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

Percentage Accurate: 96.9% → 96.9%

Time: 8.0s

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

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

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 98.9%

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

2. Final simplification 98.9%

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

Alternative 2: 90.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+144} \lor \neg \left(y \leq 3.7 \cdot 10^{+154}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.95e+144) (not (<= y 3.7e+154)))
   (* t (- 1.0 (/ x y)))
   (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.95e+144) || !(y <= 3.7e+154)) {
		tmp = t * (1.0 - (x / y));
	} 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 <= (-1.95d+144)) .or. (.not. (y <= 3.7d+154))) then
        tmp = t * (1.0d0 - (x / y))
    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 <= -1.95e+144) || !(y <= 3.7e+154)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.95e+144) or not (y <= 3.7e+154):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.95e+144) || !(y <= 3.7e+154))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	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 <= -1.95e+144) || ~((y <= 3.7e+154)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.95e+144], N[Not[LessEqual[y, 3.7e+154]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.95000000000000009e144 or 3.69999999999999994e154 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around -inf 96.5%

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

      1. mul-1-neg 96.5%

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

   4. Simplified 96.5%

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

   5. Taylor expanded in z around 0 95.4%

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

   if -1.95000000000000009e144 < y < 3.69999999999999994e154

   1. Initial program 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-*r/ 92.1%

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

      3. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+144} \lor \neg \left(y \leq 3.7 \cdot 10^{+154}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 3: 70.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-18} \lor \neg \left(y \leq 2.3 \cdot 10^{-58}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3e-18) (not (<= y 2.3e-58)))
   (* t (- 1.0 (/ x y)))
   (* t (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3e-18) || !(y <= 2.3e-58)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t * (x / 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) :: tmp
    if ((y <= (-3d-18)) .or. (.not. (y <= 2.3d-58))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3e-18) || !(y <= 2.3e-58)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3e-18) or not (y <= 2.3e-58):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3e-18) || !(y <= 2.3e-58))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3e-18) || ~((y <= 2.3e-58)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3e-18], N[Not[LessEqual[y, 2.3e-58]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.99999999999999983e-18 or 2.2999999999999999e-58 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around -inf 76.5%

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

      1. mul-1-neg 76.5%

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

   4. Simplified 76.5%

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

   5. Taylor expanded in z around 0 76.3%

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

   if -2.99999999999999983e-18 < y < 2.2999999999999999e-58

   1. Initial program 97.7%

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

   2. Taylor expanded in y around 0 71.1%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-18} \lor \neg \left(y \leq 2.3 \cdot 10^{-58}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]

Alternative 4: 73.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-18} \lor \neg \left(y \leq 1.3 \cdot 10^{+79}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.9e-18) (not (<= y 1.3e+79)))
   (* t (- 1.0 (/ x y)))
   (* (- x y) (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.9e-18) || !(y <= 1.3e+79)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t / 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) :: tmp
    if ((y <= (-2.9d-18)) .or. (.not. (y <= 1.3d+79))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = (x - y) * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.9e-18) || !(y <= 1.3e+79)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.9e-18) or not (y <= 1.3e+79):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = (x - y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.9e-18) || !(y <= 1.3e+79))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(x - y) * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.9e-18) || ~((y <= 1.3e+79)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = (x - y) * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.9e-18], N[Not[LessEqual[y, 1.3e+79]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e-18 or 1.30000000000000007e79 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around -inf 85.7%

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

      1. mul-1-neg 85.7%

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

   4. Simplified 85.7%

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

   5. Taylor expanded in z around 0 85.2%

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

   if -2.9e-18 < y < 1.30000000000000007e79

   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/ 94.0%

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

      3. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around inf 74.3%

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

      1. associate-/l* 77.3%

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

      2. associate-/r/ 74.2%

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

   6. Simplified 74.2%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-18} \lor \neg \left(y \leq 1.3 \cdot 10^{+79}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]

Alternative 5: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-18} \lor \neg \left(y \leq 3.5 \cdot 10^{+104}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.7e-18) (not (<= y 3.5e+104)))
   (* t (- 1.0 (/ x y)))
   (* t (/ x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.7e-18) || !(y <= 3.5e+104)) {
		tmp = t * (1.0 - (x / y));
	} 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 <= (-4.7d-18)) .or. (.not. (y <= 3.5d+104))) then
        tmp = t * (1.0d0 - (x / y))
    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 <= -4.7e-18) || !(y <= 3.5e+104)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.7e-18) or not (y <= 3.5e+104):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.7e-18) || !(y <= 3.5e+104))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	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 <= -4.7e-18) || ~((y <= 3.5e+104)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.7e-18], N[Not[LessEqual[y, 3.5e+104]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.6999999999999996e-18 or 3.5000000000000002e104 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around -inf 87.1%

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

      1. mul-1-neg 87.1%

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

   4. Simplified 87.1%

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

   5. Taylor expanded in z around 0 86.6%

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

   if -4.6999999999999996e-18 < y < 3.5000000000000002e104

   1. Initial program 98.2%

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

   2. Taylor expanded in x around inf 79.9%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-18} \lor \neg \left(y \leq 3.5 \cdot 10^{+104}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]

Alternative 6: 60.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-18}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+105}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.4e-18) t (if (<= y 2.5e+105) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e-18) {
		tmp = t;
	} else if (y <= 2.5e+105) {
		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 <= (-4.4d-18)) then
        tmp = t
    else if (y <= 2.5d+105) 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 <= -4.4e-18) {
		tmp = t;
	} else if (y <= 2.5e+105) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.4e-18:
		tmp = t
	elif y <= 2.5e+105:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.4e-18)
		tmp = t;
	elseif (y <= 2.5e+105)
		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 <= -4.4e-18)
		tmp = t;
	elseif (y <= 2.5e+105)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.4e-18], t, If[LessEqual[y, 2.5e+105], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999997e-18 or 2.50000000000000023e105 < y

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*r/ 75.1%

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

      3. associate-*l/ 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in y around inf 72.4%

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

   if -4.3999999999999997e-18 < y < 2.50000000000000023e105

   1. Initial program 98.2%

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

   2. Taylor expanded in y around 0 64.6%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-18}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+105}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 35.1% 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 98.9%

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

   1. *-commutative 98.9%

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

   2. associate-*r/ 86.0%

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

   3. associate-*l/ 83.6%

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

3. Simplified 83.6%

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

4. Taylor expanded in y around inf 36.1%

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

5. Final simplification 36.1%

   \[\leadsto t \]

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 2023301 
(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))