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

Percentage Accurate: 96.9% → 96.9%

Time: 8.1s

Alternatives: 7

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: 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: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / ((y - z) / (y - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. *-commutative 97.2%

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

   2. associate-*r/ 82.9%

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

   3. associate-/l* 97.2%

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

   4. sub-neg 97.2%

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

   5. +-commutative 97.2%

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

   6. neg-sub0 97.2%

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

   7. associate-+l- 97.2%

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

   8. sub0-neg 97.2%

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

   9. neg-mul-1 97.2%

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

   10. associate-/r* 97.2%

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

3. Simplified 97.2%

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

4. Final simplification 97.2%

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

Alternative 2: 69.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - x}{y}\\ t_2 := \left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-104}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- y x) y))) (t_2 (* (- x y) (/ t z))))
   (if (<= z -4.7e+49)
     t_2
     (if (<= z 2.4e-152)
       t_1
       (if (<= z 4e-104) (/ (* t x) z) (if (<= z 1.14e+61) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double t_2 = (x - y) * (t / z);
	double tmp;
	if (z <= -4.7e+49) {
		tmp = t_2;
	} else if (z <= 2.4e-152) {
		tmp = t_1;
	} else if (z <= 4e-104) {
		tmp = (t * x) / z;
	} else if (z <= 1.14e+61) {
		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 * ((y - x) / y)
    t_2 = (x - y) * (t / z)
    if (z <= (-4.7d+49)) then
        tmp = t_2
    else if (z <= 2.4d-152) then
        tmp = t_1
    else if (z <= 4d-104) then
        tmp = (t * x) / z
    else if (z <= 1.14d+61) 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 * ((y - x) / y);
	double t_2 = (x - y) * (t / z);
	double tmp;
	if (z <= -4.7e+49) {
		tmp = t_2;
	} else if (z <= 2.4e-152) {
		tmp = t_1;
	} else if (z <= 4e-104) {
		tmp = (t * x) / z;
	} else if (z <= 1.14e+61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((y - x) / y)
	t_2 = (x - y) * (t / z)
	tmp = 0
	if z <= -4.7e+49:
		tmp = t_2
	elif z <= 2.4e-152:
		tmp = t_1
	elif z <= 4e-104:
		tmp = (t * x) / z
	elif z <= 1.14e+61:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(y - x) / y))
	t_2 = Float64(Float64(x - y) * Float64(t / z))
	tmp = 0.0
	if (z <= -4.7e+49)
		tmp = t_2;
	elseif (z <= 2.4e-152)
		tmp = t_1;
	elseif (z <= 4e-104)
		tmp = Float64(Float64(t * x) / z);
	elseif (z <= 1.14e+61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((y - x) / y);
	t_2 = (x - y) * (t / z);
	tmp = 0.0;
	if (z <= -4.7e+49)
		tmp = t_2;
	elseif (z <= 2.4e-152)
		tmp = t_1;
	elseif (z <= 4e-104)
		tmp = (t * x) / z;
	elseif (z <= 1.14e+61)
		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[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.7e+49], t$95$2, If[LessEqual[z, 2.4e-152], t$95$1, If[LessEqual[z, 4e-104], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.14e+61], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6999999999999997e49 or 1.13999999999999996e61 < z

   1. Initial program 97.0%

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

   2. Taylor expanded in z around inf 72.5%

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

      1. associate-/l* 79.1%

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

      2. associate-/r/ 77.1%

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

   4. Simplified 77.1%

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

   if -4.6999999999999997e49 < z < 2.4e-152 or 3.99999999999999971e-104 < z < 1.13999999999999996e61

   1. Initial program 99.2%

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

   2. Taylor expanded in z around 0 83.5%

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

      1. associate-*r/ 83.5%

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

      2. neg-mul-1 83.5%

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

      3. neg-sub0 83.5%

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

      4. associate--r- 83.5%

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

      5. neg-sub0 83.5%

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

      6. +-commutative 83.5%

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

      7. sub-neg 83.5%

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

   4. Simplified 83.5%

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

   if 2.4e-152 < z < 3.99999999999999971e-104

   1. Initial program 73.8%

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

   2. Taylor expanded in y around 0 99.6%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+49}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-152}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-104}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]

