}} \]

   10. Simplified 95.0%

       \[\leadsto \color{blue}{\frac{t}{b - y} - \frac{x}{z}} \]

   if -2.2500000000000001e-27 < z < -2.0499999999999999e-67 or -8.20000000000000057e-99 < z < 2.80000000000000013e-102

   1. Initial program 90.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 71.8%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y}} \]

   if -2.0499999999999999e-67 < z < -8.20000000000000057e-99

   1. Initial program 82.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around -inf 64.7%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. +-commutative 64.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]

      2. associate--l+ 64.7%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   4. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]

   5. Taylor expanded in x around inf 66.9%

      \[\leadsto \color{blue}{\frac{y \cdot x}{\left(b - y\right) \cdot z}} + \frac{t - a}{b - y} \]
   6. Step-by-step derivation

      1. times-frac 53.9%

         \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]

   7. Simplified 53.9%

      \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]

   8. Taylor expanded in b around inf 64.8%

      \[\leadsto \color{blue}{\frac{\left(\frac{y \cdot x}{z} + t\right) - a}{b}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+162}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+85}:\\ \;\;\;\;\frac{t}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-27}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-67}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-99}:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-102}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 5: 65.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+86}:\\ \;\;\;\;\frac{t}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-117}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-152}:\\ \;\;\;\;\frac{t - a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-102}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -7.5e+162)
     t_1
     (if (<= z -1e+86)
       (- (/ t (- b y)) (/ x z))
       (if (<= z -1.5e-27)
         t_1
         (if (<= z -1.7e-117)
           (+ x (* z (/ t y)))
           (if (<= z -1.76e-152)
             (/ (- t a) (/ y z))
             (if (<= z 2.8e-102) (- x (* z (/ a y))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.5e+162) {
		tmp = t_1;
	} else if (z <= -1e+86) {
		tmp = (t / (b - y)) - (x / z);
	} else if (z <= -1.5e-27) {
		tmp = t_1;
	} else if (z <= -1.7e-117) {
		tmp = x + (z * (t / y));
	} else if (z <= -1.76e-152) {
		tmp = (t - a) / (y / z);
	} else if (z <= 2.8e-102) {
		tmp = x - (z * (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-7.5d+162)) then
        tmp = t_1
    else if (z <= (-1d+86)) then
        tmp = (t / (b - y)) - (x / z)
    else if (z <= (-1.5d-27)) then
        tmp = t_1
    else if (z <= (-1.7d-117)) then
        tmp = x + (z * (t / y))
    else if (z <= (-1.76d-152)) then
        tmp = (t - a) / (y / z)
    else if (z <= 2.8d-102) then
        tmp = x - (z * (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.5e+162) {
		tmp = t_1;
	} else if (z <= -1e+86) {
		tmp = (t / (b - y)) - (x / z);
	} else if (z <= -1.5e-27) {
		tmp = t_1;
	} else if (z <= -1.7e-117) {
		tmp = x + (z * (t / y));
	} else if (z <= -1.76e-152) {
		tmp = (t - a) / (y / z);
	} else if (z <= 2.8e-102) {
		tmp = x - (z * (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -7.5e+162:
		tmp = t_1
	elif z <= -1e+86:
		tmp = (t / (b - y)) - (x / z)
	elif z <= -1.5e-27:
		tmp = t_1
	elif z <= -1.7e-117:
		tmp = x + (z * (t / y))
	elif z <= -1.76e-152:
		tmp = (t - a) / (y / z)
	elif z <= 2.8e-102:
		tmp = x - (z * (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -7.5e+162)
		tmp = t_1;
	elseif (z <= -1e+86)
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(x / z));
	elseif (z <= -1.5e-27)
		tmp = t_1;
	elseif (z <= -1.7e-117)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	elseif (z <= -1.76e-152)
		tmp = Float64(Float64(t - a) / Float64(y / z));
	elseif (z <= 2.8e-102)
		tmp = Float64(x - Float64(z * Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -7.5e+162)
		tmp = t_1;
	elseif (z <= -1e+86)
		tmp = (t / (b - y)) - (x / z);
	elseif (z <= -1.5e-27)
		tmp = t_1;
	elseif (z <= -1.7e-117)
		tmp = x + (z * (t / y));
	elseif (z <= -1.76e-152)
		tmp = (t - a) / (y / z);
	elseif (z <= 2.8e-102)
		tmp = x - (z * (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+162], t$95$1, If[LessEqual[z, -1e+86], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5e-27], t$95$1, If[LessEqual[z, -1.7e-117], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.76e-152], N[(N[(t - a), $MachinePrecision] / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-102], N[(x - N[(z * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.50000000000000033e162 or -1e86 < z < -1.5000000000000001e-27 or 2.80000000000000013e-102 < z

   1. Initial program 49.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 77.9%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -7.50000000000000033e162 < z < -1e86

   1. Initial program 32.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around -inf 21.6%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. +-commutative 21.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]

      2. associate--l+ 21.6%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   4. Simplified 84.1%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]

   5. Taylor expanded in y around inf 95.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]
   6. Step-by-step derivation

      1. associate-*r/ 95.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z}} + \frac{t - a}{b - y} \]

      2. mul-1-neg 95.0%

         \[\leadsto \frac{\color{blue}{-x}}{z} + \frac{t - a}{b - y} \]

   7. Simplified 95.0%

      \[\leadsto \color{blue}{\frac{-x}{z}} + \frac{t - a}{b - y} \]

   8. Taylor expanded in a around 0 95.0%

      \[\leadsto \color{blue}{\frac{t}{b - y} + -1 \cdot \frac{x}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 95.0%

         \[\leadsto \frac{t}{b - y} + \color{blue}{\left(-\frac{x}{z}\right)} \]

      2. unsub-neg 95.0%

         \[\leadsto \color{blue}{\frac{t}{b - y} - \frac{x}{z}} \]

