Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A

Percentage Accurate: 85.2% → 97.4%

Time: 10.7s

Alternatives: 18

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x + \frac{\left(y - z\right) \cdot t}{a - z} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - z) * t) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{\left(y - z\right) \cdot t}{a - z} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - z) * t) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 3 \cdot 10^{-203}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (/ (* (- y z) t) (- a z)) 3e-203)
   (+ x (* t (/ (- y z) (- a z))))
   (+ x (/ (- y z) (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((((y - z) * t) / (a - z)) <= 3e-203) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((((y - z) * t) / (a - z)) <= 3d-203) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = x + ((y - z) / ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((((y - z) * t) / (a - z)) <= 3e-203) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (((y - z) * t) / (a - z)) <= 3e-203:
		tmp = x + (t * ((y - z) / (a - z)))
	else:
		tmp = x + ((y - z) / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(Float64(y - z) * t) / Float64(a - z)) <= 3e-203)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((((y - z) * t) / (a - z)) <= 3e-203)
		tmp = x + (t * ((y - z) / (a - z)));
	else
		tmp = x + ((y - z) / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], 3e-203], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 3.0000000000000001e-203

   1. Initial program 84.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   if 3.0000000000000001e-203 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 84.2%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 3 \cdot 10^{-203}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 2: 76.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0012:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+113}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.0012)
   (+ t x)
   (if (<= z 7.5e-81)
     (+ x (/ y (/ a t)))
     (if (<= z 5e+113) (- x (* t (/ y z))) (+ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.0012) {
		tmp = t + x;
	} else if (z <= 7.5e-81) {
		tmp = x + (y / (a / t));
	} else if (z <= 5e+113) {
		tmp = x - (t * (y / z));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-0.0012d0)) then
        tmp = t + x
    else if (z <= 7.5d-81) then
        tmp = x + (y / (a / t))
    else if (z <= 5d+113) then
        tmp = x - (t * (y / z))
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.0012) {
		tmp = t + x;
	} else if (z <= 7.5e-81) {
		tmp = x + (y / (a / t));
	} else if (z <= 5e+113) {
		tmp = x - (t * (y / z));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.0012:
		tmp = t + x
	elif z <= 7.5e-81:
		tmp = x + (y / (a / t))
	elif z <= 5e+113:
		tmp = x - (t * (y / z))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.0012)
		tmp = Float64(t + x);
	elseif (z <= 7.5e-81)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 5e+113)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.0012)
		tmp = t + x;
	elseif (z <= 7.5e-81)
		tmp = x + (y / (a / t));
	elseif (z <= 5e+113)
		tmp = x - (t * (y / z));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.0012], N[(t + x), $MachinePrecision], If[LessEqual[z, 7.5e-81], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+113], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.00119999999999999989 or 5e113 < z

   1. Initial program 68.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 82.4%

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

   if -0.00119999999999999989 < z < 7.50000000000000018e-81

   1. Initial program 94.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in z around 0 74.4%

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

      1. associate-/l* 78.3%

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

   6. Simplified 78.3%

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

   if 7.50000000000000018e-81 < z < 5e113

   1. Initial program 95.4%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around inf 74.4%

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

   5. Taylor expanded in a around 0 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

      4. associate-/l* 69.9%

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

      5. associate-/r/ 67.6%

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

   7. Simplified 67.6%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0012:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+113}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 3: 76.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00042:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-78}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+112}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.00042)
   (+ t x)
   (if (<= z 1.85e-78)
     (+ x (/ y (/ a t)))
     (if (<= z 2.2e+112) (- x (/ (* y t) z)) (+ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.00042) {
		tmp = t + x;
	} else if (z <= 1.85e-78) {
		tmp = x + (y / (a / t));
	} else if (z <= 2.2e+112) {
		tmp = x - ((y * t) / z);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-0.00042d0)) then
        tmp = t + x
    else if (z <= 1.85d-78) then
        tmp = x + (y / (a / t))
    else if (z <= 2.2d+112) then
        tmp = x - ((y * t) / z)
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.00042) {
		tmp = t + x;
	} else if (z <= 1.85e-78) {
		tmp = x + (y / (a / t));
	} else if (z <= 2.2e+112) {
		tmp = x - ((y * t) / z);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.00042:
		tmp = t + x
	elif z <= 1.85e-78:
		tmp = x + (y / (a / t))
	elif z <= 2.2e+112:
		tmp = x - ((y * t) / z)
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.00042)
		tmp = Float64(t + x);
	elseif (z <= 1.85e-78)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 2.2e+112)
		tmp = Float64(x - Float64(Float64(y * t) / z));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.00042)
		tmp = t + x;
	elseif (z <= 1.85e-78)
		tmp = x + (y / (a / t));
	elseif (z <= 2.2e+112)
		tmp = x - ((y * t) / z);
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.00042], N[(t + x), $MachinePrecision], If[LessEqual[z, 1.85e-78], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+112], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2000000000000002e-4 or 2.1999999999999999e112 < z