Alternative 3: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - x}{y}\\ t_2 := \frac{t}{\frac{z}{x - y}}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-104}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- y x) y))) (t_2 (/ t (/ z (- x y)))))
   (if (<= z -4.6e+38)
     t_2
     (if (<= z 2.4e-152)
       t_1
       (if (<= z 4e-104) (/ (* t x) z) (if (<= z 1.14e+61) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double t_2 = t / (z / (x - y));
	double tmp;
	if (z <= -4.6e+38) {
		tmp = t_2;
	} else if (z <= 2.4e-152) {
		tmp = t_1;
	} else if (z <= 4e-104) {
		tmp = (t * x) / z;
	} else if (z <= 1.14e+61) {
		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 * ((y - x) / y)
    t_2 = t / (z / (x - y))
    if (z <= (-4.6d+38)) then
        tmp = t_2
    else if (z <= 2.4d-152) then
        tmp = t_1
    else if (z <= 4d-104) then
        tmp = (t * x) / z
    else if (z <= 1.14d+61) 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 * ((y - x) / y);
	double t_2 = t / (z / (x - y));
	double tmp;
	if (z <= -4.6e+38) {
		tmp = t_2;
	} else if (z <= 2.4e-152) {
		tmp = t_1;
	} else if (z <= 4e-104) {
		tmp = (t * x) / z;
	} else if (z <= 1.14e+61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((y - x) / y)
	t_2 = t / (z / (x - y))
	tmp = 0
	if z <= -4.6e+38:
		tmp = t_2
	elif z <= 2.4e-152:
		tmp = t_1
	elif z <= 4e-104:
		tmp = (t * x) / z
	elif z <= 1.14e+61:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(y - x) / y))
	t_2 = Float64(t / Float64(z / Float64(x - y)))
	tmp = 0.0
	if (z <= -4.6e+38)
		tmp = t_2;
	elseif (z <= 2.4e-152)
		tmp = t_1;
	elseif (z <= 4e-104)
		tmp = Float64(Float64(t * x) / z);
	elseif (z <= 1.14e+61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((y - x) / y);
	t_2 = t / (z / (x - y));
	tmp = 0.0;
	if (z <= -4.6e+38)
		tmp = t_2;
	elseif (z <= 2.4e-152)
		tmp = t_1;
	elseif (z <= 4e-104)
		tmp = (t * x) / z;
	elseif (z <= 1.14e+61)
		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[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+38], t$95$2, If[LessEqual[z, 2.4e-152], t$95$1, If[LessEqual[z, 4e-104], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.14e+61], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6000000000000002e38 or 1.13999999999999996e61 < z

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf 72.2%

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

      1. associate-/l* 78.6%

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

   4. Simplified 78.6%

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

   if -4.6000000000000002e38 < z < 2.4e-152 or 3.99999999999999971e-104 < z < 1.13999999999999996e61

   1. Initial program 99.2%

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

   2. Taylor expanded in z around 0 83.9%

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

      1. associate-*r/ 83.9%

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

      2. neg-mul-1 83.9%

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

      3. neg-sub0 83.9%

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

      4. associate--r- 83.9%

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

      5. neg-sub0 83.9%

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

      6. +-commutative 83.9%

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

      7. sub-neg 83.9%

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

   4. Simplified 83.9%

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

   if 2.4e-152 < z < 3.99999999999999971e-104

   1. Initial program 73.8%

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

   2. Taylor expanded in y around 0 99.6%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-152}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-104}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \end{array} \]

Alternative 4: 67.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+62}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+45}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.7e+62) t (if (<= y 7e+45) (* (- x y) (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.7e+62) {
		tmp = t;
	} else if (y <= 7e+45) {
		tmp = (x - 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 <= (-2.7d+62)) then
        tmp = t
    else if (y <= 7d+45) then
        tmp = (x - 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 <= -2.7e+62) {
		tmp = t;
	} else if (y <= 7e+45) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.7e+62:
		tmp = t
	elif y <= 7e+45:
		tmp = (x - y) * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.7e+62)
		tmp = t;
	elseif (y <= 7e+45)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.7e+62)
		tmp = t;
	elseif (y <= 7e+45)
		tmp = (x - y) * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.7e+62], t, If[LessEqual[y, 7e+45], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e62 or 7.00000000000000046e45 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 69.2%

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

   if -2.7e62 < y < 7.00000000000000046e45

   1. Initial program 95.4%

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

   2. Taylor expanded in z around inf 68.2%

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

      1. associate-/l* 68.6%

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

      2. associate-/r/ 69.5%

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

   4. Simplified 69.5%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+62}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+45}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 60.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-20}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e-20) t (if (<= y 7e-34) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-20) {
		tmp = t;
	} else if (y <= 7e-34) {
		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 <= (-1.45d-20)) then
        tmp = t
    else if (y <= 7d-34) 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 <= -1.45e-20) {
		tmp = t;
	} else if (y <= 7e-34) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e-20:
		tmp = t
	elif y <= 7e-34:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e-20)
		tmp = t;
	elseif (y <= 7e-34)
		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 <= -1.45e-20)
		tmp = t;
	elseif (y <= 7e-34)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e-20], t, If[LessEqual[y, 7e-34], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45e-20 or 7e-34 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 59.7%

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

   if -1.45e-20 < y < 7e-34

   1. Initial program 94.0%

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

   2. Taylor expanded in y around 0 66.3%

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

      1. associate-/l* 67.2%

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

      2. associate-/r/ 69.6%

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

   4. Simplified 69.6%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-20}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

2. Final simplification 97.2%

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

Alternative 7: 35.8% 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 97.2%

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

2. Taylor expanded in y around inf 37.4%

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

3. Final simplification 37.4%

   \[\leadsto t \]

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 2023279 
(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))