Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B

Percentage Accurate: 85.1% → 96.0%

Time: 12.6s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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 - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((z - t) / ((a - t) / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.7%

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

   1. *-commutative 85.7%

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

   2. associate-/l* 98.2%

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

3. Simplified 98.2%

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

4. Final simplification 98.2%

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

Alternative 2: 94.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{elif}\;t_1 \leq 10^{+298}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) (- a t))))
   (if (<= t_1 (- INFINITY))
     (- x (/ y (/ t (- z t))))
     (if (<= t_1 1e+298) (+ x t_1) (* y (/ (- z t) (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (a - t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x - (y / (t / (z - t)));
	} else if (t_1 <= 1e+298) {
		tmp = x + t_1;
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (a - t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x - (y / (t / (z - t)));
	} else if (t_1 <= 1e+298) {
		tmp = x + t_1;
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((z - t) * y) / (a - t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x - (y / (t / (z - t)))
	elif t_1 <= 1e+298:
		tmp = x + t_1
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x - Float64(y / Float64(t / Float64(z - t))));
	elseif (t_1 <= 1e+298)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((z - t) * y) / (a - t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x - (y / (t / (z - t)));
	elseif (t_1 <= 1e+298)
		tmp = x + t_1;
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x - N[(y / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+298], N[(x + t$95$1), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -inf.0

   1. Initial program 33.6%

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

   2. Taylor expanded in a around 0 33.1%

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

      1. mul-1-neg 33.1%

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

      2. *-commutative 33.1%

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

      3. associate-/l* 77.6%

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

   4. Simplified 77.6%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 9.9999999999999996e297

   1. Initial program 99.8%

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

   if 9.9999999999999996e297 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 24.3%

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

      1. +-commutative 24.3%

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

      2. associate-*l/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 24.3%

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

      1. associate-*l/ 77.6%

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

   6. Applied egg-rr 77.6%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a - t} \leq -\infty:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a - t} \leq 10^{+298}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 3: 77.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-27}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-50}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.6e+22)
   (+ x y)
   (if (<= t -4.6e-27)
     (+ x (* y (/ z a)))
     (if (<= t -8.2e-50)
       (+ x y)
       (if (<= t 6.5e+29) (+ x (/ z (/ a y))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.6e+22) {
		tmp = x + y;
	} else if (t <= -4.6e-27) {
		tmp = x + (y * (z / a));
	} else if (t <= -8.2e-50) {
		tmp = x + y;
	} else if (t <= 6.5e+29) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x + y;
	}
	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 <= (-2.6d+22)) then
        tmp = x + y
    else if (t <= (-4.6d-27)) then
        tmp = x + (y * (z / a))
    else if (t <= (-8.2d-50)) then
        tmp = x + y
    else if (t <= 6.5d+29) then
        tmp = x + (z / (a / y))
    else
        tmp = x + y
    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 <= -2.6e+22) {
		tmp = x + y;
	} else if (t <= -4.6e-27) {
		tmp = x + (y * (z / a));
	} else if (t <= -8.2e-50) {
		tmp = x + y;
	} else if (t <= 6.5e+29) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.6e+22:
		tmp = x + y
	elif t <= -4.6e-27:
		tmp = x + (y * (z / a))
	elif t <= -8.2e-50:
		tmp = x + y
	elif t <= 6.5e+29:
		tmp = x + (z / (a / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.6e+22)
		tmp = Float64(x + y);
	elseif (t <= -4.6e-27)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= -8.2e-50)
		tmp = Float64(x + y);
	elseif (t <= 6.5e+29)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.6e+22)
		tmp = x + y;
	elseif (t <= -4.6e-27)
		tmp = x + (y * (z / a));
	elseif (t <= -8.2e-50)
		tmp = x + y;
	elseif (t <= 6.5e+29)
		tmp = x + (z / (a / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.6e+22], N[(x + y), $MachinePrecision], If[LessEqual[t, -4.6e-27], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.2e-50], N[(x + y), $MachinePrecision], If[LessEqual[t, 6.5e+29], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6e22 or -4.5999999999999999e-27 < t < -8.19999999999999971e-50 or 6.49999999999999971e29 < t

