Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Percentage Accurate: 96.9% → 97.6%

Time: 9.0s

Alternatives: 9

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+131}:\\ \;\;\;\;t_1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-t}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 2e+131) (* t_1 t) (* x (/ (- t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 2e+131) {
		tmp = t_1 * t;
	} else {
		tmp = x * (-t / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 2d+131) then
        tmp = t_1 * t
    else
        tmp = x * (-t / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 2e+131) {
		tmp = t_1 * t;
	} else {
		tmp = x * (-t / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 2e+131:
		tmp = t_1 * t
	else:
		tmp = x * (-t / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 2e+131)
		tmp = Float64(t_1 * t);
	else
		tmp = Float64(x * Float64(Float64(-t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 2e+131)
		tmp = t_1 * t;
	else
		tmp = x * (-t / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+131], N[(t$95$1 * t), $MachinePrecision], N[(x * N[((-t) / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 1.9999999999999998e131

   1. Initial program 97.7%

      \[\frac{x - y}{z - y} \cdot t \]

   if 1.9999999999999998e131 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 75.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 75.7%

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

      2. associate-*r/ 99.8%

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

      3. associate-/l* 77.4%

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

      4. sub-neg 77.4%

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

      5. +-commutative 77.4%

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

      6. neg-sub0 77.4%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{\left(0 - y\right)} + x}} \]

      7. associate-+l- 77.4%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{0 - \left(y - x\right)}}} \]

      8. sub0-neg 77.4%

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

      9. neg-mul-1 77.4%

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

      10. associate-/r* 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in x around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*r/ 99.8%

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

      3. neg-mul-1 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{+131}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-t}{y - z}\\ \end{array} \]

Alternative 2: 63.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ t_2 := y \cdot \frac{t}{y - z}\\ \mathbf{if}\;y \leq -2.65 \cdot 10^{+166}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-121}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-149}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+207}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))) (t_2 (* y (/ t (- y z)))))
   (if (<= y -2.65e+166)
     t
     (if (<= y -1.45e-74)
       t_2
       (if (<= y -3.9e-116)
         t_1
         (if (<= y -2.8e-121)
           t
           (if (<= y -9.5e-149)
             (* x (/ (- t) y))
             (if (<= y 3.9e-129)
               t_1
               (if (<= y 2.05e-51)
                 t_2
                 (if (<= y 7.8e-15) t_1 (if (<= y 5.1e+207) t_2 t)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double t_2 = y * (t / (y - z));
	double tmp;
	if (y <= -2.65e+166) {
		tmp = t;
	} else if (y <= -1.45e-74) {
		tmp = t_2;
	} else if (y <= -3.9e-116) {
		tmp = t_1;
	} else if (y <= -2.8e-121) {
		tmp = t;
	} else if (y <= -9.5e-149) {
		tmp = x * (-t / y);
	} else if (y <= 3.9e-129) {
		tmp = t_1;
	} else if (y <= 2.05e-51) {
		tmp = t_2;
	} else if (y <= 7.8e-15) {
		tmp = t_1;
	} else if (y <= 5.1e+207) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t / z)
    t_2 = y * (t / (y - z))
    if (y <= (-2.65d+166)) then
        tmp = t
    else if (y <= (-1.45d-74)) then
        tmp = t_2
    else if (y <= (-3.9d-116)) then
        tmp = t_1
    else if (y <= (-2.8d-121)) then
        tmp = t
    else if (y <= (-9.5d-149)) then
        tmp = x * (-t / y)
    else if (y <= 3.9d-129) then
        tmp = t_1
    else if (y <= 2.05d-51) then
        tmp = t_2
    else if (y <= 7.8d-15) then
        tmp = t_1
    else if (y <= 5.1d+207) then
        tmp = t_2
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double t_2 = y * (t / (y - z));
	double tmp;
	if (y <= -2.65e+166) {
		tmp = t;
	} else if (y <= -1.45e-74) {
		tmp = t_2;
	} else if (y <= -3.9e-116) {
		tmp = t_1;
	} else if (y <= -2.8e-121) {
		tmp = t;
	} else if (y <= -9.5e-149) {
		tmp = x * (-t / y);
	} else if (y <= 3.9e-129) {
		tmp = t_1;
	} else if (y <= 2.05e-51) {
		tmp = t_2;
	} else if (y <= 7.8e-15) {
		tmp = t_1;
	} else if (y <= 5.1e+207) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	t_2 = y * (t / (y - z))
	tmp = 0
	if y <= -2.65e+166:
		tmp = t
	elif y <= -1.45e-74:
		tmp = t_2
	elif y <= -3.9e-116:
		tmp = t_1
	elif y <= -2.8e-121:
		tmp = t
	elif y <= -9.5e-149:
		tmp = x * (-t / y)
	elif y <= 3.9e-129:
		tmp = t_1
	elif y <= 2.05e-51:
		tmp = t_2
	elif y <= 7.8e-15:
		tmp = t_1
	elif y <= 5.1e+207:
		tmp = t_2
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	t_2 = Float64(y * Float64(t / Float64(y - z)))
	tmp = 0.0
	if (y <= -2.65e+166)
		tmp = t;
	elseif (y <= -1.45e-74)
		tmp = t_2;
	elseif (y <= -3.9e-116)
		tmp = t_1;
	elseif (y <= -2.8e-121)
		tmp = t;
	elseif (y <= -9.5e-149)
		tmp = Float64(x * Float64(Float64(-t) / y));
	elseif (y <= 3.9e-129)
		tmp = t_1;
	elseif (y <= 2.05e-51)
		tmp = t_2;
	elseif (y <= 7.8e-15)
		tmp = t_1;
	elseif (y <= 5.1e+207)
		tmp = t_2;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	t_2 = y * (t / (y - z));
	tmp = 0.0;
	if (y <= -2.65e+166)
		tmp = t;
	elseif (y <= -1.45e-74)
		tmp = t_2;
	elseif (y <= -3.9e-116)
		tmp = t_1;
	elseif (y <= -2.8e-121)
		tmp = t;
	elseif (y <= -9.5e-149)
		tmp = x * (-t / y);
	elseif (y <= 3.9e-129)
		tmp = t_1;
	elseif (y <= 2.05e-51)
		tmp = t_2;
	elseif (y <= 7.8e-15)
		tmp = t_1;
	elseif (y <= 5.1e+207)
		tmp = t_2;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.65e+166], t, If[LessEqual[y, -1.45e-74], t$95$2, If[LessEqual[y, -3.9e-116], t$95$1, If[LessEqual[y, -2.8e-121], t, If[LessEqual[y, -9.5e-149], N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e-129], t$95$1, If[LessEqual[y, 2.05e-51], t$95$2, If[LessEqual[y, 7.8e-15], t$95$1, If[LessEqual[y, 5.1e+207], t$95$2, t]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.65e166 or -3.9000000000000001e-116 < y < -2.8000000000000001e-121 or 5.0999999999999998e207 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around inf 89.9%