   10. Simplified 95.0%

       \[\leadsto \color{blue}{\frac{t}{b - y} - \frac{x}{z}} \]

   if -1.5000000000000001e-27 < z < -1.70000000000000017e-117

   1. Initial program 85.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 38.3%

      \[\leadsto \color{blue}{z \cdot \left(\frac{t}{y} - \left(\frac{\left(b - y\right) \cdot x}{y} + \frac{a}{y}\right)\right) + x} \]

   3. Taylor expanded in t around inf 48.7%

      \[\leadsto z \cdot \color{blue}{\frac{t}{y}} + x \]

   if -1.70000000000000017e-117 < z < -1.76000000000000001e-152

   1. Initial program 100.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 64.2%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y}} \]

   3. Taylor expanded in x around 0 64.4%

      \[\leadsto \color{blue}{\frac{\left(t - a\right) \cdot z}{y}} \]
   4. Step-by-step derivation

      1. associate-/l* 64.0%

         \[\leadsto \color{blue}{\frac{t - a}{\frac{y}{z}}} \]

   5. Simplified 64.0%

      \[\leadsto \color{blue}{\frac{t - a}{\frac{y}{z}}} \]

   if -1.76000000000000001e-152 < z < 2.80000000000000013e-102

   1. Initial program 89.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 57.7%

      \[\leadsto \color{blue}{z \cdot \left(\frac{t}{y} - \left(\frac{\left(b - y\right) \cdot x}{y} + \frac{a}{y}\right)\right) + x} \]

   3. Taylor expanded in a around inf 68.0%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \frac{a}{y}\right)} + x \]
   4. Step-by-step derivation

      1. associate-*r/ 68.0%

         \[\leadsto z \cdot \color{blue}{\frac{-1 \cdot a}{y}} + x \]

      2. mul-1-neg 68.0%

         \[\leadsto z \cdot \frac{\color{blue}{-a}}{y} + x \]

   5. Simplified 68.0%

      \[\leadsto z \cdot \color{blue}{\frac{-a}{y}} + x \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+162}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+86}:\\ \;\;\;\;\frac{t}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-117}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-152}:\\ \;\;\;\;\frac{t - a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-102}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 6: 69.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+86}:\\ \;\;\;\;\frac{t}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-27} \lor \neg \left(z \leq 2 \cdot 10^{-103}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(\frac{t}{y} - \frac{a}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -7.2e+162)
     t_1
     (if (<= z -1.06e+86)
       (- (/ t (- b y)) (/ x z))
       (if (or (<= z -2.4e-27) (not (<= z 2e-103)))
         t_1
         (+ x (* z (- (/ t y) (/ a y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.2e+162) {
		tmp = t_1;
	} else if (z <= -1.06e+86) {
		tmp = (t / (b - y)) - (x / z);
	} else if ((z <= -2.4e-27) || !(z <= 2e-103)) {
		tmp = t_1;
	} else {
		tmp = x + (z * ((t / y) - (a / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-7.2d+162)) then
        tmp = t_1
    else if (z <= (-1.06d+86)) then
        tmp = (t / (b - y)) - (x / z)
    else if ((z <= (-2.4d-27)) .or. (.not. (z <= 2d-103))) then
        tmp = t_1
    else
        tmp = x + (z * ((t / y) - (a / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.2e+162) {
		tmp = t_1;
	} else if (z <= -1.06e+86) {
		tmp = (t / (b - y)) - (x / z);
	} else if ((z <= -2.4e-27) || !(z <= 2e-103)) {
		tmp = t_1;
	} else {
		tmp = x + (z * ((t / y) - (a / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -7.2e+162:
		tmp = t_1
	elif z <= -1.06e+86:
		tmp = (t / (b - y)) - (x / z)
	elif (z <= -2.4e-27) or not (z <= 2e-103):
		tmp = t_1
	else:
		tmp = x + (z * ((t / y) - (a / y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -7.2e+162)
		tmp = t_1;
	elseif (z <= -1.06e+86)
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(x / z));
	elseif ((z <= -2.4e-27) || !(z <= 2e-103))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * Float64(Float64(t / y) - Float64(a / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -7.2e+162)
		tmp = t_1;
	elseif (z <= -1.06e+86)
		tmp = (t / (b - y)) - (x / z);
	elseif ((z <= -2.4e-27) || ~((z <= 2e-103)))
		tmp = t_1;
	else
		tmp = x + (z * ((t / y) - (a / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+162], t$95$1, If[LessEqual[z, -1.06e+86], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.4e-27], N[Not[LessEqual[z, 2e-103]], $MachinePrecision]], t$95$1, N[(x + N[(z * N[(N[(t / y), $MachinePrecision] - N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.19999999999999987e162 or -1.06e86 < z < -2.40000000000000002e-27 or 1.99999999999999992e-103 < z

   1. Initial program 49.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 77.9%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -7.19999999999999987e162 < z < -1.06e86

   1. Initial program 32.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around -inf 21.6%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. +-commutative 21.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]

      2. associate--l+ 21.6%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   4. Simplified 84.1%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]

   5. Taylor expanded in y around inf 95.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]
   6. Step-by-step derivation

      1. associate-*r/ 95.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z}} + \frac{t - a}{b - y} \]

      2. mul-1-neg 95.0%

         \[\leadsto \frac{\color{blue}{-x}}{z} + \frac{t - a}{b - y} \]

   7. Simplified 95.0%

      \[\leadsto \color{blue}{\frac{-x}{z}} + \frac{t - a}{b - y} \]

   8. Taylor expanded in a around 0 95.0%

      \[\leadsto \color{blue}{\frac{t}{b - y} + -1 \cdot \frac{x}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 95.0%

         \[\leadsto \frac{t}{b - y} + \color{blue}{\left(-\frac{x}{z}\right)} \]

      2. unsub-neg 95.0%

         \[\leadsto \color{blue}{\frac{t}{b - y} - \frac{x}{z}} \]

   10. Simplified 95.0%

       \[\leadsto \color{blue}{\frac{t}{b - y} - \frac{x}{z}} \]

   if -2.40000000000000002e-27 < z < 1.99999999999999992e-103

   1. Initial program 89.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 66.8%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y}} \]

