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

Percentage Accurate: 97.3% → 97.3%

Time: 6.4s

Alternatives: 8

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: 97.3% 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: 97.3% 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 97.3%

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

2. Final simplification 97.3%

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

Alternative 2: 76.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - x}{y}\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-94}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- y x) y))))
   (if (<= y -1.85e-17)
     t_1
     (if (<= y -2.1e-94)
       (* (- x y) (/ t z))
       (if (<= y 3.3e+31) (* x (/ t (- z y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double tmp;
	if (y <= -1.85e-17) {
		tmp = t_1;
	} else if (y <= -2.1e-94) {
		tmp = (x - y) * (t / z);
	} else if (y <= 3.3e+31) {
		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 - x) / y)
    if (y <= (-1.85d-17)) then
        tmp = t_1
    else if (y <= (-2.1d-94)) then
        tmp = (x - y) * (t / z)
    else if (y <= 3.3d+31) 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 - x) / y);
	double tmp;
	if (y <= -1.85e-17) {
		tmp = t_1;
	} else if (y <= -2.1e-94) {
		tmp = (x - y) * (t / z);
	} else if (y <= 3.3e+31) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((y - x) / y)
	tmp = 0
	if y <= -1.85e-17:
		tmp = t_1
	elif y <= -2.1e-94:
		tmp = (x - y) * (t / z)
	elif y <= 3.3e+31:
		tmp = x * (t / (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(y - x) / y))
	tmp = 0.0
	if (y <= -1.85e-17)
		tmp = t_1;
	elseif (y <= -2.1e-94)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 3.3e+31)
		tmp = Float64(x * Float64(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 - x) / y);
	tmp = 0.0;
	if (y <= -1.85e-17)
		tmp = t_1;
	elseif (y <= -2.1e-94)
		tmp = (x - y) * (t / z);
	elseif (y <= 3.3e+31)
		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[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e-17], t$95$1, If[LessEqual[y, -2.1e-94], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+31], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8499999999999999e-17 or 3.29999999999999992e31 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 62.3%

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

      1. associate-*r/ 62.3%

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

      2. *-commutative 62.3%

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

      3. neg-mul-1 62.3%

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

      4. distribute-lft-neg-in 62.3%

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

      5. *-commutative 62.3%

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

      6. associate-/l* 79.8%

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

      7. neg-sub0 79.8%

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

      8. associate--r- 79.8%

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

      9. neg-sub0 79.8%

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

      10. +-commutative 79.8%

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

      11. sub-neg 79.8%

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

   4. Simplified 79.8%

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

   5. Taylor expanded in t around 0 62.3%

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

      1. associate-*r/ 79.8%

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

   7. Simplified 79.8%

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

   if -1.8499999999999999e-17 < y < -2.1000000000000001e-94

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 73.0%

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

      1. associate-/l* 78.2%

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

      2. associate-/r/ 78.1%

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

   4. Simplified 78.1%

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

   if -2.1000000000000001e-94 < y < 3.29999999999999992e31

   1. Initial program 94.7%

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

      1. *-commutative 94.7%

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

      2. associate-*r/ 87.0%

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

      3. associate-/l* 94.5%

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

      4. sub-neg 94.5%

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

      5. +-commutative 94.5%

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

      6. neg-sub0 94.5%

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

      7. associate-+l- 94.5%

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

      8. sub0-neg 94.5%

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

      9. neg-mul-1 94.5%

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

      10. associate-/r* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in x around inf 82.7%

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

      1. associate-*r/ 82.7%

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

      2. neg-mul-1 82.7%

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

      3. neg-sub0 82.7%

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

      4. associate--r- 82.7%

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

      5. neg-sub0 82.7%

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

      6. neg-mul-1 82.7%

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

      7. +-commutative 82.7%

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

      8. neg-mul-1 82.7%

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

      9. sub-neg 82.7%

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

   6. Simplified 82.7%

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

      1. associate-/r/ 82.0%

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

   8. Applied egg-rr 82.0%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-94}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]