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

   if -2.65e166 < y < -1.45e-74 or 3.9000000000000001e-129 < y < 2.04999999999999987e-51 or 7.80000000000000053e-15 < y < 5.0999999999999998e207

   1. Initial program 98.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 98.1%

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

      2. associate-*r/ 87.1%

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

      3. associate-/l* 98.1%

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

      4. sub-neg 98.1%

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

      5. +-commutative 98.1%

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

      6. neg-sub0 98.1%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{\left(0 - y\right)} + x}} \]

      7. associate-+l- 98.1%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{0 - \left(y - x\right)}}} \]

      8. sub0-neg 98.1%

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

      9. neg-mul-1 98.1%

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

      10. associate-/r* 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in x around 0 58.6%

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

      1. associate-*l/ 58.3%

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

      2. *-commutative 58.3%

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

   6. Simplified 58.3%

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

   if -1.45e-74 < y < -3.9000000000000001e-116 or -9.50000000000000034e-149 < y < 3.9000000000000001e-129 or 2.04999999999999987e-51 < y < 7.80000000000000053e-15

   1. Initial program 92.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. clear-num 91.8%

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

      2. associate-/r/ 92.6%

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

   3. Applied egg-rr 92.6%

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

   4. Taylor expanded in y around 0 75.7%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   5. Step-by-step derivation

      1. associate-*l/ 79.2%

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

      2. *-commutative 79.2%

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

   6. Simplified 79.2%

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

   if -2.8000000000000001e-121 < y < -9.50000000000000034e-149

   1. Initial program 63.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 63.1%

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

      2. associate-*r/ 100.0%

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

      3. associate-/l* 70.1%

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

      4. sub-neg 70.1%

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

      5. +-commutative 70.1%

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

      6. neg-sub0 70.1%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{\left(0 - y\right)} + x}} \]

      7. associate-+l- 70.1%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{0 - \left(y - x\right)}}} \]

      8. sub0-neg 70.1%

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

      9. neg-mul-1 70.1%

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

      10. associate-/r* 70.1%

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

   3. Simplified 70.1%

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

   4. Taylor expanded in z around 0 80.0%

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

   5. Taylor expanded in y around 0 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

      3. associate-/l* 68.5%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in y around 0 80.0%

