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

Percentage Accurate: 97.1% → 97.1%

Time: 9.0s

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: 97.1% 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: 97.1% 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 97.7%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 67.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+52}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+56}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e+52)
   t
   (if (<= y 3.7e-103)
     (* x (/ t (- z y)))
     (if (<= y 5.8e+56) (* (- x y) (/ t z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+52) {
		tmp = t;
	} else if (y <= 3.7e-103) {
		tmp = x * (t / (z - y));
	} else if (y <= 5.8e+56) {
		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 <= (-1.7d+52)) then
        tmp = t
    else if (y <= 3.7d-103) then
        tmp = x * (t / (z - y))
    else if (y <= 5.8d+56) 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 <= -1.7e+52) {
		tmp = t;
	} else if (y <= 3.7e-103) {
		tmp = x * (t / (z - y));
	} else if (y <= 5.8e+56) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e+52:
		tmp = t
	elif y <= 3.7e-103:
		tmp = x * (t / (z - y))
	elif y <= 5.8e+56:
		tmp = (x - y) * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e+52)
		tmp = t;
	elseif (y <= 3.7e-103)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 5.8e+56)
		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 <= -1.7e+52)
		tmp = t;
	elseif (y <= 3.7e-103)
		tmp = x * (t / (z - y));
	elseif (y <= 5.8e+56)
		tmp = (x - y) * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e+52], t, If[LessEqual[y, 3.7e-103], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+56], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e52 or 5.80000000000000014e56 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 72.9%

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

      2. associate-/l* 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in y around inf 68.3%

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

   if -1.7e52 < y < 3.6999999999999999e-103

   1. Initial program 95.2%

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

      1. associate-*l/ 93.4%

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

      2. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x around inf 75.0%

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

   if 3.6999999999999999e-103 < y < 5.80000000000000014e56

   1. Initial program 99.7%

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

      1. associate-*l/ 96.7%

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

      2. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in z around inf 74.6%

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

Alternative 3: 89.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+146} \lor \neg \left(y \leq 8.2 \cdot 10^{+157}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4e+146) (not (<= y 8.2e+157)))
   (* t (/ y (- y z)))
   (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4e+146) || !(y <= 8.2e+157)) {
		tmp = t * (y / (y - z));
	} 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 <= (-4d+146)) .or. (.not. (y <= 8.2d+157))) then
        tmp = t * (y / (y - z))
    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 <= -4e+146) || !(y <= 8.2e+157)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4e+146) or not (y <= 8.2e+157):
		tmp = t * (y / (y - z))
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4e+146) || !(y <= 8.2e+157))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	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 <= -4e+146) || ~((y <= 8.2e+157)))
		tmp = t * (y / (y - z));
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4e+146], N[Not[LessEqual[y, 8.2e+157]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $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 < -3.99999999999999973e146 or 8.20000000000000032e157 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 90.9%

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

      1. neg-mul-1 90.9%

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

      2. distribute-neg-frac2 90.9%

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

      3. neg-sub0 90.9%

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

      4. sub-neg 90.9%

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

      5. +-commutative 90.9%

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

      6. associate--r+ 90.9%

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

      7. neg-sub0 90.9%

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

      8. remove-double-neg 90.9%

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

   5. Simplified 90.9%

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

   if -3.99999999999999973e146 < y < 8.20000000000000032e157

   1. Initial program 97.1%

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

      1. associate-*l/ 93.1%

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

      2. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+146} \lor \neg \left(y \leq 8.2 \cdot 10^{+157}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+19} \lor \neg \left(y \leq 1.65 \cdot 10^{-5}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.9e+19) (not (<= y 1.65e-5)))
   (* t (- 1.0 (/ x y)))
   (* t (/ (- x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.9e+19) || !(y <= 1.65e-5)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.9d+19)) .or. (.not. (y <= 1.65d-5))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t * ((x - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.9e+19) || !(y <= 1.65e-5)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.9e+19) or not (y <= 1.65e-5):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t * ((x - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.9e+19) || !(y <= 1.65e-5))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.9e+19) || ~((y <= 1.65e-5)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.9e+19], N[Not[LessEqual[y, 1.65e-5]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9e19 or 1.6500000000000001e-5 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 77.5%