   1. Initial program 68.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 82.4%

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

   if -4.2000000000000002e-4 < z < 1.85000000000000003e-78

   1. Initial program 94.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in z around 0 74.4%

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

      1. associate-/l* 78.3%

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

   6. Simplified 78.3%

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

   if 1.85000000000000003e-78 < z < 2.1999999999999999e112

   1. Initial program 95.4%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around inf 74.4%

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

   5. Taylor expanded in a around 0 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

      4. associate-/l* 69.9%

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

      5. associate-/r/ 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in y around 0 67.8%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00042:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-78}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+112}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 4: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.82 \cdot 10^{-124} \lor \neg \left(z \leq 3.3 \cdot 10^{-80}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.82e-124) (not (<= z 3.3e-80)))
   (+ x (* t (- 1.0 (/ y z))))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.82e-124) || !(z <= 3.3e-80)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.82d-124)) .or. (.not. (z <= 3.3d-80))) then
        tmp = x + (t * (1.0d0 - (y / z)))
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.82e-124) || !(z <= 3.3e-80)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.82e-124) or not (z <= 3.3e-80):
		tmp = x + (t * (1.0 - (y / z)))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.82e-124) || !(z <= 3.3e-80))
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.82e-124) || ~((z <= 3.3e-80)))
		tmp = x + (t * (1.0 - (y / z)));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.82e-124], N[Not[LessEqual[z, 3.3e-80]], $MachinePrecision]], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.82000000000000009e-124 or 3.3e-80 < z

   1. Initial program 78.4%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.3%

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

   3. Simplified 99.3%

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

      1. clear-num 99.3%

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

      2. associate-/r/ 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in a around 0 82.8%

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

      1. div-sub 82.8%

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

      2. sub-neg 82.8%

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

      3. *-inverses 82.8%

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

      4. metadata-eval 82.8%

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

      5. distribute-lft-in 82.8%

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

      6. metadata-eval 82.8%

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

      7. +-commutative 82.8%

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

      8. mul-1-neg 82.8%

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

      9. unsub-neg 82.8%

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

   8. Simplified 82.8%

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

   if -1.82000000000000009e-124 < z < 3.3e-80

   1. Initial program 95.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in z around 0 81.6%

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

      1. associate-/l* 84.5%

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

   6. Simplified 84.5%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.82 \cdot 10^{-124} \lor \neg \left(z \leq 3.3 \cdot 10^{-80}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 5: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.031 \lor \neg \left(z \leq 5.6 \cdot 10^{+120}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -0.031) (not (<= z 5.6e+120)))
   (+ x (* t (- 1.0 (/ y z))))
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.031) || !(z <= 5.6e+120)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-0.031d0)) .or. (.not. (z <= 5.6d+120))) then
        tmp = x + (t * (1.0d0 - (y / z)))
    else
        tmp = x + (t * (y / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.031) || !(z <= 5.6e+120)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -0.031) or not (z <= 5.6e+120):
		tmp = x + (t * (1.0 - (y / z)))
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -0.031) || !(z <= 5.6e+120))
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -0.031) || ~((z <= 5.6e+120)))
		tmp = x + (t * (1.0 - (y / z)));
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -0.031], N[Not[LessEqual[z, 5.6e+120]], $MachinePrecision]], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.031 or 5.6000000000000001e120 < z