   3. Taylor expanded in z around 0 63.9%

      \[\leadsto \color{blue}{\left(\frac{t}{y} - \frac{a}{y}\right) \cdot z + x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+162}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+86}:\\ \;\;\;\;\frac{t}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-27} \lor \neg \left(z \leq 2 \cdot 10^{-103}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(\frac{t}{y} - \frac{a}{y}\right)\\ \end{array} \]

Alternative 7: 67.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+86}:\\ \;\;\;\;\frac{t}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-27} \lor \neg \left(z \leq 2.8 \cdot 10^{-102}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -7e+162)
     t_1
     (if (<= z -1.06e+86)
       (- (/ t (- b y)) (/ x z))
       (if (or (<= z -2.55e-27) (not (<= z 2.8e-102)))
         t_1
         (/ (+ (* y x) (* z (- t a))) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7e+162) {
		tmp = t_1;
	} else if (z <= -1.06e+86) {
		tmp = (t / (b - y)) - (x / z);
	} else if ((z <= -2.55e-27) || !(z <= 2.8e-102)) {
		tmp = t_1;
	} else {
		tmp = ((y * x) + (z * (t - a))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-7d+162)) then
        tmp = t_1
    else if (z <= (-1.06d+86)) then
        tmp = (t / (b - y)) - (x / z)
    else if ((z <= (-2.55d-27)) .or. (.not. (z <= 2.8d-102))) then
        tmp = t_1
    else
        tmp = ((y * x) + (z * (t - a))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7e+162) {
		tmp = t_1;
	} else if (z <= -1.06e+86) {
		tmp = (t / (b - y)) - (x / z);
	} else if ((z <= -2.55e-27) || !(z <= 2.8e-102)) {
		tmp = t_1;
	} else {
		tmp = ((y * x) + (z * (t - a))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -7e+162:
		tmp = t_1
	elif z <= -1.06e+86:
		tmp = (t / (b - y)) - (x / z)
	elif (z <= -2.55e-27) or not (z <= 2.8e-102):
		tmp = t_1
	else:
		tmp = ((y * x) + (z * (t - a))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -7e+162)
		tmp = t_1;
	elseif (z <= -1.06e+86)
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(x / z));
	elseif ((z <= -2.55e-27) || !(z <= 2.8e-102))
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -7e+162)
		tmp = t_1;
	elseif (z <= -1.06e+86)
		tmp = (t / (b - y)) - (x / z);
	elseif ((z <= -2.55e-27) || ~((z <= 2.8e-102)))
		tmp = t_1;
	else
		tmp = ((y * x) + (z * (t - a))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+162], t$95$1, If[LessEqual[z, -1.06e+86], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.55e-27], N[Not[LessEqual[z, 2.8e-102]], $MachinePrecision]], t$95$1, N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.00000000000000036e162 or -1.06e86 < z < -2.55e-27 or 2.80000000000000013e-102 < z

   1. Initial program 49.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 77.9%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -7.00000000000000036e162 < z < -1.06e86

   1. Initial program 32.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around -inf 21.6%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. +-commutative 21.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]

      2. associate--l+ 21.6%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   4. Simplified 84.1%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]

   5. Taylor expanded in y around inf 95.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]
   6. Step-by-step derivation

      1. associate-*r/ 95.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z}} + \frac{t - a}{b - y} \]

      2. mul-1-neg 95.0%

         \[\leadsto \frac{\color{blue}{-x}}{z} + \frac{t - a}{b - y} \]

   7. Simplified 95.0%

      \[\leadsto \color{blue}{\frac{-x}{z}} + \frac{t - a}{b - y} \]

   8. Taylor expanded in a around 0 95.0%

      \[\leadsto \color{blue}{\frac{t}{b - y} + -1 \cdot \frac{x}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 95.0%

         \[\leadsto \frac{t}{b - y} + \color{blue}{\left(-\frac{x}{z}\right)} \]

      2. unsub-neg 95.0%

         \[\leadsto \color{blue}{\frac{t}{b - y} - \frac{x}{z}} \]

   10. Simplified 95.0%

       \[\leadsto \color{blue}{\frac{t}{b - y} - \frac{x}{z}} \]

   if -2.55e-27 < z < 2.80000000000000013e-102

   1. Initial program 89.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 66.8%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+162}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+86}:\\ \;\;\;\;\frac{t}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-27} \lor \neg \left(z \leq 2.8 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \end{array} \]

Alternative 8: 71.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-104}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y - z \cdot y}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+17}:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- t a) (- b y)) (/ x z))))
   (if (<= z -6.6e-8)
     t_1
     (if (<= z 4.6e-104)
       (/ (+ (* y x) (* z (- t a))) (- y (* z y)))
       (if (<= z 2e+17) (/ (- (+ t (/ (* y x) z)) a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -6.6e-8) {
		tmp = t_1;
	} else if (z <= 4.6e-104) {
		tmp = ((y * x) + (z * (t - a))) / (y - (z * y));
	} else if (z <= 2e+17) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t - a) / (b - y)) - (x / z)
    if (z <= (-6.6d-8)) then
        tmp = t_1
    else if (z <= 4.6d-104) then
        tmp = ((y * x) + (z * (t - a))) / (y - (z * y))
    else if (z <= 2d+17) then
        tmp = ((t + ((y * x) / z)) - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -6.6e-8) {
		tmp = t_1;
	} else if (z <= 4.6e-104) {
		tmp = ((y * x) + (z * (t - a))) / (y - (z * y));
	} else if (z <= 2e+17) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t - a) / (b - y)) - (x / z)
	tmp = 0
	if z <= -6.6e-8:
		tmp = t_1
	elif z <= 4.6e-104:
		tmp = ((y * x) + (z * (t - a))) / (y - (z * y))
	elif z <= 2e+17:
		tmp = ((t + ((y * x) / z)) - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	tmp = 0.0
	if (z <= -6.6e-8)
		tmp = t_1;
	elseif (z <= 4.6e-104)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / Float64(y - Float64(z * y)));
	elseif (z <= 2e+17)
		tmp = Float64(Float64(Float64(t + Float64(Float64(y * x) / z)) - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t - a) / (b - y)) - (x / z);
	tmp = 0.0;
	if (z <= -6.6e-8)
		tmp = t_1;
	elseif (z <= 4.6e-104)
		tmp = ((y * x) + (z * (t - a))) / (y - (z * y));
	elseif (z <= 2e+17)
		tmp = ((t + ((y * x) / z)) - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e-8], t$95$1, If[LessEqual[z, 4.6e-104], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+17], N[(N[(N[(t + N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.59999999999999954e-8 or 2e17 < z