Alternative 3: 75.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+183}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))))
   (if (<= y -1.45e-78)
     t_1
     (if (<= y 1.95e+28)
       (* x (/ t (- z y)))
       (if (<= y 1.2e+183) (* t (/ (- y x) y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -1.45e-78) {
		tmp = t_1;
	} else if (y <= 1.95e+28) {
		tmp = x * (t / (z - y));
	} else if (y <= 1.2e+183) {
		tmp = t * ((y - x) / 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 / (1.0d0 - (z / y))
    if (y <= (-1.45d-78)) then
        tmp = t_1
    else if (y <= 1.95d+28) then
        tmp = x * (t / (z - y))
    else if (y <= 1.2d+183) then
        tmp = t * ((y - x) / 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 / (1.0 - (z / y));
	double tmp;
	if (y <= -1.45e-78) {
		tmp = t_1;
	} else if (y <= 1.95e+28) {
		tmp = x * (t / (z - y));
	} else if (y <= 1.2e+183) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -1.45e-78:
		tmp = t_1
	elif y <= 1.95e+28:
		tmp = x * (t / (z - y))
	elif y <= 1.2e+183:
		tmp = t * ((y - x) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -1.45e-78)
		tmp = t_1;
	elseif (y <= 1.95e+28)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 1.2e+183)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -1.45e-78)
		tmp = t_1;
	elseif (y <= 1.95e+28)
		tmp = x * (t / (z - y));
	elseif (y <= 1.2e+183)
		tmp = t * ((y - x) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e-78], t$95$1, If[LessEqual[y, 1.95e+28], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+183], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45e-78 or 1.2000000000000001e183 < y

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*r/ 73.9%

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

      3. associate-/l* 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. neg-sub0 99.9%

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

      7. associate-+l- 99.9%

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

      8. sub0-neg 99.9%

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

      9. neg-mul-1 99.9%

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

      10. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 84.9%

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

      1. div-sub 84.9%

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

      2. *-inverses 84.9%

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

   6. Simplified 84.9%

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

   if -1.45e-78 < y < 1.9499999999999999e28

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-*r/ 86.6%

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

      3. associate-/l* 94.7%

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

      4. sub-neg 94.7%

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

      5. +-commutative 94.7%

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

      6. neg-sub0 94.7%

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

      7. associate-+l- 94.7%

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

      8. sub0-neg 94.7%

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

      9. neg-mul-1 94.7%

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

      10. associate-/r* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in x around inf 82.6%

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

      1. associate-*r/ 82.6%

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

      2. neg-mul-1 82.6%

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

      3. neg-sub0 82.6%

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

      4. associate--r- 82.6%

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

      5. neg-sub0 82.6%

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

      6. neg-mul-1 82.6%

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

      7. +-commutative 82.6%

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

      8. neg-mul-1 82.6%

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

      9. sub-neg 82.6%

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

   6. Simplified 82.6%

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

      1. associate-/r/ 81.9%

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

   8. Applied egg-rr 81.9%

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

   if 1.9499999999999999e28 < y < 1.2000000000000001e183

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 70.6%

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

      1. associate-*r/ 70.6%

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

      2. *-commutative 70.6%

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

      3. neg-mul-1 70.6%

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

      4. distribute-lft-neg-in 70.6%

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

      5. *-commutative 70.6%

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

      6. associate-/l* 82.2%

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

      7. neg-sub0 82.2%

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

      8. associate--r- 82.2%

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

      9. neg-sub0 82.2%

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

      10. +-commutative 82.2%

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

      11. sub-neg 82.2%

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

   4. Simplified 82.2%

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

   5. Taylor expanded in t around 0 70.6%

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

      1. associate-*r/ 82.2%

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

   7. Simplified 82.2%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-78}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+183}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]