   1. Initial program 68.2%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 91.8%

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

      1. div-sub 91.8%

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

      2. sub-neg 91.8%

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

      3. *-inverses 91.8%

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

      4. metadata-eval 91.8%

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

      5. distribute-lft-in 91.8%

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

      6. metadata-eval 91.8%

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

      7. +-commutative 91.8%

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

      8. mul-1-neg 91.8%

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

      9. unsub-neg 91.8%

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

   8. Simplified 91.8%

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

   if -0.031 < z < 5.6000000000000001e120

   1. Initial program 95.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in y around inf 83.4%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.031 \lor \neg \left(z \leq 5.6 \cdot 10^{+120}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 6: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-59} \lor \neg \left(y \leq 1.45 \cdot 10^{-113}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3e-59) (not (<= y 1.45e-113)))
   (+ x (* t (/ y (- a z))))
   (- x (* z (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3e-59) || !(y <= 1.45e-113)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x - (z * (t / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-3d-59)) .or. (.not. (y <= 1.45d-113))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x - (z * (t / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3e-59) || !(y <= 1.45e-113)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x - (z * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3e-59) or not (y <= 1.45e-113):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x - (z * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3e-59) || !(y <= 1.45e-113))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x - Float64(z * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3e-59) || ~((y <= 1.45e-113)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x - (z * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3e-59], N[Not[LessEqual[y, 1.45e-113]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0000000000000001e-59 or 1.45000000000000002e-113 < y

   1. Initial program 83.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in y around inf 85.5%

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

   if -3.0000000000000001e-59 < y < 1.45000000000000002e-113

   1. Initial program 85.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

      1. associate-/r/ 94.6%

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

      2. div-inv 94.4%

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

      3. associate-/r* 97.5%

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

   5. Applied egg-rr 97.5%

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

   6. Taylor expanded in y around 0 81.7%

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

      1. +-commutative 81.7%

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

      2. mul-1-neg 81.7%

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

      3. *-commutative 81.7%

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

      4. associate-*r/ 90.2%

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

      5. sub-neg 90.2%

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

   8. Simplified 90.2%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-59} \lor \neg \left(y \leq 1.45 \cdot 10^{-113}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \end{array} \]

Alternative 7: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-59} \lor \neg \left(y \leq 7.6 \cdot 10^{-112}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.9e-59) (not (<= y 7.6e-112)))
   (+ x (* t (/ y (- a z))))
   (- x (/ t (+ (/ a z) -1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.9e-59) || !(y <= 7.6e-112)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x - (t / ((a / z) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.9d-59)) .or. (.not. (y <= 7.6d-112))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x - (t / ((a / z) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.9e-59) || !(y <= 7.6e-112)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x - (t / ((a / z) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.9e-59) or not (y <= 7.6e-112):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x - (t / ((a / z) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.9e-59) || !(y <= 7.6e-112))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x - Float64(t / Float64(Float64(a / z) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.9e-59) || ~((y <= 7.6e-112)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x - (t / ((a / z) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.9e-59], N[Not[LessEqual[y, 7.6e-112]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.89999999999999992e-59 or 7.59999999999999989e-112 < y

   1. Initial program 83.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in y around inf 85.5%

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

   if -1.89999999999999992e-59 < y < 7.59999999999999989e-112

   1. Initial program 85.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in y around 0 81.7%

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

      1. +-commutative 81.7%

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

      2. mul-1-neg 81.7%

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

      3. *-commutative 81.7%

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

      4. associate-*r/ 90.2%

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

      5. unsub-neg 90.2%

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

      6. associate-*r/ 81.7%

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

      7. *-commutative 81.7%

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

      8. associate-/l* 94.5%

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

      9. div-sub 94.5%

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

      10. *-inverses 94.5%

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

   6. Simplified 94.5%

      \[\leadsto \color{blue}{x - \frac{t}{\frac{a}{z} - 1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-59} \lor \neg \left(y \leq 7.6 \cdot 10^{-112}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \end{array} \]

Alternative 8: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-59} \lor \neg \left(y \leq 3.1 \cdot 10^{-112}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.15e-59) (not (<= y 3.1e-112)))
   (+ x (* t (/ y (- a z))))
   (- x (* t (/ z (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.15e-59) || !(y <= 3.1e-112)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x - (t * (z / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.15d-59)) .or. (.not. (y <= 3.1d-112))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x - (t * (z / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.15e-59) || !(y <= 3.1e-112)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x - (t * (z / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.15e-59) or not (y <= 3.1e-112):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x - (t * (z / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.15e-59) || !(y <= 3.1e-112))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x - Float64(t * Float64(z / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.15e-59) || ~((y <= 3.1e-112)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x - (t * (z / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.15e-59], N[Not[LessEqual[y, 3.1e-112]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1499999999999999e-59 or 3.0999999999999998e-112 < y