   1. Initial program 35.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around -inf 59.0%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. +-commutative 59.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]

      2. associate--l+ 59.0%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   4. Simplified 90.9%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]

   5. Taylor expanded in y around inf 91.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]
   6. Step-by-step derivation

      1. associate-*r/ 91.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z}} + \frac{t - a}{b - y} \]

      2. mul-1-neg 91.8%

         \[\leadsto \frac{\color{blue}{-x}}{z} + \frac{t - a}{b - y} \]

   7. Simplified 91.8%

      \[\leadsto \color{blue}{\frac{-x}{z}} + \frac{t - a}{b - y} \]

   if -6.59999999999999954e-8 < z < 4.5999999999999999e-104

   1. Initial program 89.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around inf 66.3%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{\left(-1 \cdot z + 1\right) \cdot y}} \]
   3. Step-by-step derivation

      1. *-commutative 66.3%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y \cdot \left(-1 \cdot z + 1\right)}} \]

      2. +-commutative 66.3%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y \cdot \color{blue}{\left(1 + -1 \cdot z\right)}} \]

      3. distribute-lft-in 66.3%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y \cdot 1 + y \cdot \left(-1 \cdot z\right)}} \]

      4. *-rgt-identity 66.3%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y} + y \cdot \left(-1 \cdot z\right)} \]

      5. mul-1-neg 66.3%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + y \cdot \color{blue}{\left(-z\right)}} \]

      6. distribute-rgt-neg-in 66.3%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{\left(-y \cdot z\right)}} \]

      7. unsub-neg 66.3%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y - y \cdot z}} \]

      8. *-commutative 66.3%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y - \color{blue}{z \cdot y}} \]

   4. Simplified 66.3%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y - z \cdot y}} \]

   if 4.5999999999999999e-104 < z < 2e17

   1. Initial program 99.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around -inf 57.0%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. +-commutative 57.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]

      2. associate--l+ 57.0%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   4. Simplified 62.2%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]

   5. Taylor expanded in x around inf 68.0%

      \[\leadsto \color{blue}{\frac{y \cdot x}{\left(b - y\right) \cdot z}} + \frac{t - a}{b - y} \]
   6. Step-by-step derivation

      1. times-frac 63.0%

         \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]

   7. Simplified 63.0%

      \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]

   8. Taylor expanded in b around inf 64.3%

      \[\leadsto \color{blue}{\frac{\left(\frac{y \cdot x}{z} + t\right) - a}{b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-8}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-104}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y - z \cdot y}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+17}:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]

Alternative 9: 71.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-103}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 10^{+18}:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- t a) (- b y)) (/ x z))))
   (if (<= z -3.6e-10)
     t_1
     (if (<= z 4.2e-103)
       (/ (+ (* y x) (* z (- t a))) y)
       (if (<= z 1e+18) (/ (- (+ t (/ (* y x) z)) a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -3.6e-10) {
		tmp = t_1;
	} else if (z <= 4.2e-103) {
		tmp = ((y * x) + (z * (t - a))) / y;
	} else if (z <= 1e+18) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t - a) / (b - y)) - (x / z)
    if (z <= (-3.6d-10)) then
        tmp = t_1
    else if (z <= 4.2d-103) then
        tmp = ((y * x) + (z * (t - a))) / y
    else if (z <= 1d+18) then
        tmp = ((t + ((y * x) / z)) - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -3.6e-10) {
		tmp = t_1;
	} else if (z <= 4.2e-103) {
		tmp = ((y * x) + (z * (t - a))) / y;
	} else if (z <= 1e+18) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t - a) / (b - y)) - (x / z)
	tmp = 0
	if z <= -3.6e-10:
		tmp = t_1
	elif z <= 4.2e-103:
		tmp = ((y * x) + (z * (t - a))) / y
	elif z <= 1e+18:
		tmp = ((t + ((y * x) / z)) - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	tmp = 0.0
	if (z <= -3.6e-10)
		tmp = t_1;
	elseif (z <= 4.2e-103)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / y);
	elseif (z <= 1e+18)
		tmp = Float64(Float64(Float64(t + Float64(Float64(y * x) / z)) - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t - a) / (b - y)) - (x / z);
	tmp = 0.0;
	if (z <= -3.6e-10)
		tmp = t_1;
	elseif (z <= 4.2e-103)
		tmp = ((y * x) + (z * (t - a))) / y;
	elseif (z <= 1e+18)
		tmp = ((t + ((y * x) / z)) - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e-10], t$95$1, If[LessEqual[z, 4.2e-103], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1e+18], N[(N[(N[(t + N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e-10 or 1e18 < z

   1. Initial program 35.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around -inf 59.0%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. +-commutative 59.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]

      2. associate--l+ 59.0%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   4. Simplified 90.9%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]

   5. Taylor expanded in y around inf 91.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]
   6. Step-by-step derivation

      1. associate-*r/ 91.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z}} + \frac{t - a}{b - y} \]

      2. mul-1-neg 91.8%

         \[\leadsto \frac{\color{blue}{-x}}{z} + \frac{t - a}{b - y} \]

   7. Simplified 91.8%

      \[\leadsto \color{blue}{\frac{-x}{z}} + \frac{t - a}{b - y} \]

   if -3.6e-10 < z < 4.20000000000000009e-103

   1. Initial program 89.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 66.1%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y}} \]

   if 4.20000000000000009e-103 < z < 1e18

   1. Initial program 99.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around -inf 57.0%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. +-commutative 57.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]