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

      1. mul-1-neg 80.0%

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

      2. associate-*l/ 80.0%

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

      3. distribute-lft-neg-out 80.0%

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

      4. *-commutative 80.0%

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

      5. distribute-neg-frac 80.0%

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

   10. Simplified 80.0%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+166}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-121}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-149}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-129}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-51}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+207}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 68.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ t_2 := t - \frac{t}{\frac{y}{x}}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-51}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))) (t_2 (- t (/ t (/ y x)))))
   (if (<= y -4.5e-39)
     t_2
     (if (<= y -3.9e-116)
       t_1
       (if (<= y -2.75e-148)
         t_2
         (if (<= y 1.12e-131)
           t_1
           (if (<= y 1.18e-51)
             (* y (/ t (- y z)))
             (if (<= y 8.6e-23) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double t_2 = t - (t / (y / x));
	double tmp;
	if (y <= -4.5e-39) {
		tmp = t_2;
	} else if (y <= -3.9e-116) {
		tmp = t_1;
	} else if (y <= -2.75e-148) {
		tmp = t_2;
	} else if (y <= 1.12e-131) {
		tmp = t_1;
	} else if (y <= 1.18e-51) {
		tmp = y * (t / (y - z));
	} else if (y <= 8.6e-23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t / z)
    t_2 = t - (t / (y / x))
    if (y <= (-4.5d-39)) then
        tmp = t_2
    else if (y <= (-3.9d-116)) then
        tmp = t_1
    else if (y <= (-2.75d-148)) then
        tmp = t_2
    else if (y <= 1.12d-131) then
        tmp = t_1
    else if (y <= 1.18d-51) then
        tmp = y * (t / (y - z))
    else if (y <= 8.6d-23) 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 t_1 = x * (t / z);
	double t_2 = t - (t / (y / x));
	double tmp;
	if (y <= -4.5e-39) {
		tmp = t_2;
	} else if (y <= -3.9e-116) {
		tmp = t_1;
	} else if (y <= -2.75e-148) {
		tmp = t_2;
	} else if (y <= 1.12e-131) {
		tmp = t_1;
	} else if (y <= 1.18e-51) {
		tmp = y * (t / (y - z));
	} else if (y <= 8.6e-23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	t_2 = t - (t / (y / x))
	tmp = 0
	if y <= -4.5e-39:
		tmp = t_2
	elif y <= -3.9e-116:
		tmp = t_1
	elif y <= -2.75e-148:
		tmp = t_2
	elif y <= 1.12e-131:
		tmp = t_1
	elif y <= 1.18e-51:
		tmp = y * (t / (y - z))
	elif y <= 8.6e-23:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	t_2 = Float64(t - Float64(t / Float64(y / x)))
	tmp = 0.0
	if (y <= -4.5e-39)
		tmp = t_2;
	elseif (y <= -3.9e-116)
		tmp = t_1;
	elseif (y <= -2.75e-148)
		tmp = t_2;
	elseif (y <= 1.12e-131)
		tmp = t_1;
	elseif (y <= 1.18e-51)
		tmp = Float64(y * Float64(t / Float64(y - z)));
	elseif (y <= 8.6e-23)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	t_2 = t - (t / (y / x));
	tmp = 0.0;
	if (y <= -4.5e-39)
		tmp = t_2;
	elseif (y <= -3.9e-116)
		tmp = t_1;
	elseif (y <= -2.75e-148)
		tmp = t_2;
	elseif (y <= 1.12e-131)
		tmp = t_1;
	elseif (y <= 1.18e-51)
		tmp = y * (t / (y - z));
	elseif (y <= 8.6e-23)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e-39], t$95$2, If[LessEqual[y, -3.9e-116], t$95$1, If[LessEqual[y, -2.75e-148], t$95$2, If[LessEqual[y, 1.12e-131], t$95$1, If[LessEqual[y, 1.18e-51], N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e-23], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5000000000000001e-39 or -3.9000000000000001e-116 < y < -2.7500000000000001e-148 or 8.60000000000000004e-23 < y

   1. Initial program 98.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 98.7%

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

      2. associate-*r/ 80.3%

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

      3. associate-/l* 98.9%

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

      4. sub-neg 98.9%

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

      5. +-commutative 98.9%

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

      6. neg-sub0 98.9%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{\left(0 - y\right)} + x}} \]

      7. associate-+l- 98.9%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{0 - \left(y - x\right)}}} \]

      8. sub0-neg 98.9%

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

      9. neg-mul-1 98.9%

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

      10. associate-/r* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 58.1%

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

   5. Taylor expanded in y around 0 68.5%

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

      1. mul-1-neg 68.5%

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

      2. unsub-neg 68.5%

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

      3. associate-/l* 72.5%

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

   7. Simplified 72.5%

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

   if -4.5000000000000001e-39 < y < -3.9000000000000001e-116 or -2.7500000000000001e-148 < y < 1.12000000000000001e-131 or 1.18000000000000004e-51 < y < 8.60000000000000004e-23

   1. Initial program 93.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. clear-num 92.1%

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

      2. associate-/r/ 92.8%

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

   3. Applied egg-rr 92.8%

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

   4. Taylor expanded in y around 0 74.7%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   5. Step-by-step derivation

      1. associate-*l/ 78.0%

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

      2. *-commutative 78.0%

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

   6. Simplified 78.0%

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

   if 1.12000000000000001e-131 < y < 1.18000000000000004e-51

   1. Initial program 87.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 87.4%

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

      2. associate-*r/ 99.4%

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

      3. associate-/l* 87.4%

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

      4. sub-neg 87.4%

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

      5. +-commutative 87.4%

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

      6. neg-sub0 87.4%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{\left(0 - y\right)} + x}} \]

      7. associate-+l- 87.4%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{0 - \left(y - x\right)}}} \]

      8. sub0-neg 87.4%

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

      9. neg-mul-1 87.4%

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

      10. associate-/r* 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in x around 0 67.3%

