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

Percentage Accurate: 97.0% → 97.0%

Time: 9.6s

Alternatives: 11

Speedup: 1.0×

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: 97.0% 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: 97.0% 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]

Derivation

1. Initial program 95.4%

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

2. Final simplification 95.4%

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

Alternative 2: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{x}{y} + -1\right) \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-255}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-153}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 450:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ (/ x y) -1.0) (- t))))
   (if (<= y -5e+46)
     t_1
     (if (<= y -9.6e-255)
       (/ t (/ (- z y) x))
       (if (<= y 1.3e-153)
         (/ (- x y) (/ z t))
         (if (<= y 450.0)
           (/ (* x t) (- z y))
           (if (<= y 4.5e+87) (* t (/ y (- y z))) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) + -1.0) * -t;
	double tmp;
	if (y <= -5e+46) {
		tmp = t_1;
	} else if (y <= -9.6e-255) {
		tmp = t / ((z - y) / x);
	} else if (y <= 1.3e-153) {
		tmp = (x - y) / (z / t);
	} else if (y <= 450.0) {
		tmp = (x * t) / (z - y);
	} else if (y <= 4.5e+87) {
		tmp = t * (y / (y - z));
	} 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) :: tmp
    t_1 = ((x / y) + (-1.0d0)) * -t
    if (y <= (-5d+46)) then
        tmp = t_1
    else if (y <= (-9.6d-255)) then
        tmp = t / ((z - y) / x)
    else if (y <= 1.3d-153) then
        tmp = (x - y) / (z / t)
    else if (y <= 450.0d0) then
        tmp = (x * t) / (z - y)
    else if (y <= 4.5d+87) then
        tmp = t * (y / (y - z))
    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 = ((x / y) + -1.0) * -t;
	double tmp;
	if (y <= -5e+46) {
		tmp = t_1;
	} else if (y <= -9.6e-255) {
		tmp = t / ((z - y) / x);
	} else if (y <= 1.3e-153) {
		tmp = (x - y) / (z / t);
	} else if (y <= 450.0) {
		tmp = (x * t) / (z - y);
	} else if (y <= 4.5e+87) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x / y) + -1.0) * -t
	tmp = 0
	if y <= -5e+46:
		tmp = t_1
	elif y <= -9.6e-255:
		tmp = t / ((z - y) / x)
	elif y <= 1.3e-153:
		tmp = (x - y) / (z / t)
	elif y <= 450.0:
		tmp = (x * t) / (z - y)
	elif y <= 4.5e+87:
		tmp = t * (y / (y - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x / y) + -1.0) * Float64(-t))
	tmp = 0.0
	if (y <= -5e+46)
		tmp = t_1;
	elseif (y <= -9.6e-255)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	elseif (y <= 1.3e-153)
		tmp = Float64(Float64(x - y) / Float64(z / t));
	elseif (y <= 450.0)
		tmp = Float64(Float64(x * t) / Float64(z - y));
	elseif (y <= 4.5e+87)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x / y) + -1.0) * -t;
	tmp = 0.0;
	if (y <= -5e+46)
		tmp = t_1;
	elseif (y <= -9.6e-255)
		tmp = t / ((z - y) / x);
	elseif (y <= 1.3e-153)
		tmp = (x - y) / (z / t);
	elseif (y <= 450.0)
		tmp = (x * t) / (z - y);
	elseif (y <= 4.5e+87)
		tmp = t * (y / (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision] * (-t)), $MachinePrecision]}, If[LessEqual[y, -5e+46], t$95$1, If[LessEqual[y, -9.6e-255], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-153], N[(N[(x - y), $MachinePrecision] / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 450.0], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+87], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.0000000000000002e46 or 4.5000000000000003e87 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 88.5%