   1. Initial program 74.9%

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

   2. Taylor expanded in t around inf 79.2%

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

   if -2.6e22 < t < -4.5999999999999999e-27

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-/l* 78.7%

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

      3. associate-/r/ 96.2%

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

   4. Applied egg-rr 96.2%

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

   if -8.19999999999999971e-50 < t < 6.49999999999999971e29

   1. Initial program 95.2%

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

   2. Taylor expanded in t around 0 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-/l* 84.7%

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

      3. add-cube-cbrt 84.4%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}{\frac{a}{y}} + x \]

      4. *-un-lft-identity 84.4%

         \[\leadsto \frac{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}{\color{blue}{1 \cdot \frac{a}{y}}} + x \]

      5. times-frac 84.4%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{1} \cdot \frac{\sqrt[3]{z}}{\frac{a}{y}}} + x \]

      6. pow2 84.4%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{z}}{\frac{a}{y}} + x \]

   4. Applied egg-rr 84.4%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{z}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z}}{\frac{a}{y}}} + x \]
   5. Step-by-step derivation

      1. /-rgt-identity 84.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{z}\right)}^{2}} \cdot \frac{\sqrt[3]{z}}{\frac{a}{y}} + x \]

      2. associate-*r/ 84.4%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{z}\right)}^{2} \cdot \sqrt[3]{z}}{\frac{a}{y}}} + x \]

      3. unpow2 84.4%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)} \cdot \sqrt[3]{z}}{\frac{a}{y}} + x \]

      4. rem-3cbrt-lft 84.7%

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

   6. Simplified 84.7%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-27}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-50}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 77.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+94}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-39}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-49}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.5e+94)
   (+ x y)
   (if (<= t -2.3e-39)
     (- x (* z (/ y t)))
     (if (<= t -3.5e-49)
       (+ x y)
       (if (<= t 4.6e+29) (+ x (/ z (/ a y))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.5e+94) {
		tmp = x + y;
	} else if (t <= -2.3e-39) {
		tmp = x - (z * (y / t));
	} else if (t <= -3.5e-49) {
		tmp = x + y;
	} else if (t <= 4.6e+29) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x + y;
	}
	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 <= (-1.5d+94)) then
        tmp = x + y
    else if (t <= (-2.3d-39)) then
        tmp = x - (z * (y / t))
    else if (t <= (-3.5d-49)) then
        tmp = x + y
    else if (t <= 4.6d+29) then
        tmp = x + (z / (a / y))
    else
        tmp = x + y
    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 <= -1.5e+94) {
		tmp = x + y;
	} else if (t <= -2.3e-39) {
		tmp = x - (z * (y / t));
	} else if (t <= -3.5e-49) {
		tmp = x + y;
	} else if (t <= 4.6e+29) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.5e+94:
		tmp = x + y
	elif t <= -2.3e-39:
		tmp = x - (z * (y / t))
	elif t <= -3.5e-49:
		tmp = x + y
	elif t <= 4.6e+29:
		tmp = x + (z / (a / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.5e+94)
		tmp = Float64(x + y);
	elseif (t <= -2.3e-39)
		tmp = Float64(x - Float64(z * Float64(y / t)));
	elseif (t <= -3.5e-49)
		tmp = Float64(x + y);
	elseif (t <= 4.6e+29)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.5e+94)
		tmp = x + y;
	elseif (t <= -2.3e-39)
		tmp = x - (z * (y / t));
	elseif (t <= -3.5e-49)
		tmp = x + y;
	elseif (t <= 4.6e+29)
		tmp = x + (z / (a / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.5e+94], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.3e-39], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.5e-49], N[(x + y), $MachinePrecision], If[LessEqual[t, 4.6e+29], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.5e94 or -2.30000000000000008e-39 < t < -3.50000000000000006e-49 or 4.6000000000000002e29 < t