Alternative 4: 76.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -2 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+182}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))))
   (if (<= y -2e-78)
     t_1
     (if (<= y 5.3e+28)
       (/ t (/ (- z y) x))
       (if (<= y 9.8e+182) (* t (/ (- y x) y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -2e-78) {
		tmp = t_1;
	} else if (y <= 5.3e+28) {
		tmp = t / ((z - y) / x);
	} else if (y <= 9.8e+182) {
		tmp = t * ((y - x) / 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 / (1.0d0 - (z / y))
    if (y <= (-2d-78)) then
        tmp = t_1
    else if (y <= 5.3d+28) then
        tmp = t / ((z - y) / x)
    else if (y <= 9.8d+182) then
        tmp = t * ((y - x) / 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 / (1.0 - (z / y));
	double tmp;
	if (y <= -2e-78) {
		tmp = t_1;
	} else if (y <= 5.3e+28) {
		tmp = t / ((z - y) / x);
	} else if (y <= 9.8e+182) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -2e-78:
		tmp = t_1
	elif y <= 5.3e+28:
		tmp = t / ((z - y) / x)
	elif y <= 9.8e+182:
		tmp = t * ((y - x) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -2e-78)
		tmp = t_1;
	elseif (y <= 5.3e+28)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	elseif (y <= 9.8e+182)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -2e-78)
		tmp = t_1;
	elseif (y <= 5.3e+28)
		tmp = t / ((z - y) / x);
	elseif (y <= 9.8e+182)
		tmp = t * ((y - x) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e-78], t$95$1, If[LessEqual[y, 5.3e+28], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e+182], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2e-78 or 9.7999999999999999e182 < y

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*r/ 73.9%

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

      3. associate-/l* 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. neg-sub0 99.9%

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

      7. associate-+l- 99.9%

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

      8. sub0-neg 99.9%

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

      9. neg-mul-1 99.9%

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

      10. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 84.9%

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

      1. div-sub 84.9%

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

      2. *-inverses 84.9%

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

   6. Simplified 84.9%

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

   if -2e-78 < y < 5.3000000000000004e28

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-*r/ 86.6%

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

      3. associate-/l* 94.7%

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

      4. sub-neg 94.7%

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

      5. +-commutative 94.7%

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

      6. neg-sub0 94.7%

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

      7. associate-+l- 94.7%

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

      8. sub0-neg 94.7%

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

      9. neg-mul-1 94.7%

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

      10. associate-/r* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in x around inf 82.6%

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

      1. associate-*r/ 82.6%

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

      2. neg-mul-1 82.6%

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

      3. neg-sub0 82.6%

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

      4. associate--r- 82.6%

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

      5. neg-sub0 82.6%

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

      6. neg-mul-1 82.6%

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

      7. +-commutative 82.6%

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

      8. neg-mul-1 82.6%

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

      9. sub-neg 82.6%

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

   6. Simplified 82.6%

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

   if 5.3000000000000004e28 < y < 9.7999999999999999e182

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 70.6%

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

      1. associate-*r/ 70.6%

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

      2. *-commutative 70.6%

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

      3. neg-mul-1 70.6%

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

      4. distribute-lft-neg-in 70.6%

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

      5. *-commutative 70.6%

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

      6. associate-/l* 82.2%

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

      7. neg-sub0 82.2%

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

      8. associate--r- 82.2%

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

      9. neg-sub0 82.2%

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

      10. +-commutative 82.2%

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

      11. sub-neg 82.2%

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

   4. Simplified 82.2%

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

   5. Taylor expanded in t around 0 70.6%

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

      1. associate-*r/ 82.2%

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

   7. Simplified 82.2%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-78}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+182}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]

Alternative 5: 69.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-19} \lor \neg \left(y \leq 1.85 \cdot 10^{-163}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8e-19) (not (<= y 1.85e-163)))
   (* t (/ (- y x) y))
   (* t (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e-19) || !(y <= 1.85e-163)) {
		tmp = t * ((y - 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 <= (-8d-19)) .or. (.not. (y <= 1.85d-163))) then
        tmp = t * ((y - 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 <= -8e-19) || !(y <= 1.85e-163)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8e-19) or not (y <= 1.85e-163):
		tmp = t * ((y - x) / y)
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8e-19) || !(y <= 1.85e-163))
		tmp = Float64(t * Float64(Float64(y - 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 <= -8e-19) || ~((y <= 1.85e-163)))
		tmp = t * ((y - x) / y);
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8e-19], N[Not[LessEqual[y, 1.85e-163]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.9999999999999998e-19 or 1.85e-163 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 58.9%