   1. Initial program 83.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in y around inf 85.5%

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

   if -1.1499999999999999e-59 < y < 3.0999999999999998e-112

   1. Initial program 85.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in y around 0 94.5%

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

      1. neg-mul-1 94.5%

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

      2. distribute-neg-frac 94.5%

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

   6. Simplified 94.5%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-59} \lor \neg \left(y \leq 3.1 \cdot 10^{-112}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \end{array} \]

Alternative 9: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0215:\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+120}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.0215)
   (+ x (- t (* t (/ y z))))
   (if (<= z 5.6e+120) (+ x (* t (/ y (- a z)))) (+ x (* t (- 1.0 (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.0215) {
		tmp = x + (t - (t * (y / z)));
	} else if (z <= 5.6e+120) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (t * (1.0 - (y / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-0.0215d0)) then
        tmp = x + (t - (t * (y / z)))
    else if (z <= 5.6d+120) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + (t * (1.0d0 - (y / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.0215) {
		tmp = x + (t - (t * (y / z)));
	} else if (z <= 5.6e+120) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (t * (1.0 - (y / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.0215:
		tmp = x + (t - (t * (y / z)))
	elif z <= 5.6e+120:
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (t * (1.0 - (y / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.0215)
		tmp = Float64(x + Float64(t - Float64(t * Float64(y / z))));
	elseif (z <= 5.6e+120)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.0215)
		tmp = x + (t - (t * (y / z)));
	elseif (z <= 5.6e+120)
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (t * (1.0 - (y / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.0215], N[(x + N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+120], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.021499999999999998

   1. Initial program 74.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in a around 0 90.1%

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

      1. neg-mul-1 90.1%

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

      2. distribute-neg-frac 90.1%

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

   6. Simplified 90.1%

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

   7. Taylor expanded in y around 0 82.2%

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

      1. +-commutative 82.2%

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

      2. mul-1-neg 82.2%

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

      3. unsub-neg 82.2%

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

      4. associate-/l* 91.8%

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

      5. associate-/r/ 91.8%

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

   9. Simplified 91.8%

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

   if -0.021499999999999998 < z < 5.6000000000000001e120

   1. Initial program 95.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in y around inf 83.4%

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

   if 5.6000000000000001e120 < z

   1. Initial program 59.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 91.8%

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

      1. div-sub 91.9%

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

      2. sub-neg 91.9%

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

      3. *-inverses 91.9%

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

      4. metadata-eval 91.9%

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

      5. distribute-lft-in 91.9%

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

      6. metadata-eval 91.9%

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

      7. +-commutative 91.9%

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

      8. mul-1-neg 91.9%

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

      9. unsub-neg 91.9%

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

   8. Simplified 91.9%

      \[\leadsto x + \color{blue}{\left(1 - \frac{y}{z}\right)} \cdot t \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0215:\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+120}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 10: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0046 \lor \neg \left(z \leq 3.7 \cdot 10^{-16}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -0.0046) (not (<= z 3.7e-16))) (+ t x) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.0046) || !(z <= 3.7e-16)) {
		tmp = t + x;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-0.0046d0)) .or. (.not. (z <= 3.7d-16))) then
        tmp = t + x
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.0046) || !(z <= 3.7e-16)) {
		tmp = t + x;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -0.0046) or not (z <= 3.7e-16):
		tmp = t + x
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -0.0046) || !(z <= 3.7e-16))
		tmp = Float64(t + x);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -0.0046) || ~((z <= 3.7e-16)))
		tmp = t + x;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -0.0046], N[Not[LessEqual[z, 3.7e-16]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0045999999999999999 or 3.7e-16 < z