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

      1. associate-*l/ 67.6%

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

      2. *-commutative 67.6%

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

   6. Simplified 67.6%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-39}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-148}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-51}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]

Alternative 4: 71.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t}{\frac{y}{x}}\\ t_2 := \frac{t}{\frac{z}{x - y}}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-90}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;z \leq 420000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- t (/ t (/ y x)))) (t_2 (/ t (/ z (- x y)))))
   (if (<= z -3.8e+62)
     t_2
     (if (<= z -8.2e+30)
       t_1
       (if (<= z -2.25e-38)
         t_2
         (if (<= z 1.35e-132)
           t_1
           (if (<= z 5.5e-90)
             (/ (* x t) z)
             (if (<= z 420000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t - (t / (y / x));
	double t_2 = t / (z / (x - y));
	double tmp;
	if (z <= -3.8e+62) {
		tmp = t_2;
	} else if (z <= -8.2e+30) {
		tmp = t_1;
	} else if (z <= -2.25e-38) {
		tmp = t_2;
	} else if (z <= 1.35e-132) {
		tmp = t_1;
	} else if (z <= 5.5e-90) {
		tmp = (x * t) / z;
	} else if (z <= 420000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (t / (y / x))
    t_2 = t / (z / (x - y))
    if (z <= (-3.8d+62)) then
        tmp = t_2
    else if (z <= (-8.2d+30)) then
        tmp = t_1
    else if (z <= (-2.25d-38)) then
        tmp = t_2
    else if (z <= 1.35d-132) then
        tmp = t_1
    else if (z <= 5.5d-90) then
        tmp = (x * t) / z
    else if (z <= 420000000.0d0) 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 t_1 = t - (t / (y / x));
	double t_2 = t / (z / (x - y));
	double tmp;
	if (z <= -3.8e+62) {
		tmp = t_2;
	} else if (z <= -8.2e+30) {
		tmp = t_1;
	} else if (z <= -2.25e-38) {
		tmp = t_2;
	} else if (z <= 1.35e-132) {
		tmp = t_1;
	} else if (z <= 5.5e-90) {
		tmp = (x * t) / z;
	} else if (z <= 420000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t - (t / (y / x))
	t_2 = t / (z / (x - y))
	tmp = 0
	if z <= -3.8e+62:
		tmp = t_2
	elif z <= -8.2e+30:
		tmp = t_1
	elif z <= -2.25e-38:
		tmp = t_2
	elif z <= 1.35e-132:
		tmp = t_1
	elif z <= 5.5e-90:
		tmp = (x * t) / z
	elif z <= 420000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t - Float64(t / Float64(y / x)))
	t_2 = Float64(t / Float64(z / Float64(x - y)))
	tmp = 0.0
	if (z <= -3.8e+62)
		tmp = t_2;
	elseif (z <= -8.2e+30)
		tmp = t_1;
	elseif (z <= -2.25e-38)
		tmp = t_2;
	elseif (z <= 1.35e-132)
		tmp = t_1;
	elseif (z <= 5.5e-90)
		tmp = Float64(Float64(x * t) / z);
	elseif (z <= 420000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t - (t / (y / x));
	t_2 = t / (z / (x - y));
	tmp = 0.0;
	if (z <= -3.8e+62)
		tmp = t_2;
	elseif (z <= -8.2e+30)
		tmp = t_1;
	elseif (z <= -2.25e-38)
		tmp = t_2;
	elseif (z <= 1.35e-132)
		tmp = t_1;
	elseif (z <= 5.5e-90)
		tmp = (x * t) / z;
	elseif (z <= 420000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+62], t$95$2, If[LessEqual[z, -8.2e+30], t$95$1, If[LessEqual[z, -2.25e-38], t$95$2, If[LessEqual[z, 1.35e-132], t$95$1, If[LessEqual[z, 5.5e-90], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 420000000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.79999999999999984e62 or -8.20000000000000011e30 < z < -2.25000000000000004e-38 or 4.2e8 < z

   1. Initial program 97.2%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in z around inf 70.9%

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

      1. associate-/l* 76.2%

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

   4. Simplified 76.2%

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

   if -3.79999999999999984e62 < z < -8.20000000000000011e30 or -2.25000000000000004e-38 < z < 1.34999999999999995e-132 or 5.5000000000000003e-90 < z < 4.2e8

   1. Initial program 96.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 96.1%

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

      2. associate-*r/ 83.3%

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

      3. associate-/l* 96.4%

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

      4. sub-neg 96.4%

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

      5. +-commutative 96.4%

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

      6. neg-sub0 96.4%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{\left(0 - y\right)} + x}} \]

      7. associate-+l- 96.4%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{0 - \left(y - x\right)}}} \]