      2. associate--l+ 57.0%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   4. Simplified 62.2%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]

   5. Taylor expanded in x around inf 68.0%

      \[\leadsto \color{blue}{\frac{y \cdot x}{\left(b - y\right) \cdot z}} + \frac{t - a}{b - y} \]
   6. Step-by-step derivation

      1. times-frac 63.0%

         \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]

   7. Simplified 63.0%

      \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]

   8. Taylor expanded in b around inf 64.3%

      \[\leadsto \color{blue}{\frac{\left(\frac{y \cdot x}{z} + t\right) - a}{b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-10}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-103}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 10^{+18}:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]

Alternative 10: 67.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{t}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{-27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-152}:\\ \;\;\;\;\frac{t - a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ t y)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -2.15e-27)
     t_2
     (if (<= z -1.22e-117)
       t_1
       (if (<= z -1.76e-152)
         (/ (- t a) (/ y z))
         (if (<= z 2.7e-102) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (t / y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.15e-27) {
		tmp = t_2;
	} else if (z <= -1.22e-117) {
		tmp = t_1;
	} else if (z <= -1.76e-152) {
		tmp = (t - a) / (y / z);
	} else if (z <= 2.7e-102) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (t / y))
    t_2 = (t - a) / (b - y)
    if (z <= (-2.15d-27)) then
        tmp = t_2
    else if (z <= (-1.22d-117)) then
        tmp = t_1
    else if (z <= (-1.76d-152)) then
        tmp = (t - a) / (y / z)
    else if (z <= 2.7d-102) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (t / y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.15e-27) {
		tmp = t_2;
	} else if (z <= -1.22e-117) {
		tmp = t_1;
	} else if (z <= -1.76e-152) {
		tmp = (t - a) / (y / z);
	} else if (z <= 2.7e-102) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (t / y))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.15e-27:
		tmp = t_2
	elif z <= -1.22e-117:
		tmp = t_1
	elif z <= -1.76e-152:
		tmp = (t - a) / (y / z)
	elif z <= 2.7e-102:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(t / y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.15e-27)
		tmp = t_2;
	elseif (z <= -1.22e-117)
		tmp = t_1;
	elseif (z <= -1.76e-152)
		tmp = Float64(Float64(t - a) / Float64(y / z));
	elseif (z <= 2.7e-102)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (t / y));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.15e-27)
		tmp = t_2;
	elseif (z <= -1.22e-117)
		tmp = t_1;
	elseif (z <= -1.76e-152)
		tmp = (t - a) / (y / z);
	elseif (z <= 2.7e-102)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.15e-27], t$95$2, If[LessEqual[z, -1.22e-117], t$95$1, If[LessEqual[z, -1.76e-152], N[(N[(t - a), $MachinePrecision] / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e-102], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.15000000000000001e-27 or 2.7e-102 < z

   1. Initial program 46.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 76.8%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -2.15000000000000001e-27 < z < -1.21999999999999997e-117 or -1.76000000000000001e-152 < z < 2.7e-102

   1. Initial program 88.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 52.6%

      \[\leadsto \color{blue}{z \cdot \left(\frac{t}{y} - \left(\frac{\left(b - y\right) \cdot x}{y} + \frac{a}{y}\right)\right) + x} \]

   3. Taylor expanded in t around inf 56.6%

      \[\leadsto z \cdot \color{blue}{\frac{t}{y}} + x \]

   if -1.21999999999999997e-117 < z < -1.76000000000000001e-152

   1. Initial program 100.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 64.2%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y}} \]

   3. Taylor expanded in x around 0 64.4%

      \[\leadsto \color{blue}{\frac{\left(t - a\right) \cdot z}{y}} \]
   4. Step-by-step derivation

      1. associate-/l* 64.0%

         \[\leadsto \color{blue}{\frac{t - a}{\frac{y}{z}}} \]

   5. Simplified 64.0%

      \[\leadsto \color{blue}{\frac{t - a}{\frac{y}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-27}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-117}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-152}:\\ \;\;\;\;\frac{t - a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-102}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 11: 67.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-117}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-152}:\\ \;\;\;\;\frac{t - a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-102}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.9e-27)
     t_1
     (if (<= z -1.22e-117)
       (+ x (* z (/ t y)))
       (if (<= z -1.76e-152)
         (/ (- t a) (/ y z))
         (if (<= z 2.8e-102) (- x (* z (/ a y))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.9e-27) {
		tmp = t_1;
	} else if (z <= -1.22e-117) {
		tmp = x + (z * (t / y));
	} else if (z <= -1.76e-152) {
		tmp = (t - a) / (y / z);
	} else if (z <= 2.8e-102) {
		tmp = x - (z * (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.9d-27)) then
        tmp = t_1
    else if (z <= (-1.22d-117)) then
        tmp = x + (z * (t / y))
    else if (z <= (-1.76d-152)) then
        tmp = (t - a) / (y / z)
    else if (z <= 2.8d-102) then
        tmp = x - (z * (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.9e-27) {
		tmp = t_1;
	} else if (z <= -1.22e-117) {
		tmp = x + (z * (t / y));
	} else if (z <= -1.76e-152) {
		tmp = (t - a) / (y / z);
	} else if (z <= 2.8e-102) {
		tmp = x - (z * (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.9e-27:
		tmp = t_1
	elif z <= -1.22e-117:
		tmp = x + (z * (t / y))
	elif z <= -1.76e-152:
		tmp = (t - a) / (y / z)
	elif z <= 2.8e-102:
		tmp = x - (z * (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.9e-27)
		tmp = t_1;
	elseif (z <= -1.22e-117)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	elseif (z <= -1.76e-152)
		tmp = Float64(Float64(t - a) / Float64(y / z));
	elseif (z <= 2.8e-102)
		tmp = Float64(x - Float64(z * Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.9e-27)
		tmp = t_1;
	elseif (z <= -1.22e-117)
		tmp = x + (z * (t / y));
	elseif (z <= -1.76e-152)
		tmp = (t - a) / (y / z);
	elseif (z <= 2.8e-102)
		tmp = x - (z * (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e-27], t$95$1, If[LessEqual[z, -1.22e-117], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.76e-152], N[(N[(t - a), $MachinePrecision] / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-102], N[(x - N[(z * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9e-27 or 2.80000000000000013e-102 < z