   1. Initial program 68.5%

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

   2. Taylor expanded in t around inf 85.3%

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

   if -1.5e94 < t < -2.30000000000000008e-39

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 75.3%

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

      1. associate-*l/ 73.4%

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

      2. *-commutative 73.4%

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

   4. Simplified 73.4%

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

   5. Taylor expanded in a around 0 70.0%

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

      1. +-commutative 70.0%

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

      2. mul-1-neg 70.0%

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

      3. unsub-neg 70.0%

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

      4. *-commutative 70.0%

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

      5. associate-/l* 70.0%

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

   7. Simplified 70.0%

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

      1. clear-num 69.9%

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

      2. associate-/r/ 70.0%

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

      3. clear-num 70.0%

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

   9. Applied egg-rr 70.0%

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

   if -3.50000000000000006e-49 < t < 4.6000000000000002e29

   1. Initial program 95.2%

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

   2. Taylor expanded in t around 0 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-/l* 84.7%

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

      3. add-cube-cbrt 84.4%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}{\frac{a}{y}} + x \]

      4. *-un-lft-identity 84.4%

         \[\leadsto \frac{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}{\color{blue}{1 \cdot \frac{a}{y}}} + x \]

      5. times-frac 84.4%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{1} \cdot \frac{\sqrt[3]{z}}{\frac{a}{y}}} + x \]

      6. pow2 84.4%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{z}}{\frac{a}{y}} + x \]

   4. Applied egg-rr 84.4%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{z}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z}}{\frac{a}{y}}} + x \]
   5. Step-by-step derivation

      1. /-rgt-identity 84.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{z}\right)}^{2}} \cdot \frac{\sqrt[3]{z}}{\frac{a}{y}} + x \]

      2. associate-*r/ 84.4%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{z}\right)}^{2} \cdot \sqrt[3]{z}}{\frac{a}{y}}} + x \]

      3. unpow2 84.4%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)} \cdot \sqrt[3]{z}}{\frac{a}{y}} + x \]

      4. rem-3cbrt-lft 84.7%

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

   6. Simplified 84.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+94}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-39}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-49}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-84}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.5e-84)
   (+ x y)
   (if (<= t 3.4e-190)
     x
     (if (<= t 4e-122) (* y (/ z (- a t))) (if (<= t 7.2e+22) x (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.5e-84) {
		tmp = x + y;
	} else if (t <= 3.4e-190) {
		tmp = x;
	} else if (t <= 4e-122) {
		tmp = y * (z / (a - t));
	} else if (t <= 7.2e+22) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	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 <= (-8.5d-84)) then
        tmp = x + y
    else if (t <= 3.4d-190) then
        tmp = x
    else if (t <= 4d-122) then
        tmp = y * (z / (a - t))
    else if (t <= 7.2d+22) then
        tmp = x
    else
        tmp = x + y
    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 <= -8.5e-84) {
		tmp = x + y;
	} else if (t <= 3.4e-190) {
		tmp = x;
	} else if (t <= 4e-122) {
		tmp = y * (z / (a - t));
	} else if (t <= 7.2e+22) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.5e-84:
		tmp = x + y
	elif t <= 3.4e-190:
		tmp = x
	elif t <= 4e-122:
		tmp = y * (z / (a - t))
	elif t <= 7.2e+22:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.5e-84)
		tmp = Float64(x + y);
	elseif (t <= 3.4e-190)
		tmp = x;
	elseif (t <= 4e-122)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 7.2e+22)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8.5e-84)
		tmp = x + y;
	elseif (t <= 3.4e-190)
		tmp = x;
	elseif (t <= 4e-122)
		tmp = y * (z / (a - t));
	elseif (t <= 7.2e+22)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.5e-84], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.4e-190], x, If[LessEqual[t, 4e-122], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+22], x, N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.4999999999999994e-84 or 7.2e22 < t

   1. Initial program 78.2%

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

   2. Taylor expanded in t around inf 76.1%

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

   if -8.4999999999999994e-84 < t < 3.39999999999999981e-190 or 4.00000000000000024e-122 < t < 7.2e22

   1. Initial program 96.3%

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

   2. Taylor expanded in x around inf 63.9%

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

   if 3.39999999999999981e-190 < t < 4.00000000000000024e-122

   1. Initial program 79.4%

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

      1. +-commutative 79.4%

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

      2. associate-*l/ 89.7%

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

      3. fma-def 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in x around 0 68.9%