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

      1. mul-1-neg 88.5%

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

      2. div-sub 88.6%

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

      3. sub-neg 88.6%

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

      4. *-inverses 88.6%

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

      5. metadata-eval 88.6%

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

   4. Simplified 88.6%

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

   if -5.0000000000000002e46 < y < -9.5999999999999993e-255

   1. Initial program 95.1%

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

      1. associate-*l/ 94.2%

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

      2. *-commutative 94.2%

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

      3. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

      1. *-commutative 89.3%

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

      2. clear-num 88.4%

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

      3. div-inv 89.2%

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

      4. div-inv 89.2%

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

      5. associate-/r* 95.1%

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

   5. Applied egg-rr 95.1%

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

   6. Taylor expanded in x around inf 78.9%

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

      1. associate-/l* 80.3%

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

   8. Simplified 80.3%

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

   if -9.5999999999999993e-255 < y < 1.3000000000000001e-153

   1. Initial program 88.6%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 98.2%

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

   if 1.3000000000000001e-153 < y < 450

   1. Initial program 91.1%

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

      1. associate-*l/ 96.0%

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

      2. *-commutative 96.0%

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

      3. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in x around inf 74.2%

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

   if 450 < y < 4.5000000000000003e87

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 76.5%

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

      1. neg-mul-1 76.5%

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

      2. distribute-neg-frac 76.5%

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

   4. Simplified 76.5%

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

      1. frac-2neg 76.5%

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

      2. remove-double-neg 76.5%

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

      3. associate-*l/ 69.7%

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

      4. sub-neg 69.7%

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

      5. distribute-neg-in 69.7%

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

      6. remove-double-neg 69.7%

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

   6. Applied egg-rr 69.7%

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

      1. associate-/l* 76.3%

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

      2. associate-/r/ 76.5%

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

      3. +-commutative 76.5%

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

      4. unsub-neg 76.5%

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

   8. Simplified 76.5%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+46}:\\ \;\;\;\;\left(\frac{x}{y} + -1\right) \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-255}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-153}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 450:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{y} + -1\right) \cdot \left(-t\right)\\ \end{array} \]

Alternative 3: 66.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;y \leq -1.42 \cdot 10^{+47}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1100:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- z y)))))
   (if (<= y -1.42e+47)
     t
     (if (<= y 1100.0)
       t_1
       (if (<= y 1.02e+119) (* t (/ (- y) z)) (if (<= y 2.2e+157) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double tmp;
	if (y <= -1.42e+47) {
		tmp = t;
	} else if (y <= 1100.0) {
		tmp = t_1;
	} else if (y <= 1.02e+119) {
		tmp = t * (-y / z);
	} else if (y <= 2.2e+157) {
		tmp = t_1;
	} 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) :: tmp
    t_1 = t * (x / (z - y))
    if (y <= (-1.42d+47)) then
        tmp = t
    else if (y <= 1100.0d0) then
        tmp = t_1
    else if (y <= 1.02d+119) then
        tmp = t * (-y / z)
    else if (y <= 2.2d+157) then
        tmp = t_1
    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 = t * (x / (z - y));
	double tmp;
	if (y <= -1.42e+47) {
		tmp = t;
	} else if (y <= 1100.0) {
		tmp = t_1;
	} else if (y <= 1.02e+119) {
		tmp = t * (-y / z);
	} else if (y <= 2.2e+157) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z - y))
	tmp = 0
	if y <= -1.42e+47:
		tmp = t
	elif y <= 1100.0:
		tmp = t_1
	elif y <= 1.02e+119:
		tmp = t * (-y / z)
	elif y <= 2.2e+157:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (y <= -1.42e+47)
		tmp = t;
	elseif (y <= 1100.0)
		tmp = t_1;
	elseif (y <= 1.02e+119)
		tmp = Float64(t * Float64(Float64(-y) / z));
	elseif (y <= 2.2e+157)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z - y));
	tmp = 0.0;
	if (y <= -1.42e+47)
		tmp = t;
	elseif (y <= 1100.0)
		tmp = t_1;
	elseif (y <= 1.02e+119)
		tmp = t * (-y / z);
	elseif (y <= 2.2e+157)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.42e+47], t, If[LessEqual[y, 1100.0], t$95$1, If[LessEqual[y, 1.02e+119], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+157], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.42e47 or 2.2000000000000001e157 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 68.8%