   1. Initial program 74.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.3%

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

   if -0.0045999999999999999 < z < 3.7e-16

   1. Initial program 94.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around 0 72.5%

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

      1. associate-/l* 76.8%

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

   6. Simplified 76.8%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0046 \lor \neg \left(z \leq 3.7 \cdot 10^{-16}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 11: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.000155:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-14}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.000155) (+ t x) (if (<= z 1.9e-14) (+ x (* t (/ y a))) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.000155) {
		tmp = t + x;
	} else if (z <= 1.9e-14) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-0.000155d0)) then
        tmp = t + x
    else if (z <= 1.9d-14) then
        tmp = x + (t * (y / a))
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.000155) {
		tmp = t + x;
	} else if (z <= 1.9e-14) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.000155:
		tmp = t + x
	elif z <= 1.9e-14:
		tmp = x + (t * (y / a))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.000155)
		tmp = Float64(t + x);
	elseif (z <= 1.9e-14)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.000155)
		tmp = t + x;
	elseif (z <= 1.9e-14)
		tmp = x + (t * (y / a));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.000155], N[(t + x), $MachinePrecision], If[LessEqual[z, 1.9e-14], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55e-4 or 1.9000000000000001e-14 < z

   1. Initial program 74.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.3%

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

   if -1.55e-4 < z < 1.9000000000000001e-14

   1. Initial program 94.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around 0 74.6%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.000155:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-14}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 12: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0002:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-19}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.0002) (+ t x) (if (<= z 7.5e-19) (+ x (* y (/ t a))) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.0002) {
		tmp = t + x;
	} else if (z <= 7.5e-19) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-0.0002d0)) then
        tmp = t + x
    else if (z <= 7.5d-19) then
        tmp = x + (y * (t / a))
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.0002) {
		tmp = t + x;
	} else if (z <= 7.5e-19) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.0002:
		tmp = t + x
	elif z <= 7.5e-19:
		tmp = x + (y * (t / a))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.0002)
		tmp = Float64(t + x);
	elseif (z <= 7.5e-19)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.0002)
		tmp = t + x;
	elseif (z <= 7.5e-19)
		tmp = x + (y * (t / a));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.0002], N[(t + x), $MachinePrecision], If[LessEqual[z, 7.5e-19], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000001e-4 or 7.49999999999999957e-19 < z

   1. Initial program 74.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.3%

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

   if -2.0000000000000001e-4 < z < 7.49999999999999957e-19

   1. Initial program 94.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around 0 72.5%

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

      1. associate-/l* 76.8%

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

   6. Simplified 76.8%

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

      1. div-inv 76.2%

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

      2. clear-num 76.2%

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

   8. Applied egg-rr 76.2%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0002:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-19}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 13: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (t * ((y - z) / (a - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.4%

   \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
2. Step-by-step derivation

   1. associate-*l/ 97.2%

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

3. Simplified 97.2%

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

4. Final simplification 97.2%

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

Alternative 14: 60.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+101}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 4.6e+101) (+ t x) (* t (- 1.0 (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 4.6e+101) {
		tmp = t + x;
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 4.6d+101) then
        tmp = t + x
    else
        tmp = t * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 4.6e+101) {
		tmp = t + x;
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 4.6e+101:
		tmp = t + x
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 4.6e+101)
		tmp = Float64(t + x);
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 4.6e+101)
		tmp = t + x;
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 4.6e+101], N[(t + x), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.6000000000000003e101

   1. Initial program 84.4%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around inf 63.8%

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

   if 4.6000000000000003e101 < y

   1. Initial program 84.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in a around 0 75.0%

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

      1. neg-mul-1 75.0%

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

      2. distribute-neg-frac 75.0%

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

   6. Simplified 75.0%

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

   7. Taylor expanded in t around -inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. *-commutative 55.2%

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

      3. distribute-rgt-neg-in 55.2%

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

      4. mul-1-neg 55.2%

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

      5. sub-neg 55.2%

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

      6. metadata-eval 55.2%

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

      7. distribute-lft-in 55.2%

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

      8. metadata-eval 55.2%

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

      9. +-commutative 55.2%

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

      10. mul-1-neg 55.2%

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

      11. unsub-neg 55.2%

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

   9. Simplified 55.2%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+101}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 15: 59.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.3 \cdot 10^{+150}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 2.3e+150) (+ t x) (* t (/ (- y) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 2.3e+150) {
		tmp = t + x;
	} else {
		tmp = t * (-y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 2.3d+150) then
        tmp = t + x
    else
        tmp = t * (-y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 2.3e+150) {
		tmp = t + x;
	} else {
		tmp = t * (-y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 2.3e+150:
		tmp = t + x
	else:
		tmp = t * (-y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 2.3e+150)
		tmp = Float64(t + x);
	else
		tmp = Float64(t * Float64(Float64(-y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 2.3e+150)
		tmp = t + x;
	else
		tmp = t * (-y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 2.3e+150], N[(t + x), $MachinePrecision], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.30000000000000001e150