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

      2. associate-/l* 80.6%

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

   3. Simplified 80.6%

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

      1. associate-*r/ 77.5%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 61.3%

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

      1. mul-1-neg 61.3%

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

      2. associate-/l* 80.5%

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

      3. distribute-rgt-neg-in 80.5%

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

      4. div-sub 80.6%

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

      5. *-inverses 80.6%

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

   9. Simplified 80.6%

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

   if -4.9e19 < y < 1.6500000000000001e-5

   1. Initial program 95.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 79.1%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+19} \lor \neg \left(y \leq 1.65 \cdot 10^{-5}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+18} \lor \neg \left(y \leq 2.7 \cdot 10^{-6}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9e+18) (not (<= y 2.7e-6)))
   (* t (/ (- y x) y))
   (* t (/ (- x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9e+18) || !(y <= 2.7e-6)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-9d+18)) .or. (.not. (y <= 2.7d-6))) then
        tmp = t * ((y - x) / y)
    else
        tmp = t * ((x - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9e+18) || !(y <= 2.7e-6)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9e+18) or not (y <= 2.7e-6):
		tmp = t * ((y - x) / y)
	else:
		tmp = t * ((x - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9e+18) || !(y <= 2.7e-6))
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = Float64(t * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9e+18) || ~((y <= 2.7e-6)))
		tmp = t * ((y - x) / y);
	else
		tmp = t * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9e+18], N[Not[LessEqual[y, 2.7e-6]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9e18 or 2.69999999999999998e-6 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. neg-mul-1 80.5%

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

      3. neg-sub0 80.5%

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

      4. sub-neg 80.5%

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

      5. +-commutative 80.5%

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

      6. associate--r+ 80.5%

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

      7. neg-sub0 80.5%

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

      8. remove-double-neg 80.5%

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

   5. Simplified 80.5%

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

   if -9e18 < y < 2.69999999999999998e-6

   1. Initial program 95.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 79.1%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+18} \lor \neg \left(y \leq 2.7 \cdot 10^{-6}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+19} \lor \neg \left(y \leq 2.3 \cdot 10^{-13}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.4e+19) (not (<= y 2.3e-13)))
   (* t (/ y (- y z)))
   (* t (/ (- x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.4e+19) || !(y <= 2.3e-13)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.4d+19)) .or. (.not. (y <= 2.3d-13))) then
        tmp = t * (y / (y - z))
    else
        tmp = t * ((x - y) / z)
    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+19) || !(y <= 2.3e-13)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.4e+19) or not (y <= 2.3e-13):
		tmp = t * (y / (y - z))
	else:
		tmp = t * ((x - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.4e+19) || !(y <= 2.3e-13))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(t * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.4e+19) || ~((y <= 2.3e-13)))
		tmp = t * (y / (y - z));
	else
		tmp = t * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.4e+19], N[Not[LessEqual[y, 2.3e-13]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4e19 or 2.29999999999999979e-13 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 77.7%

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

      1. neg-mul-1 77.7%

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

      2. distribute-neg-frac2 77.7%

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

      3. neg-sub0 77.7%

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

      4. sub-neg 77.7%

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

      5. +-commutative 77.7%

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

      6. associate--r+ 77.7%

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

      7. neg-sub0 77.7%

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

      8. remove-double-neg 77.7%

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

   5. Simplified 77.7%

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

   if -4.4e19 < y < 2.29999999999999979e-13

   1. Initial program 95.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.6%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+19} \lor \neg \left(y \leq 2.3 \cdot 10^{-13}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+16} \lor \neg \left(y \leq 4.3 \cdot 10^{-13}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.2e+16) (not (<= y 4.3e-13)))
   (* t (/ y (- y z)))
   (* x (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2e+16) || !(y <= 4.3e-13)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = x * (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 <= (-4.2d+16)) .or. (.not. (y <= 4.3d-13))) then
        tmp = t * (y / (y - z))
    else
        tmp = x * (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 <= -4.2e+16) || !(y <= 4.3e-13)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.2e+16) or not (y <= 4.3e-13):
		tmp = t * (y / (y - z))
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.2e+16) || !(y <= 4.3e-13))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.2e+16) || ~((y <= 4.3e-13)))
		tmp = t * (y / (y - z));
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.2e+16], N[Not[LessEqual[y, 4.3e-13]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e16 or 4.2999999999999999e-13 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 77.9%