      8. sub0-neg 96.4%

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

      9. neg-mul-1 96.4%

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

      10. associate-/r* 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 73.7%

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

   5. Taylor expanded in y around 0 83.5%

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

      1. mul-1-neg 83.5%

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

      2. unsub-neg 83.5%

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

      3. associate-/l* 85.5%

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

   7. Simplified 85.5%

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

   if 1.34999999999999995e-132 < z < 5.5000000000000003e-90

   1. Initial program 76.4%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around 0 87.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+62}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+30}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-38}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-132}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-90}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;z \leq 420000000:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \end{array} \]

Alternative 5: 70.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{z}{x - y}}\\ t_2 := t - \frac{t}{\frac{y}{x}}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-90}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;z \leq 1500000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ z (- x y)))) (t_2 (- t (/ t (/ y x)))))
   (if (<= z -2.7e+184)
     t_1
     (if (<= z -1.26e+29)
       (/ t (/ (- y z) y))
       (if (<= z -4.2e-38)
         t_1
         (if (<= z 1.35e-132)
           t_2
           (if (<= z 4.8e-90)
             (/ (* x t) z)
             (if (<= z 1500000000.0) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (z / (x - y));
	double t_2 = t - (t / (y / x));
	double tmp;
	if (z <= -2.7e+184) {
		tmp = t_1;
	} else if (z <= -1.26e+29) {
		tmp = t / ((y - z) / y);
	} else if (z <= -4.2e-38) {
		tmp = t_1;
	} else if (z <= 1.35e-132) {
		tmp = t_2;
	} else if (z <= 4.8e-90) {
		tmp = (x * t) / z;
	} else if (z <= 1500000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (z / (x - y))
    t_2 = t - (t / (y / x))
    if (z <= (-2.7d+184)) then
        tmp = t_1
    else if (z <= (-1.26d+29)) then
        tmp = t / ((y - z) / y)
    else if (z <= (-4.2d-38)) then
        tmp = t_1
    else if (z <= 1.35d-132) then
        tmp = t_2
    else if (z <= 4.8d-90) then
        tmp = (x * t) / z
    else if (z <= 1500000000.0d0) 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 t_1 = t / (z / (x - y));
	double t_2 = t - (t / (y / x));
	double tmp;
	if (z <= -2.7e+184) {
		tmp = t_1;
	} else if (z <= -1.26e+29) {
		tmp = t / ((y - z) / y);
	} else if (z <= -4.2e-38) {
		tmp = t_1;
	} else if (z <= 1.35e-132) {
		tmp = t_2;
	} else if (z <= 4.8e-90) {
		tmp = (x * t) / z;
	} else if (z <= 1500000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (z / (x - y))
	t_2 = t - (t / (y / x))
	tmp = 0
	if z <= -2.7e+184:
		tmp = t_1
	elif z <= -1.26e+29:
		tmp = t / ((y - z) / y)
	elif z <= -4.2e-38:
		tmp = t_1
	elif z <= 1.35e-132:
		tmp = t_2
	elif z <= 4.8e-90:
		tmp = (x * t) / z
	elif z <= 1500000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(z / Float64(x - y)))
	t_2 = Float64(t - Float64(t / Float64(y / x)))
	tmp = 0.0
	if (z <= -2.7e+184)
		tmp = t_1;
	elseif (z <= -1.26e+29)
		tmp = Float64(t / Float64(Float64(y - z) / y));
	elseif (z <= -4.2e-38)
		tmp = t_1;
	elseif (z <= 1.35e-132)
		tmp = t_2;
	elseif (z <= 4.8e-90)
		tmp = Float64(Float64(x * t) / z);
	elseif (z <= 1500000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (z / (x - y));
	t_2 = t - (t / (y / x));
	tmp = 0.0;
	if (z <= -2.7e+184)
		tmp = t_1;
	elseif (z <= -1.26e+29)
		tmp = t / ((y - z) / y);
	elseif (z <= -4.2e-38)
		tmp = t_1;
	elseif (z <= 1.35e-132)
		tmp = t_2;
	elseif (z <= 4.8e-90)
		tmp = (x * t) / z;
	elseif (z <= 1500000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+184], t$95$1, If[LessEqual[z, -1.26e+29], N[(t / N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e-38], t$95$1, If[LessEqual[z, 1.35e-132], t$95$2, If[LessEqual[z, 4.8e-90], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1500000000.0], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6999999999999999e184 or -1.26e29 < z < -4.20000000000000026e-38 or 1.5e9 < z

   1. Initial program 96.7%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in z around inf 73.0%

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

      1. associate-/l* 79.5%

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

   4. Simplified 79.5%

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

   if -2.6999999999999999e184 < z < -1.26e29

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. associate-*r/ 85.6%

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

      3. associate-/l* 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{\left(0 - y\right)} + x}} \]

      7. associate-+l- 99.8%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{0 - \left(y - x\right)}}} \]

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 73.9%

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

   if -4.20000000000000026e-38 < z < 1.34999999999999995e-132 or 4.8000000000000003e-90 < z < 1.5e9

   1. Initial program 95.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 95.8%

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

      2. associate-*r/ 85.3%

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

      3. associate-/l* 96.1%

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

      4. sub-neg 96.1%

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

      5. +-commutative 96.1%

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

      6. neg-sub0 96.1%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{\left(0 - y\right)} + x}} \]