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

      2. *-commutative 68.8%

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

      3. associate-*l/ 68.5%

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

   3. Simplified 68.5%

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

   4. Taylor expanded in y around inf 76.1%

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

   if -1.42e47 < y < 1100 or 1.02e119 < y < 2.2000000000000001e157

   1. Initial program 92.7%

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

   2. Taylor expanded in x around inf 77.3%

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

   if 1100 < y < 1.02e119

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 72.1%

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

      1. neg-mul-1 72.1%

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

      2. distribute-neg-frac 72.1%

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

   4. Simplified 72.1%

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

   5. Taylor expanded in y around 0 57.4%

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

      1. mul-1-neg 57.4%

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

      2. distribute-neg-frac 57.4%

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

   7. Simplified 57.4%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+47}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1100:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+157}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.46 \cdot 10^{-255}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-153}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 0.118:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -2.25e+44)
     t_1
     (if (<= y -1.46e-255)
       (/ t (/ (- z y) x))
       (if (<= y 1.06e-153)
         (/ (- x y) (/ z t))
         (if (<= y 0.118) (/ (* x t) (- z y)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -2.25e+44) {
		tmp = t_1;
	} else if (y <= -1.46e-255) {
		tmp = t / ((z - y) / x);
	} else if (y <= 1.06e-153) {
		tmp = (x - y) / (z / t);
	} else if (y <= 0.118) {
		tmp = (x * t) / (z - y);
	} 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) :: tmp
    t_1 = t * (y / (y - z))
    if (y <= (-2.25d+44)) then
        tmp = t_1
    else if (y <= (-1.46d-255)) then
        tmp = t / ((z - y) / x)
    else if (y <= 1.06d-153) then
        tmp = (x - y) / (z / t)
    else if (y <= 0.118d0) then
        tmp = (x * t) / (z - 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 t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -2.25e+44) {
		tmp = t_1;
	} else if (y <= -1.46e-255) {
		tmp = t / ((z - y) / x);
	} else if (y <= 1.06e-153) {
		tmp = (x - y) / (z / t);
	} else if (y <= 0.118) {
		tmp = (x * t) / (z - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -2.25e+44:
		tmp = t_1
	elif y <= -1.46e-255:
		tmp = t / ((z - y) / x)
	elif y <= 1.06e-153:
		tmp = (x - y) / (z / t)
	elif y <= 0.118:
		tmp = (x * t) / (z - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -2.25e+44)
		tmp = t_1;
	elseif (y <= -1.46e-255)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	elseif (y <= 1.06e-153)
		tmp = Float64(Float64(x - y) / Float64(z / t));
	elseif (y <= 0.118)
		tmp = Float64(Float64(x * t) / Float64(z - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -2.25e+44)
		tmp = t_1;
	elseif (y <= -1.46e-255)
		tmp = t / ((z - y) / x);
	elseif (y <= 1.06e-153)
		tmp = (x - y) / (z / t);
	elseif (y <= 0.118)
		tmp = (x * t) / (z - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.25e+44], t$95$1, If[LessEqual[y, -1.46e-255], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e-153], N[(N[(x - y), $MachinePrecision] / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.118], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.25e44 or 0.11799999999999999 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 78.9%