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

      1. neg-mul-1 77.9%

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

      2. distribute-neg-frac2 77.9%

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

      3. neg-sub0 77.9%

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

      4. sub-neg 77.9%

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

      5. +-commutative 77.9%

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

      6. associate--r+ 77.9%

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

      7. neg-sub0 77.9%

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

      8. remove-double-neg 77.9%

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

   5. Simplified 77.9%

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

   if -4.2e16 < y < 4.2999999999999999e-13

   1. Initial program 95.4%

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

      1. associate-*l/ 92.8%

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

      2. associate-/l* 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in x around inf 77.5%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+16} \lor \neg \left(y \leq 4.3 \cdot 10^{-13}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+52}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.7e+52) t (if (<= y 1.7e+24) (* x (/ t (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.7e+52) {
		tmp = t;
	} else if (y <= 1.7e+24) {
		tmp = x * (t / (z - y));
	} 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 <= (-3.7d+52)) then
        tmp = t
    else if (y <= 1.7d+24) then
        tmp = x * (t / (z - y))
    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 <= -3.7e+52) {
		tmp = t;
	} else if (y <= 1.7e+24) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.7e+52:
		tmp = t
	elif y <= 1.7e+24:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.7e+52)
		tmp = t;
	elseif (y <= 1.7e+24)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.7e+52)
		tmp = t;
	elseif (y <= 1.7e+24)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.7e+52], t, If[LessEqual[y, 1.7e+24], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7e52 or 1.7e24 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 74.1%

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

      2. associate-/l* 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in y around inf 67.0%

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

   if -3.7e52 < y < 1.7e24

   1. Initial program 96.0%

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

      1. associate-*l/ 93.9%

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

      2. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in x around inf 72.1%

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

Alternative 9: 60.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+19}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-12}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.05e+19) t (if (<= y 1.55e-12) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.05e+19) {
		tmp = t;
	} else if (y <= 1.55e-12) {
		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 <= (-2.05d+19)) then
        tmp = t
    else if (y <= 1.55d-12) 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 <= -2.05e+19) {
		tmp = t;
	} else if (y <= 1.55e-12) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.05e+19:
		tmp = t
	elif y <= 1.55e-12:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.05e+19)
		tmp = t;
	elseif (y <= 1.55e-12)
		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 <= -2.05e+19)
		tmp = t;
	elseif (y <= 1.55e-12)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.05e+19], t, If[LessEqual[y, 1.55e-12], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.05e19 or 1.5500000000000001e-12 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 78.0%

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

      2. associate-/l* 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in y around inf 62.5%

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

   if -2.05e19 < y < 1.5500000000000001e-12

   1. Initial program 95.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 71.4%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+19}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-12}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+20}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e+20) t (if (<= y 9.6e-13) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e+20) {
		tmp = t;
	} else if (y <= 9.6e-13) {
		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 <= (-1.05d+20)) then
        tmp = t
    else if (y <= 9.6d-13) 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 <= -1.05e+20) {
		tmp = t;
	} else if (y <= 9.6e-13) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e+20:
		tmp = t
	elif y <= 9.6e-13:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e+20)
		tmp = t;
	elseif (y <= 9.6e-13)
		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 <= -1.05e+20)
		tmp = t;
	elseif (y <= 9.6e-13)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e+20], t, If[LessEqual[y, 9.6e-13], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e20 or 9.5999999999999995e-13 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 78.0%

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

      2. associate-/l* 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in y around inf 62.5%

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

   if -1.05e20 < y < 9.5999999999999995e-13

   1. Initial program 95.4%

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

      1. associate-*l/ 92.9%

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

      2. associate-/l* 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in z around inf 73.2%

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

   6. Taylor expanded in x around inf 66.8%

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

Alternative 11: 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 97.7%

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

   1. associate-*l/ 85.1%

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

   2. associate-/l* 85.3%

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

3. Simplified 85.3%

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

5. Taylor expanded in y around inf 37.9%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Developer Target 1: 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 2024181 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (/ t (/ (- z y) (- x y))))

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