   1. Initial program 46.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 76.8%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -1.9e-27 < z < -1.21999999999999997e-117

   1. Initial program 85.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 38.3%

      \[\leadsto \color{blue}{z \cdot \left(\frac{t}{y} - \left(\frac{\left(b - y\right) \cdot x}{y} + \frac{a}{y}\right)\right) + x} \]

   3. Taylor expanded in t around inf 48.7%

      \[\leadsto z \cdot \color{blue}{\frac{t}{y}} + x \]

   if -1.21999999999999997e-117 < z < -1.76000000000000001e-152

   1. Initial program 100.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 64.2%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y}} \]

   3. Taylor expanded in x around 0 64.4%

      \[\leadsto \color{blue}{\frac{\left(t - a\right) \cdot z}{y}} \]
   4. Step-by-step derivation

      1. associate-/l* 64.0%

         \[\leadsto \color{blue}{\frac{t - a}{\frac{y}{z}}} \]

   5. Simplified 64.0%

      \[\leadsto \color{blue}{\frac{t - a}{\frac{y}{z}}} \]

   if -1.76000000000000001e-152 < z < 2.80000000000000013e-102

   1. Initial program 89.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 57.7%

      \[\leadsto \color{blue}{z \cdot \left(\frac{t}{y} - \left(\frac{\left(b - y\right) \cdot x}{y} + \frac{a}{y}\right)\right) + x} \]

   3. Taylor expanded in a around inf 68.0%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \frac{a}{y}\right)} + x \]
   4. Step-by-step derivation

      1. associate-*r/ 68.0%

         \[\leadsto z \cdot \color{blue}{\frac{-1 \cdot a}{y}} + x \]

      2. mul-1-neg 68.0%

         \[\leadsto z \cdot \frac{\color{blue}{-a}}{y} + x \]

   5. Simplified 68.0%

      \[\leadsto z \cdot \color{blue}{\frac{-a}{y}} + x \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-27}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-117}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-152}:\\ \;\;\;\;\frac{t - a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-102}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 12: 67.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-27} \lor \neg \left(z \leq 2.8 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.6e-27) (not (<= z 2.8e-102)))
   (/ (- t a) (- b y))
   (+ x (* z (/ t y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.6e-27) || !(z <= 2.8e-102)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.6d-27)) .or. (.not. (z <= 2.8d-102))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (z * (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.6e-27) || !(z <= 2.8e-102)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.6e-27) or not (z <= 2.8e-102):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (z * (t / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.6e-27) || !(z <= 2.8e-102))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.6e-27) || ~((z <= 2.8e-102)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (z * (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.6e-27], N[Not[LessEqual[z, 2.8e-102]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999995e-27 or 2.80000000000000013e-102 < z

   1. Initial program 46.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 76.8%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -1.59999999999999995e-27 < z < 2.80000000000000013e-102

   1. Initial program 89.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 51.7%

      \[\leadsto \color{blue}{z \cdot \left(\frac{t}{y} - \left(\frac{\left(b - y\right) \cdot x}{y} + \frac{a}{y}\right)\right) + x} \]

   3. Taylor expanded in t around inf 52.9%

      \[\leadsto z \cdot \color{blue}{\frac{t}{y}} + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-27} \lor \neg \left(z \leq 2.8 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \]

Alternative 13: 36.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-21}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+182}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.65e-21)
   (/ t b)
   (if (<= z 2.7e-102) x (if (<= z 3.5e+182) (/ t b) (/ (- a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.65e-21) {
		tmp = t / b;
	} else if (z <= 2.7e-102) {
		tmp = x;
	} else if (z <= 3.5e+182) {
		tmp = t / b;
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.65d-21)) then
        tmp = t / b
    else if (z <= 2.7d-102) then
        tmp = x
    else if (z <= 3.5d+182) then
        tmp = t / b
    else
        tmp = -a / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.65e-21) {
		tmp = t / b;
	} else if (z <= 2.7e-102) {
		tmp = x;
	} else if (z <= 3.5e+182) {
		tmp = t / b;
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.65e-21:
		tmp = t / b
	elif z <= 2.7e-102:
		tmp = x
	elif z <= 3.5e+182:
		tmp = t / b
	else:
		tmp = -a / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.65e-21)
		tmp = Float64(t / b);
	elseif (z <= 2.7e-102)
		tmp = x;
	elseif (z <= 3.5e+182)
		tmp = Float64(t / b);
	else
		tmp = Float64(Float64(-a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.65e-21)
		tmp = t / b;
	elseif (z <= 2.7e-102)
		tmp = x;
	elseif (z <= 3.5e+182)
		tmp = t / b;
	else
		tmp = -a / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.65e-21], N[(t / b), $MachinePrecision], If[LessEqual[z, 2.7e-102], x, If[LessEqual[z, 3.5e+182], N[(t / b), $MachinePrecision], N[((-a) / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65000000000000004e-21 or 2.7e-102 < z < 3.50000000000000023e182

   1. Initial program 49.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in b around inf 32.4%

      \[\leadsto \color{blue}{\frac{y \cdot x + \left(t - a\right) \cdot z}{b \cdot z}} \]

   3. Taylor expanded in t around inf 30.9%

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

   if -1.65000000000000004e-21 < z < 2.7e-102

   1. Initial program 89.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 47.7%

      \[\leadsto \color{blue}{x} \]

   if 3.50000000000000023e182 < z

   1. Initial program 28.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in b around inf 24.7%

      \[\leadsto \color{blue}{\frac{y \cdot x + \left(t - a\right) \cdot z}{b \cdot z}} \]