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

      1. neg-mul-1 78.9%

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

      2. distribute-neg-frac 78.9%

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

   4. Simplified 78.9%

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

      1. frac-2neg 78.9%

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

      2. remove-double-neg 78.9%

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

      3. associate-*l/ 57.6%

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

      4. sub-neg 57.6%

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

      5. distribute-neg-in 57.6%

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

      6. remove-double-neg 57.6%

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

   6. Applied egg-rr 57.6%

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

      1. associate-/l* 56.9%

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

      2. associate-/r/ 78.9%

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

      3. +-commutative 78.9%

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

      4. unsub-neg 78.9%

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

   8. Simplified 78.9%

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

   if -2.25e44 < y < -1.46e-255

   1. Initial program 95.1%

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

      1. associate-*l/ 94.2%

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

      2. *-commutative 94.2%

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

      3. associate-*l/ 89.2%

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

   3. Simplified 89.2%

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

      1. *-commutative 89.2%

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

      2. clear-num 88.2%

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

      3. div-inv 89.1%

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

      4. div-inv 89.1%

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

      5. associate-/r* 95.0%

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

   5. Applied egg-rr 95.0%

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

   6. Taylor expanded in x around inf 80.0%

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

      1. associate-/l* 81.4%

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

   8. Simplified 81.4%

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

   if -1.46e-255 < y < 1.06e-153

   1. Initial program 88.6%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 98.2%

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

   if 1.06e-153 < y < 0.11799999999999999

   1. Initial program 91.1%

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

      1. associate-*l/ 96.0%

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

      2. *-commutative 96.0%

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

      3. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in x around inf 74.2%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -1.46 \cdot 10^{-255}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-153}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 0.118:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]

Alternative 5: 89.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+107} \lor \neg \left(y \leq 2 \cdot 10^{+113}\right):\\ \;\;\;\;\left(\frac{x}{y} + -1\right) \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.3e+107) (not (<= y 2e+113)))
   (* (+ (/ x y) -1.0) (- t))
   (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.3e+107) || !(y <= 2e+113)) {
		tmp = ((x / y) + -1.0) * -t;
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	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 <= (-1.3d+107)) .or. (.not. (y <= 2d+113))) then
        tmp = ((x / y) + (-1.0d0)) * -t
    else
        tmp = (x - y) * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.3e+107) || !(y <= 2e+113)) {
		tmp = ((x / y) + -1.0) * -t;
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.3e+107) or not (y <= 2e+113):
		tmp = ((x / y) + -1.0) * -t
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.3e+107) || !(y <= 2e+113))
		tmp = Float64(Float64(Float64(x / y) + -1.0) * Float64(-t));
	else
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.3e+107) || ~((y <= 2e+113)))
		tmp = ((x / y) + -1.0) * -t;
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.3e+107], N[Not[LessEqual[y, 2e+113]], $MachinePrecision]], N[(N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision] * (-t)), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3000000000000001e107 or 2e113 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 88.9%

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

      1. mul-1-neg 88.9%

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

      2. div-sub 88.9%

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

      3. sub-neg 88.9%

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

      4. *-inverses 88.9%

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

      5. metadata-eval 88.9%

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

   4. Simplified 88.9%

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

   if -1.3000000000000001e107 < y < 2e113

   1. Initial program 93.5%

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

      1. associate-*l/ 91.6%

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

      2. *-commutative 91.6%

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

      3. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+107} \lor \neg \left(y \leq 2 \cdot 10^{+113}\right):\\ \;\;\;\;\left(\frac{x}{y} + -1\right) \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 6: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 82:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.9e+46)
   t
   (if (<= y 82.0) (* t (/ x z)) (if (<= y 3.5e+108) (* y (- (/ t z))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.9e+46) {
		tmp = t;
	} else if (y <= 82.0) {
		tmp = t * (x / z);
	} else if (y <= 3.5e+108) {
		tmp = y * -(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 <= (-5.9d+46)) then
        tmp = t
    else if (y <= 82.0d0) then
        tmp = t * (x / z)
    else if (y <= 3.5d+108) then
        tmp = y * -(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 <= -5.9e+46) {
		tmp = t;
	} else if (y <= 82.0) {
		tmp = t * (x / z);
	} else if (y <= 3.5e+108) {
		tmp = y * -(t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.9e+46:
		tmp = t
	elif y <= 82.0:
		tmp = t * (x / z)
	elif y <= 3.5e+108:
		tmp = y * -(t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.9e+46)
		tmp = t;
	elseif (y <= 82.0)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= 3.5e+108)
		tmp = Float64(y * Float64(-Float64(t / z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.9e+46)
		tmp = t;
	elseif (y <= 82.0)
		tmp = t * (x / z);
	elseif (y <= 3.5e+108)
		tmp = y * -(t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.9e+46], t, If[LessEqual[y, 82.0], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+108], N[(y * (-N[(t / z), $MachinePrecision])), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8999999999999999e46 or 3.5000000000000002e108 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-*l/ 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in y around inf 71.1%