      7. associate-+l- 96.1%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{0 - \left(y - x\right)}}} \]

      8. sub0-neg 96.1%

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

      9. neg-mul-1 96.1%

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

      10. associate-/r* 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in z around 0 74.9%

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

   5. Taylor expanded in y around 0 83.9%

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

      1. mul-1-neg 83.9%

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

      2. unsub-neg 83.9%

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

      3. associate-/l* 85.2%

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

   7. Simplified 85.2%

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

   if 1.34999999999999995e-132 < z < 4.8000000000000003e-90

   1. Initial program 76.4%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around 0 87.1%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+184}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-38}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-132}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-90}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;z \leq 1500000000:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \end{array} \]

Alternative 6: 70.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{z}{x - y}}\\ t_2 := t - \frac{t}{\frac{y}{x}}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-47}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-90}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;z \leq 700000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ z (- x y)))) (t_2 (- t (/ t (/ y x)))))
   (if (<= z -4.2e+184)
     t_1
     (if (<= z -9.2e+46)
       (/ t (/ (- y z) y))
       (if (<= z -4.8e-47)
         (/ t (/ (- z y) x))
         (if (<= z 1.35e-132)
           t_2
           (if (<= z 4.8e-90)
             (/ (* x t) z)
             (if (<= z 700000000.0) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (z / (x - y));
	double t_2 = t - (t / (y / x));
	double tmp;
	if (z <= -4.2e+184) {
		tmp = t_1;
	} else if (z <= -9.2e+46) {
		tmp = t / ((y - z) / y);
	} else if (z <= -4.8e-47) {
		tmp = t / ((z - y) / x);
	} else if (z <= 1.35e-132) {
		tmp = t_2;
	} else if (z <= 4.8e-90) {
		tmp = (x * t) / z;
	} else if (z <= 700000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (z / (x - y))
    t_2 = t - (t / (y / x))
    if (z <= (-4.2d+184)) then
        tmp = t_1
    else if (z <= (-9.2d+46)) then
        tmp = t / ((y - z) / y)
    else if (z <= (-4.8d-47)) then
        tmp = t / ((z - y) / x)
    else if (z <= 1.35d-132) then
        tmp = t_2
    else if (z <= 4.8d-90) then
        tmp = (x * t) / z
    else if (z <= 700000000.0d0) 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 t_1 = t / (z / (x - y));
	double t_2 = t - (t / (y / x));
	double tmp;
	if (z <= -4.2e+184) {
		tmp = t_1;
	} else if (z <= -9.2e+46) {
		tmp = t / ((y - z) / y);
	} else if (z <= -4.8e-47) {
		tmp = t / ((z - y) / x);
	} else if (z <= 1.35e-132) {
		tmp = t_2;
	} else if (z <= 4.8e-90) {
		tmp = (x * t) / z;
	} else if (z <= 700000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (z / (x - y))
	t_2 = t - (t / (y / x))
	tmp = 0
	if z <= -4.2e+184:
		tmp = t_1
	elif z <= -9.2e+46:
		tmp = t / ((y - z) / y)
	elif z <= -4.8e-47:
		tmp = t / ((z - y) / x)
	elif z <= 1.35e-132:
		tmp = t_2
	elif z <= 4.8e-90:
		tmp = (x * t) / z
	elif z <= 700000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(z / Float64(x - y)))
	t_2 = Float64(t - Float64(t / Float64(y / x)))
	tmp = 0.0
	if (z <= -4.2e+184)
		tmp = t_1;
	elseif (z <= -9.2e+46)
		tmp = Float64(t / Float64(Float64(y - z) / y));
	elseif (z <= -4.8e-47)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	elseif (z <= 1.35e-132)
		tmp = t_2;
	elseif (z <= 4.8e-90)
		tmp = Float64(Float64(x * t) / z);
	elseif (z <= 700000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (z / (x - y));
	t_2 = t - (t / (y / x));
	tmp = 0.0;
	if (z <= -4.2e+184)
		tmp = t_1;
	elseif (z <= -9.2e+46)
		tmp = t / ((y - z) / y);
	elseif (z <= -4.8e-47)
		tmp = t / ((z - y) / x);
	elseif (z <= 1.35e-132)
		tmp = t_2;
	elseif (z <= 4.8e-90)
		tmp = (x * t) / z;
	elseif (z <= 700000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+184], t$95$1, If[LessEqual[z, -9.2e+46], N[(t / N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.8e-47], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-132], t$95$2, If[LessEqual[z, 4.8e-90], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 700000000.0], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.2e184 or 7e8 < z

   1. Initial program 96.3%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in z around inf 72.4%

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

      1. associate-/l* 79.7%

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

   4. Simplified 79.7%

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

   if -4.2e184 < z < -9.2000000000000002e46

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

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

      2. associate-*r/ 86.9%

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

      3. associate-/l* 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{\left(0 - y\right)} + x}} \]

      7. associate-+l- 99.8%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{0 - \left(y - x\right)}}} \]