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

      1. associate-*r/ 58.9%

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

      2. *-commutative 58.9%

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

      3. neg-mul-1 58.9%

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

      4. distribute-lft-neg-in 58.9%

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

      5. *-commutative 58.9%

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

      6. associate-/l* 73.8%

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

      7. neg-sub0 73.8%

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

      8. associate--r- 73.8%

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

      9. neg-sub0 73.8%

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

      10. +-commutative 73.8%

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

      11. sub-neg 73.8%

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

   4. Simplified 73.8%

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

   5. Taylor expanded in t around 0 58.9%

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

      1. associate-*r/ 73.8%

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

   7. Simplified 73.8%

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

   if -7.9999999999999998e-19 < y < 1.85e-163

   1. Initial program 93.5%

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

      1. associate-*l/ 88.3%

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

      2. clear-num 86.9%

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

   3. Applied egg-rr 86.9%

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

   4. Taylor expanded in y around 0 69.2%

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

      1. associate-*r/ 75.0%

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

   6. Simplified 75.0%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-19} \lor \neg \left(y \leq 1.85 \cdot 10^{-163}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]

Alternative 6: 72.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-17} \lor \neg \left(y \leq 7.2 \cdot 10^{-164}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.7e-17) (not (<= y 7.2e-164)))
   (* t (/ (- y x) y))
   (* (- x y) (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.7e-17) || !(y <= 7.2e-164)) {
		tmp = t * ((y - 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 <= (-1.7d-17)) .or. (.not. (y <= 7.2d-164))) then
        tmp = t * ((y - 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 <= -1.7e-17) || !(y <= 7.2e-164)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.7e-17) or not (y <= 7.2e-164):
		tmp = t * ((y - x) / y)
	else:
		tmp = (x - y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.7e-17) || !(y <= 7.2e-164))
		tmp = Float64(t * Float64(Float64(y - 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 <= -1.7e-17) || ~((y <= 7.2e-164)))
		tmp = t * ((y - x) / y);
	else
		tmp = (x - y) * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.7e-17], N[Not[LessEqual[y, 7.2e-164]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6999999999999999e-17 or 7.19999999999999988e-164 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 58.9%

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

      1. associate-*r/ 58.9%

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

      2. *-commutative 58.9%

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

      3. neg-mul-1 58.9%

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

      4. distribute-lft-neg-in 58.9%

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

      5. *-commutative 58.9%

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

      6. associate-/l* 73.8%

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

      7. neg-sub0 73.8%

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

      8. associate--r- 73.8%

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

      9. neg-sub0 73.8%

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

      10. +-commutative 73.8%

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

      11. sub-neg 73.8%

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

   4. Simplified 73.8%

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

   5. Taylor expanded in t around 0 58.9%

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

      1. associate-*r/ 73.8%

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

   7. Simplified 73.8%

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

   if -1.6999999999999999e-17 < y < 7.19999999999999988e-164

   1. Initial program 93.5%

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

   2. Taylor expanded in z around inf 76.3%

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

      1. associate-/l* 81.3%

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

      2. associate-/r/ 80.6%

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

   4. Simplified 80.6%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-17} \lor \neg \left(y \leq 7.2 \cdot 10^{-164}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]

Alternative 7: 62.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-16}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.02e-16) t (if (<= y 6.2e+31) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.02e-16) {
		tmp = t;
	} else if (y <= 6.2e+31) {
		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 <= (-1.02d-16)) then
        tmp = t
    else if (y <= 6.2d+31) 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 <= -1.02e-16) {
		tmp = t;
	} else if (y <= 6.2e+31) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.02e-16:
		tmp = t
	elif y <= 6.2e+31:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.02e-16)
		tmp = t;
	elseif (y <= 6.2e+31)
		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 <= -1.02e-16)
		tmp = t;
	elseif (y <= 6.2e+31)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.02e-16], t, If[LessEqual[y, 6.2e+31], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0200000000000001e-16 or 6.2000000000000004e31 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 62.0%

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

   if -1.0200000000000001e-16 < y < 6.2000000000000004e31

   1. Initial program 95.4%

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

      1. associate-*l/ 87.9%

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

      2. clear-num 86.7%

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

   3. Applied egg-rr 86.7%

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

   4. Taylor expanded in y around 0 60.7%

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

      1. associate-*r/ 66.0%

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

   6. Simplified 66.0%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-16}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 36.8% 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 97.3%

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

2. Taylor expanded in y around inf 34.7%

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

3. Final simplification 34.7%

   \[\leadsto t \]

Developer target: 97.2% 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 2023293 
(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))