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

   if -5.8999999999999999e46 < y < 82

   1. Initial program 92.2%

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

   2. Taylor expanded in y around 0 64.9%

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

   if 82 < y < 3.5000000000000002e108

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 68.8%

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

      1. neg-mul-1 68.8%

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

      2. distribute-neg-frac 68.8%

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

   4. Simplified 68.8%

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

   5. Taylor expanded in y around 0 53.4%

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

      1. mul-1-neg 53.4%

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

      2. associate-/l* 57.9%

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

      3. distribute-neg-frac 57.9%

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

   7. Simplified 57.9%

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

   8. Taylor expanded in t around 0 53.4%

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

      1. mul-1-neg 53.4%

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

      2. associate-*l/ 57.9%

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

      3. distribute-rgt-neg-out 57.9%

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

   10. Simplified 57.9%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 82:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.42:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.6e+46)
   t
   (if (<= y 1.42) (* t (/ x z)) (if (<= y 3.5e+108) (* t (/ (- y) z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.6e+46) {
		tmp = t;
	} else if (y <= 1.42) {
		tmp = t * (x / z);
	} else if (y <= 3.5e+108) {
		tmp = t * (-y / 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 <= (-5.6d+46)) then
        tmp = t
    else if (y <= 1.42d0) then
        tmp = t * (x / z)
    else if (y <= 3.5d+108) then
        tmp = t * (-y / 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 <= -5.6e+46) {
		tmp = t;
	} else if (y <= 1.42) {
		tmp = t * (x / z);
	} else if (y <= 3.5e+108) {
		tmp = t * (-y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.6e+46:
		tmp = t
	elif y <= 1.42:
		tmp = t * (x / z)
	elif y <= 3.5e+108:
		tmp = t * (-y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.6e+46)
		tmp = t;
	elseif (y <= 1.42)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= 3.5e+108)
		tmp = Float64(t * Float64(Float64(-y) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.6e+46)
		tmp = t;
	elseif (y <= 1.42)
		tmp = t * (x / z);
	elseif (y <= 3.5e+108)
		tmp = t * (-y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.6e+46], t, If[LessEqual[y, 1.42], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+108], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.60000000000000037e46 or 3.5000000000000002e108 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-*l/ 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in y around inf 71.1%

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

   if -5.60000000000000037e46 < y < 1.4199999999999999

   1. Initial program 92.2%

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

   2. Taylor expanded in y around 0 64.9%

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

   if 1.4199999999999999 < y < 3.5000000000000002e108

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 68.8%

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

      1. neg-mul-1 68.8%

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

      2. distribute-neg-frac 68.8%

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

   4. Simplified 68.8%

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

   5. Taylor expanded in y around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. distribute-neg-frac 58.1%

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

   7. Simplified 58.1%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.42:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+45} \lor \neg \left(y \leq 0.0265\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.6e+45) (not (<= y 0.0265)))
   (* t (/ y (- y z)))
   (* t (/ x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.6e+45) || !(y <= 0.0265)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t * (x / (z - y));
	}
	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 <= (-7.6d+45)) .or. (.not. (y <= 0.0265d0))) then
        tmp = t * (y / (y - z))
    else
        tmp = t * (x / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.6e+45) || !(y <= 0.0265)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.6e+45) or not (y <= 0.0265):
		tmp = t * (y / (y - z))
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.6e+45) || !(y <= 0.0265))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.6e+45) || ~((y <= 0.0265)))
		tmp = t * (y / (y - z));
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.6e+45], N[Not[LessEqual[y, 0.0265]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.6000000000000004e45 or 0.0264999999999999993 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 78.9%