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 76.8%

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

   if -9.2000000000000002e46 < z < -4.7999999999999999e-47

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in x around inf 67.0%

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

      1. associate-/l* 73.6%

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

   4. Simplified 73.6%

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

   if -4.7999999999999999e-47 < z < 1.34999999999999995e-132 or 4.8000000000000003e-90 < z < 7e8

   1. Initial program 95.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 95.8%

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

      2. associate-*r/ 85.3%

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

      3. associate-/l* 96.1%

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

      4. sub-neg 96.1%

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

      5. +-commutative 96.1%

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

      6. neg-sub0 96.1%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{\left(0 - y\right)} + x}} \]

      7. associate-+l- 96.1%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{0 - \left(y - x\right)}}} \]

      8. sub0-neg 96.1%

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

      9. neg-mul-1 96.1%

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

      10. associate-/r* 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in z around 0 74.9%

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

   5. Taylor expanded in y around 0 83.9%

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

      1. mul-1-neg 83.9%

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

      2. unsub-neg 83.9%

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

      3. associate-/l* 85.2%

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

   7. Simplified 85.2%

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

   if 1.34999999999999995e-132 < z < 4.8000000000000003e-90

   1. Initial program 76.4%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around 0 87.1%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+184}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-47}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-132}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-90}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;z \leq 700000000:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \end{array} \]

Alternative 7: 74.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-t}{y - z}\\ t_2 := y \cdot \frac{t}{y - z}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{-38}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-96}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- t) (- y z)))) (t_2 (* y (/ t (- y z)))))
   (if (<= y -2.2e-38)
     (/ t (/ (- y z) y))
     (if (<= y -6.2e-96)
       (/ (* (- x y) t) z)
       (if (<= y 1.55e-84)
         t_1
         (if (<= y 3.2e-52)
           t_2
           (if (<= y 1.12e-5)
             t_1
             (if (<= y 1.36e+48) t_2 (- t (/ t (/ y x)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (-t / (y - z));
	double t_2 = y * (t / (y - z));
	double tmp;
	if (y <= -2.2e-38) {
		tmp = t / ((y - z) / y);
	} else if (y <= -6.2e-96) {
		tmp = ((x - y) * t) / z;
	} else if (y <= 1.55e-84) {
		tmp = t_1;
	} else if (y <= 3.2e-52) {
		tmp = t_2;
	} else if (y <= 1.12e-5) {
		tmp = t_1;
	} else if (y <= 1.36e+48) {
		tmp = t_2;
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (-t / (y - z))
    t_2 = y * (t / (y - z))
    if (y <= (-2.2d-38)) then
        tmp = t / ((y - z) / y)
    else if (y <= (-6.2d-96)) then
        tmp = ((x - y) * t) / z
    else if (y <= 1.55d-84) then
        tmp = t_1
    else if (y <= 3.2d-52) then
        tmp = t_2
    else if (y <= 1.12d-5) then
        tmp = t_1
    else if (y <= 1.36d+48) then
        tmp = t_2
    else
        tmp = t - (t / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (-t / (y - z));
	double t_2 = y * (t / (y - z));
	double tmp;
	if (y <= -2.2e-38) {
		tmp = t / ((y - z) / y);
	} else if (y <= -6.2e-96) {
		tmp = ((x - y) * t) / z;
	} else if (y <= 1.55e-84) {
		tmp = t_1;
	} else if (y <= 3.2e-52) {
		tmp = t_2;
	} else if (y <= 1.12e-5) {
		tmp = t_1;
	} else if (y <= 1.36e+48) {
		tmp = t_2;
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (-t / (y - z))
	t_2 = y * (t / (y - z))
	tmp = 0
	if y <= -2.2e-38:
		tmp = t / ((y - z) / y)
	elif y <= -6.2e-96:
		tmp = ((x - y) * t) / z
	elif y <= 1.55e-84:
		tmp = t_1
	elif y <= 3.2e-52:
		tmp = t_2
	elif y <= 1.12e-5:
		tmp = t_1
	elif y <= 1.36e+48:
		tmp = t_2
	else:
		tmp = t - (t / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(-t) / Float64(y - z)))
	t_2 = Float64(y * Float64(t / Float64(y - z)))
	tmp = 0.0
	if (y <= -2.2e-38)
		tmp = Float64(t / Float64(Float64(y - z) / y));
	elseif (y <= -6.2e-96)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (y <= 1.55e-84)
		tmp = t_1;
	elseif (y <= 3.2e-52)
		tmp = t_2;
	elseif (y <= 1.12e-5)
		tmp = t_1;
	elseif (y <= 1.36e+48)
		tmp = t_2;
	else
		tmp = Float64(t - Float64(t / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (-t / (y - z));
	t_2 = y * (t / (y - z));
	tmp = 0.0;
	if (y <= -2.2e-38)
		tmp = t / ((y - z) / y);
	elseif (y <= -6.2e-96)
		tmp = ((x - y) * t) / z;
	elseif (y <= 1.55e-84)
		tmp = t_1;
	elseif (y <= 3.2e-52)
		tmp = t_2;
	elseif (y <= 1.12e-5)
		tmp = t_1;
	elseif (y <= 1.36e+48)
		tmp = t_2;
	else
		tmp = t - (t / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[((-t) / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e-38], N[(t / N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.2e-96], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.55e-84], t$95$1, If[LessEqual[y, 3.2e-52], t$95$2, If[LessEqual[y, 1.12e-5], t$95$1, If[LessEqual[y, 1.36e+48], t$95$2, N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.20000000000000007e-38