   3. Taylor expanded in a around inf 45.7%

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

      1. associate-*r/ 45.7%

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

      2. neg-mul-1 45.7%

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

   5. Simplified 45.7%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-21}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+182}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 14: 34.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;-\frac{t}{y}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+182}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.5e-43)
   (- (/ t y))
   (if (<= z 1.45e-102) x (if (<= z 3.5e+182) (/ t b) (/ (- a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.5e-43) {
		tmp = -(t / y);
	} else if (z <= 1.45e-102) {
		tmp = x;
	} else if (z <= 3.5e+182) {
		tmp = t / b;
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.5d-43)) then
        tmp = -(t / y)
    else if (z <= 1.45d-102) then
        tmp = x
    else if (z <= 3.5d+182) then
        tmp = t / b
    else
        tmp = -a / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.5e-43) {
		tmp = -(t / y);
	} else if (z <= 1.45e-102) {
		tmp = x;
	} else if (z <= 3.5e+182) {
		tmp = t / b;
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.5e-43:
		tmp = -(t / y)
	elif z <= 1.45e-102:
		tmp = x
	elif z <= 3.5e+182:
		tmp = t / b
	else:
		tmp = -a / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.5e-43)
		tmp = Float64(-Float64(t / y));
	elseif (z <= 1.45e-102)
		tmp = x;
	elseif (z <= 3.5e+182)
		tmp = Float64(t / b);
	else
		tmp = Float64(Float64(-a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.5e-43)
		tmp = -(t / y);
	elseif (z <= 1.45e-102)
		tmp = x;
	elseif (z <= 3.5e+182)
		tmp = t / b;
	else
		tmp = -a / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.5e-43], (-N[(t / y), $MachinePrecision]), If[LessEqual[z, 1.45e-102], x, If[LessEqual[z, 3.5e+182], N[(t / b), $MachinePrecision], N[((-a) / b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.49999999999999997e-43

   1. Initial program 40.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in b around 0 25.0%

      \[\leadsto \color{blue}{\frac{y \cdot x + \left(t - a\right) \cdot z}{-1 \cdot \left(y \cdot z\right) + y}} \]
   3. Step-by-step derivation

      1. +-commutative 25.0%

         \[\leadsto \frac{y \cdot x + \left(t - a\right) \cdot z}{\color{blue}{y + -1 \cdot \left(y \cdot z\right)}} \]

      2. +-commutative 25.0%

         \[\leadsto \frac{\color{blue}{\left(t - a\right) \cdot z + y \cdot x}}{y + -1 \cdot \left(y \cdot z\right)} \]

      3. *-commutative 25.0%

         \[\leadsto \frac{\left(t - a\right) \cdot z + \color{blue}{x \cdot y}}{y + -1 \cdot \left(y \cdot z\right)} \]

      4. fma-udef 25.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(t - a, z, x \cdot y\right)}}{y + -1 \cdot \left(y \cdot z\right)} \]

      5. *-commutative 25.0%

         \[\leadsto \frac{\mathsf{fma}\left(t - a, z, \color{blue}{y \cdot x}\right)}{y + -1 \cdot \left(y \cdot z\right)} \]

      6. mul-1-neg 25.0%

         \[\leadsto \frac{\mathsf{fma}\left(t - a, z, y \cdot x\right)}{y + \color{blue}{\left(-y \cdot z\right)}} \]

      7. unsub-neg 25.0%

         \[\leadsto \frac{\mathsf{fma}\left(t - a, z, y \cdot x\right)}{\color{blue}{y - y \cdot z}} \]

      8. *-commutative 25.0%

         \[\leadsto \frac{\mathsf{fma}\left(t - a, z, y \cdot x\right)}{y - \color{blue}{z \cdot y}} \]

   4. Simplified 25.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t - a, z, y \cdot x\right)}{y - z \cdot y}} \]

   5. Taylor expanded in t around inf 15.7%

      \[\leadsto \frac{\color{blue}{t \cdot z}}{y - z \cdot y} \]

   6. Taylor expanded in z around inf 33.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{t}{y}} \]
   7. Step-by-step derivation

      1. associate-*r/ 33.2%

         \[\leadsto \color{blue}{\frac{-1 \cdot t}{y}} \]

      2. mul-1-neg 33.2%

         \[\leadsto \frac{\color{blue}{-t}}{y} \]

   8. Simplified 33.2%

      \[\leadsto \color{blue}{\frac{-t}{y}} \]

   if -3.49999999999999997e-43 < z < 1.44999999999999993e-102

   1. Initial program 89.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 49.4%

      \[\leadsto \color{blue}{x} \]

   if 1.44999999999999993e-102 < z < 3.50000000000000023e182

   1. Initial program 66.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in b around inf 41.2%

      \[\leadsto \color{blue}{\frac{y \cdot x + \left(t - a\right) \cdot z}{b \cdot z}} \]

   3. Taylor expanded in t around inf 32.4%

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

   if 3.50000000000000023e182 < z

   1. Initial program 28.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in b around inf 24.7%

      \[\leadsto \color{blue}{\frac{y \cdot x + \left(t - a\right) \cdot z}{b \cdot z}} \]

   3. Taylor expanded in a around inf 45.7%

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

      1. associate-*r/ 45.7%

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

      2. neg-mul-1 45.7%

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

   5. Simplified 45.7%

      \[\leadsto \color{blue}{\frac{-a}{b}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;-\frac{t}{y}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+182}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 15: 44.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-44} \lor \neg \left(z \leq 2.8 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.9e-44) (not (<= z 2.8e-102))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.9e-44) || !(z <= 2.8e-102)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.9d-44)) .or. (.not. (z <= 2.8d-102))) then
        tmp = t / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.9e-44) || !(z <= 2.8e-102)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.9e-44) or not (z <= 2.8e-102):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.9e-44) || !(z <= 2.8e-102))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.9e-44) || ~((z <= 2.8e-102)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.9e-44], N[Not[LessEqual[z, 2.8e-102]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.9000000000000001e-44 or 2.80000000000000013e-102 < z

   1. Initial program 47.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around -inf 57.5%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. +-commutative 57.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]

      2. associate--l+ 57.5%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   4. Simplified 83.9%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]