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

      1. associate-*l/ 78.7%

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

   6. Applied egg-rr 78.7%

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

   7. Taylor expanded in z around inf 68.7%

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

      1. *-commutative 68.7%

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

      2. associate-/l* 88.8%

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

      3. associate-/r/ 78.5%

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

   9. Simplified 78.5%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-84}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+94} \lor \neg \left(t \leq 8 \cdot 10^{+30}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.8e+94) (not (<= t 8e+30)))
   (+ x y)
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.8e+94) || !(t <= 8e+30)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (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 ((t <= (-1.8d+94)) .or. (.not. (t <= 8d+30))) then
        tmp = x + y
    else
        tmp = x + (z * (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 ((t <= -1.8e+94) || !(t <= 8e+30)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.8e+94) or not (t <= 8e+30):
		tmp = x + y
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.8e+94) || !(t <= 8e+30))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.8e+94) || ~((t <= 8e+30)))
		tmp = x + y;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.8e+94], N[Not[LessEqual[t, 8e+30]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.79999999999999996e94 or 8.0000000000000002e30 < t

   1. Initial program 66.4%

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

   2. Taylor expanded in t around inf 84.3%

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

   if -1.79999999999999996e94 < t < 8.0000000000000002e30

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 86.2%

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

      1. associate-*l/ 88.1%

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

      2. *-commutative 88.1%

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

   4. Simplified 88.1%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+94} \lor \neg \left(t \leq 8 \cdot 10^{+30}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 7: 88.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+20} \lor \neg \left(z \leq 185\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.6e+20) (not (<= z 185.0)))
   (+ x (* z (/ y (- a t))))
   (- x (/ y (+ (/ a t) -1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+20) || !(z <= 185.0)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y / ((a / t) + -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 ((z <= (-2.6d+20)) .or. (.not. (z <= 185.0d0))) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x - (y / ((a / t) + (-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 ((z <= -2.6e+20) || !(z <= 185.0)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y / ((a / t) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.6e+20) or not (z <= 185.0):
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x - (y / ((a / t) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.6e+20) || !(z <= 185.0))
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.6e+20) || ~((z <= 185.0)))
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x - (y / ((a / t) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.6e+20], N[Not[LessEqual[z, 185.0]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e20 or 185 < z

   1. Initial program 82.4%

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

   2. Taylor expanded in z around inf 83.4%

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

      1. associate-*l/ 91.9%

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

      2. *-commutative 91.9%

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

   4. Simplified 91.9%

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

   if -2.6e20 < z < 185

   1. Initial program 88.0%

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

      1. +-commutative 88.0%

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

      2. associate-*l/ 96.9%

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

      3. fma-def 96.9%

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

   3. Simplified 96.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)} \]
   4. Step-by-step derivation

      1. fma-udef 96.9%

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

      2. associate-*l/ 88.0%

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

      3. associate-/l* 99.3%

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

      4. div-inv 99.3%

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

      5. clear-num 99.3%

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

   5. Applied egg-rr 99.3%

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

   6. Taylor expanded in z around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. mul-1-neg 79.9%

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

      3. unsub-neg 79.9%

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

      4. associate-/l* 91.2%

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

   8. Simplified 91.2%

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

   9. Taylor expanded in a around 0 91.2%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+20} \lor \neg \left(z \leq 185\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \]

Alternative 8: 62.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.7 \cdot 10^{-84}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.7e-84)
   (+ x y)
   (if (<= t 7.8e-191)
     x
     (if (<= t 4e-122) (* y (/ z a)) (if (<= t 1.7e+23) x (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.7e-84) {
		tmp = x + y;
	} else if (t <= 7.8e-191) {
		tmp = x;
	} else if (t <= 4e-122) {
		tmp = y * (z / a);
	} else if (t <= 1.7e+23) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	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 <= (-6.7d-84)) then
        tmp = x + y
    else if (t <= 7.8d-191) then
        tmp = x
    else if (t <= 4d-122) then
        tmp = y * (z / a)
    else if (t <= 1.7d+23) then
        tmp = x
    else
        tmp = x + y
    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 <= -6.7e-84) {
		tmp = x + y;
	} else if (t <= 7.8e-191) {
		tmp = x;
	} else if (t <= 4e-122) {
		tmp = y * (z / a);
	} else if (t <= 1.7e+23) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.7e-84:
		tmp = x + y
	elif t <= 7.8e-191:
		tmp = x
	elif t <= 4e-122:
		tmp = y * (z / a)
	elif t <= 1.7e+23:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.7e-84)
		tmp = Float64(x + y);
	elseif (t <= 7.8e-191)
		tmp = x;
	elseif (t <= 4e-122)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 1.7e+23)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.7e-84)
		tmp = x + y;
	elseif (t <= 7.8e-191)
		tmp = x;
	elseif (t <= 4e-122)
		tmp = y * (z / a);
	elseif (t <= 1.7e+23)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.7e-84], N[(x + y), $MachinePrecision], If[LessEqual[t, 7.8e-191], x, If[LessEqual[t, 4e-122], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+23], x, N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.7e-84 or 1.69999999999999996e23 < t