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

      1. neg-mul-1 78.9%

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

      2. distribute-neg-frac 78.9%

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

   4. Simplified 78.9%

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

      1. frac-2neg 78.9%

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

      2. remove-double-neg 78.9%

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

      3. associate-*l/ 57.6%

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

      4. sub-neg 57.6%

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

      5. distribute-neg-in 57.6%

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

      6. remove-double-neg 57.6%

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

   6. Applied egg-rr 57.6%

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

      1. associate-/l* 56.9%

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

      2. associate-/r/ 78.9%

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

      3. +-commutative 78.9%

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

      4. unsub-neg 78.9%

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

   8. Simplified 78.9%

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

   if -7.6000000000000004e45 < y < 0.0264999999999999993

   1. Initial program 92.2%

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

   2. Taylor expanded in x around inf 79.3%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+45} \lor \neg \left(y \leq 0.0265\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]

Alternative 9: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.8e-27) t (if (<= y 3.1e+26) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e-27) {
		tmp = t;
	} else if (y <= 3.1e+26) {
		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 <= (-2.8d-27)) then
        tmp = t
    else if (y <= 3.1d+26) 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 <= -2.8e-27) {
		tmp = t;
	} else if (y <= 3.1e+26) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.8e-27:
		tmp = t
	elif y <= 3.1e+26:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.8e-27)
		tmp = t;
	elseif (y <= 3.1e+26)
		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 <= -2.8e-27)
		tmp = t;
	elseif (y <= 3.1e+26)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.8e-27], t, If[LessEqual[y, 3.1e+26], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8e-27 or 3.1e26 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 75.9%

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

      2. *-commutative 75.9%

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

      3. associate-*l/ 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in y around inf 60.2%

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

   if -2.8e-27 < y < 3.1e26

   1. Initial program 91.8%

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

      1. associate-*l/ 92.0%

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

      2. *-commutative 92.0%

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

      3. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

      1. *-commutative 95.2%

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

      2. clear-num 94.3%

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

      3. div-inv 94.8%

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

      4. div-inv 94.7%

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

      5. associate-/r* 91.7%

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

   5. Applied egg-rr 91.7%

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

   6. Taylor expanded in y around 0 64.2%

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

      1. associate-*l/ 67.0%

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

   8. Simplified 67.0%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 62.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.6e+46) t (if (<= y 4.9e+20) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.6e+46) {
		tmp = t;
	} else if (y <= 4.9e+20) {
		tmp = t * (x / 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 <= (-5.6d+46)) then
        tmp = t
    else if (y <= 4.9d+20) then
        tmp = t * (x / 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 <= -5.6e+46) {
		tmp = t;
	} else if (y <= 4.9e+20) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.6e+46:
		tmp = t
	elif y <= 4.9e+20:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.6e+46)
		tmp = t;
	elseif (y <= 4.9e+20)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.6e+46)
		tmp = t;
	elseif (y <= 4.9e+20)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.6e+46], t, If[LessEqual[y, 4.9e+20], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -5.60000000000000037e46 or 4.9e20 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 72.8%

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

      2. *-commutative 72.8%

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

      3. associate-*l/ 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in y around inf 65.4%

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

   if -5.60000000000000037e46 < y < 4.9e20

   1. Initial program 92.5%

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

   2. Taylor expanded in y around 0 63.5%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 35.3% 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 95.4%

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

   1. associate-*l/ 84.8%

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

   2. *-commutative 84.8%

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

   3. associate-*l/ 85.9%

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

3. Simplified 85.9%

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

4. Taylor expanded in y around inf 31.0%

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

5. Final simplification 31.0%

   \[\leadsto t \]

Developer target: 97.0% 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 2023336 
(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))