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. associate-*r/ 77.4%

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

      3. associate-/l* 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{\left(0 - y\right)} + x}} \]

      7. associate-+l- 99.8%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{0 - \left(y - x\right)}}} \]

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 77.5%

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

   if -2.20000000000000007e-38 < y < -6.1999999999999998e-96

   1. Initial program 93.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in z around inf 95.5%

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

   if -6.1999999999999998e-96 < y < 1.55000000000000001e-84 or 3.2000000000000001e-52 < y < 1.11999999999999995e-5

   1. Initial program 91.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 91.5%

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

      2. associate-*r/ 91.0%

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

      3. associate-/l* 91.0%

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

      4. sub-neg 91.0%

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

      5. +-commutative 91.0%

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

      6. neg-sub0 91.0%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{\left(0 - y\right)} + x}} \]

      7. associate-+l- 91.0%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{0 - \left(y - x\right)}}} \]

      8. sub0-neg 91.0%

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

      9. neg-mul-1 91.0%

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

      10. associate-/r* 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in x around inf 82.8%

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

      1. *-commutative 82.8%

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

      2. associate-*r/ 85.8%

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

      3. neg-mul-1 85.8%

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

      4. distribute-rgt-neg-in 85.8%

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

   6. Simplified 85.8%

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

   if 1.55000000000000001e-84 < y < 3.2000000000000001e-52 or 1.11999999999999995e-5 < y < 1.3599999999999999e48

   1. Initial program 95.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 95.2%

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

      2. associate-*r/ 99.8%

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

      3. associate-/l* 95.0%

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

      4. sub-neg 95.0%

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

      5. +-commutative 95.0%

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

      6. neg-sub0 95.0%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{\left(0 - y\right)} + x}} \]

      7. associate-+l- 95.0%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{0 - \left(y - x\right)}}} \]

      8. sub0-neg 95.0%

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

      9. neg-mul-1 95.0%

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

      10. associate-/r* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in x around 0 90.1%

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

      1. associate-*l/ 90.1%

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

      2. *-commutative 90.1%

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

   6. Simplified 90.1%

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

   if 1.3599999999999999e48 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. associate-*r/ 76.3%

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

      3. associate-/l* 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. neg-sub0 99.9%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{\left(0 - y\right)} + x}} \]

      7. associate-+l- 99.9%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{0 - \left(y - x\right)}}} \]

      8. sub0-neg 99.9%

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

      9. neg-mul-1 99.9%

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

      10. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 61.9%

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

   5. Taylor expanded in y around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

      3. associate-/l* 82.5%

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

   7. Simplified 82.5%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-38}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-96}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \frac{-t}{y - z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{-t}{y - z}\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]

Alternative 8: 59.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-39}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.55e-39) t (if (<= y 4.7e-14) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.55e-39) {
		tmp = t;
	} else if (y <= 4.7e-14) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.55d-39)) then
        tmp = t
    else if (y <= 4.7d-14) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.55e-39) {
		tmp = t;
	} else if (y <= 4.7e-14) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.55e-39:
		tmp = t
	elif y <= 4.7e-14:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.55e-39)
		tmp = t;
	elseif (y <= 4.7e-14)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.55e-39)
		tmp = t;
	elseif (y <= 4.7e-14)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.55e-39], t, If[LessEqual[y, 4.7e-14], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.54999999999999994e-39 or 4.7000000000000002e-14 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around inf 57.4%

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

   if -2.54999999999999994e-39 < y < 4.7000000000000002e-14

   1. Initial program 91.3%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. clear-num 90.5%

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

      2. associate-/r/ 91.1%

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

   3. Applied egg-rr 91.1%

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

   4. Taylor expanded in y around 0 63.6%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   5. Step-by-step derivation

      1. associate-*l/ 66.1%

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

      2. *-commutative 66.1%

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

   6. Simplified 66.1%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-39}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 34.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 96.1%

   \[\frac{x - y}{z - y} \cdot t \]

2. Taylor expanded in y around inf 37.7%

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

3. Final simplification 37.7%

   \[\leadsto t \]

Developer target: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{t}{\frac{z - y}{x - y}} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ t (/ (- z y) (- x y))))

C

double code(double x, double y, double z, double t) {
	return t / ((z - y) / (x - y));
}

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return t / ((z - y) / (x - y))

Julia

function code(x, y, z, t)
	return Float64(t / Float64(Float64(z - y) / Float64(x - y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t / ((z - y) / (x - y));
end

Wolfram

code[x_, y_, z_, t_] := N[(t / N[(N[(z - y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

  (* (/ (- x y) (- z y)) t))