   1. Initial program 83.4%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around inf 62.6%

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

   if 2.30000000000000001e150 < y

   1. Initial program 91.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in a around 0 79.5%

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

      1. neg-mul-1 79.5%

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

      2. distribute-neg-frac 79.5%

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

   6. Simplified 79.5%

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

   7. Taylor expanded in t around -inf 56.7%

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

      1. mul-1-neg 56.7%

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

      2. *-commutative 56.7%

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

      3. distribute-rgt-neg-in 56.7%

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

      4. mul-1-neg 56.7%

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

      5. sub-neg 56.7%

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

      6. metadata-eval 56.7%

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

      7. distribute-lft-in 56.7%

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

      8. metadata-eval 56.7%

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

      9. +-commutative 56.7%

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

      10. mul-1-neg 56.7%

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

      11. unsub-neg 56.7%

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

   9. Simplified 56.7%

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

   10. Taylor expanded in y around inf 55.5%

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

       1. mul-1-neg 55.5%

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

       2. associate-*l/ 56.4%

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

       3. distribute-rgt-neg-in 56.4%

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

   12. Simplified 56.4%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.3 \cdot 10^{+150}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \end{array} \]

Alternative 16: 62.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-174}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-145}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e-174) (+ t x) (if (<= z 1.5e-145) x (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e-174) {
		tmp = t + x;
	} else if (z <= 1.5e-145) {
		tmp = x;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.5d-174)) then
        tmp = t + x
    else if (z <= 1.5d-145) then
        tmp = x
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e-174) {
		tmp = t + x;
	} else if (z <= 1.5e-145) {
		tmp = x;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e-174:
		tmp = t + x
	elif z <= 1.5e-145:
		tmp = x
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e-174)
		tmp = Float64(t + x);
	elseif (z <= 1.5e-145)
		tmp = x;
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e-174)
		tmp = t + x;
	elseif (z <= 1.5e-145)
		tmp = x;
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e-174], N[(t + x), $MachinePrecision], If[LessEqual[z, 1.5e-145], x, N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.50000000000000009e-174 or 1.49999999999999996e-145 < z

   1. Initial program 80.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around inf 64.8%

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

   if -6.50000000000000009e-174 < z < 1.49999999999999996e-145

   1. Initial program 97.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in x around inf 53.6%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-174}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-145}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 17: 50.4% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t -6.5e+17) t x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e+17) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.5d+17)) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e+17) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.5e+17:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.5e+17)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.5e+17)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.5e+17], t, x]

Derivation

1. Split input into 2 regimes

2. if t < -6.5e17

   1. Initial program 69.1%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in a around 0 62.5%

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

      1. neg-mul-1 62.5%

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

      2. distribute-neg-frac 62.5%

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

   6. Simplified 62.5%

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

   7. Taylor expanded in t around -inf 60.2%

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

      1. mul-1-neg 60.2%

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

      2. *-commutative 60.2%

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

      3. distribute-rgt-neg-in 60.2%

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

      4. mul-1-neg 60.2%

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

      5. sub-neg 60.2%

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

      6. metadata-eval 60.2%

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

      7. distribute-lft-in 60.2%

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

      8. metadata-eval 60.2%

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

      9. +-commutative 60.2%

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

      10. mul-1-neg 60.2%

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

      11. unsub-neg 60.2%

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

   9. Simplified 60.2%

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

   10. Taylor expanded in y around 0 39.2%

       \[\leadsto t \cdot \color{blue}{1} \]

   if -6.5e17 < t

   1. Initial program 90.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in x around inf 58.9%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 50.6% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

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

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 84.4%

   \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
2. Step-by-step derivation

   1. associate-*l/ 97.2%

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

3. Simplified 97.2%

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

4. Taylor expanded in x around inf 47.1%

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

5. Final simplification 47.1%

   \[\leadsto x \]

Developer target: 99.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023192 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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