   5. Taylor expanded in x around inf 79.2%

      \[\leadsto \color{blue}{\frac{y \cdot x}{\left(b - y\right) \cdot z}} + \frac{t - a}{b - y} \]
   6. Step-by-step derivation

      1. times-frac 92.1%

         \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]

   7. Simplified 92.1%

      \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]

   8. Taylor expanded in t around inf 47.5%

      \[\leadsto \color{blue}{\frac{t}{b - y}} \]

   if -2.9000000000000001e-44 < z < 2.80000000000000013e-102

   1. Initial program 89.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 49.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-44} \lor \neg \left(z \leq 2.8 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 43.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+57} \lor \neg \left(z \leq 1.45 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.25e+57) (not (<= z 1.45e-102)))
   (/ t (- b y))
   (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.25e+57) || !(z <= 1.45e-102)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.25d+57)) .or. (.not. (z <= 1.45d-102))) then
        tmp = t / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.25e+57) || !(z <= 1.45e-102)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.25e+57) or not (z <= 1.45e-102):
		tmp = t / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.25e+57) || !(z <= 1.45e-102))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.25e+57) || ~((z <= 1.45e-102)))
		tmp = t / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.25e+57], N[Not[LessEqual[z, 1.45e-102]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.24999999999999993e57 or 1.44999999999999993e-102 < z

   1. Initial program 42.2%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around -inf 57.7%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. +-commutative 57.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]

      2. associate--l+ 57.7%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   4. Simplified 86.9%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]

   5. Taylor expanded in x around inf 80.6%

      \[\leadsto \color{blue}{\frac{y \cdot x}{\left(b - y\right) \cdot z}} + \frac{t - a}{b - y} \]
   6. Step-by-step derivation

      1. times-frac 93.8%

         \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]

   7. Simplified 93.8%

      \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]

   8. Taylor expanded in t around inf 50.4%

      \[\leadsto \color{blue}{\frac{t}{b - y}} \]

   if -1.24999999999999993e57 < z < 1.44999999999999993e-102

   1. Initial program 89.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around inf 46.2%

      \[\leadsto \color{blue}{\frac{x}{-1 \cdot z + 1}} \]
   3. Step-by-step derivation

      1. +-commutative 46.2%

         \[\leadsto \frac{x}{\color{blue}{1 + -1 \cdot z}} \]

      2. mul-1-neg 46.2%

         \[\leadsto \frac{x}{1 + \color{blue}{\left(-z\right)}} \]

      3. unsub-neg 46.2%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   4. Simplified 46.2%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+57} \lor \neg \left(z \leq 1.45 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 17: 55.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+14} \lor \neg \left(y \leq 1.22 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9.6e+14) (not (<= y 1.22e-12))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.6e+14) || !(y <= 1.22e-12)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9.6d+14)) .or. (.not. (y <= 1.22d-12))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.6e+14) || !(y <= 1.22e-12)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9.6e+14) or not (y <= 1.22e-12):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9.6e+14) || !(y <= 1.22e-12))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9.6e+14) || ~((y <= 1.22e-12)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9.6e+14], N[Not[LessEqual[y, 1.22e-12]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.6e14 or 1.2200000000000001e-12 < y

   1. Initial program 52.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around inf 49.2%

      \[\leadsto \color{blue}{\frac{x}{-1 \cdot z + 1}} \]
   3. Step-by-step derivation

      1. +-commutative 49.2%

         \[\leadsto \frac{x}{\color{blue}{1 + -1 \cdot z}} \]

      2. mul-1-neg 49.2%

         \[\leadsto \frac{x}{1 + \color{blue}{\left(-z\right)}} \]

      3. unsub-neg 49.2%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   4. Simplified 49.2%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   if -9.6e14 < y < 1.2200000000000001e-12

   1. Initial program 78.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around 0 60.3%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+14} \lor \neg \left(y \leq 1.22 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 18: 36.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-23}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8e-23) (/ t b) (if (<= z 7e-103) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8e-23) {
		tmp = t / b;
	} else if (z <= 7e-103) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-8d-23)) then
        tmp = t / b
    else if (z <= 7d-103) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8e-23) {
		tmp = t / b;
	} else if (z <= 7e-103) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8e-23:
		tmp = t / b
	elif z <= 7e-103:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8e-23)
		tmp = Float64(t / b);
	elseif (z <= 7e-103)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8e-23)
		tmp = t / b;
	elseif (z <= 7e-103)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8e-23], N[(t / b), $MachinePrecision], If[LessEqual[z, 7e-103], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.99999999999999968e-23 or 7.00000000000000032e-103 < z

   1. Initial program 46.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in b around inf 31.0%

      \[\leadsto \color{blue}{\frac{y \cdot x + \left(t - a\right) \cdot z}{b \cdot z}} \]

   3. Taylor expanded in t around inf 30.2%

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

   if -7.99999999999999968e-23 < z < 7.00000000000000032e-103

   1. Initial program 89.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 47.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-23}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 19: 25.4% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 65.2%

   \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

2. Taylor expanded in z around 0 23.8%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 23.8%

   \[\leadsto x \]

Developer target: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \frac{z \cdot t + y \cdot x}{y + z \cdot \left(b - y\right)} - \frac{a}{\left(b - y\right) + \frac{y}{z}} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (((z * t) + (y * x)) / (y + (z * (b - y)))) - (a / ((b - y) + (y / z)));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (((z * t) + (y * x)) / (y + (z * (b - y)))) - (a / ((b - y) + (y / z)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (((z * t) + (y * x)) / (y + (z * (b - y)))) - (a / ((b - y) + (y / z)));
}

Python

def code(x, y, z, t, a, b):
	return (((z * t) + (y * x)) / (y + (z * (b - y)))) - (a / ((b - y) + (y / z)))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(z * t) + Float64(y * x)) / Float64(y + Float64(z * Float64(b - y)))) - Float64(a / Float64(Float64(b - y) + Float64(y / z))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (((z * t) + (y * x)) / (y + (z * (b - y)))) - (a / ((b - y) + (y / z)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(z * t), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(N[(b - y), $MachinePrecision] + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023238 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

  :herbie-target
  (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z))))

  (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))