   1. Initial program 78.2%

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

   2. Taylor expanded in t around inf 76.1%

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

   if -6.7e-84 < t < 7.7999999999999999e-191 or 4.00000000000000024e-122 < t < 1.69999999999999996e23

   1. Initial program 96.3%

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

   2. Taylor expanded in x around inf 63.9%

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

   if 7.7999999999999999e-191 < t < 4.00000000000000024e-122

   1. Initial program 79.4%

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

      1. +-commutative 79.4%

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

      2. associate-*l/ 89.7%

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

      3. fma-def 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in x around 0 68.9%

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

      1. associate-*l/ 78.7%

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

   6. Applied egg-rr 78.7%

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

   7. Taylor expanded in t around 0 67.6%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.7 \cdot 10^{-84}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+25} \lor \neg \left(t \leq 3.8 \cdot 10^{+30}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.8e+25) (not (<= t 3.8e+30))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.8e+25) || !(t <= 3.8e+30)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	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 <= (-1.8d+25)) .or. (.not. (t <= 3.8d+30))) then
        tmp = x + y
    else
        tmp = x + (y * (z / a))
    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 <= -1.8e+25) || !(t <= 3.8e+30)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.8e+25) or not (t <= 3.8e+30):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.8e+25) || !(t <= 3.8e+30))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.8e+25) || ~((t <= 3.8e+30)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.8e+25], N[Not[LessEqual[t, 3.8e+30]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.80000000000000008e25 or 3.8000000000000001e30 < t

   1. Initial program 73.1%

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

   2. Taylor expanded in t around inf 79.5%

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

   if -1.80000000000000008e25 < t < 3.8000000000000001e30

   1. Initial program 95.9%

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

   2. Taylor expanded in t around 0 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-/l* 82.3%

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

      3. associate-/r/ 81.4%

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

   4. Applied egg-rr 81.4%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+25} \lor \neg \left(t \leq 3.8 \cdot 10^{+30}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 10: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+21}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.5e+21) (+ x y) (if (<= t 1.7e+31) (+ x (/ y (/ a z))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e+21) {
		tmp = x + y;
	} else if (t <= 1.7e+31) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	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 <= (-4.5d+21)) then
        tmp = x + y
    else if (t <= 1.7d+31) then
        tmp = x + (y / (a / z))
    else
        tmp = x + y
    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 <= -4.5e+21) {
		tmp = x + y;
	} else if (t <= 1.7e+31) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.5e+21:
		tmp = x + y
	elif t <= 1.7e+31:
		tmp = x + (y / (a / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.5e+21)
		tmp = Float64(x + y);
	elseif (t <= 1.7e+31)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.5e+21)
		tmp = x + y;
	elseif (t <= 1.7e+31)
		tmp = x + (y / (a / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.5e+21], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.7e+31], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5e21 or 1.6999999999999999e31 < t

   1. Initial program 73.1%

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

   2. Taylor expanded in t around inf 79.5%

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

   if -4.5e21 < t < 1.6999999999999999e31

   1. Initial program 95.9%

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

   2. Taylor expanded in t around 0 80.3%

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

      1. associate-/l* 81.9%

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

   4. Simplified 81.9%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+21}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 63.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-84}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.2e-84) (+ x y) (if (<= t 2.9e+23) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.2e-84) {
		tmp = x + y;
	} else if (t <= 2.9e+23) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	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 <= (-5.2d-84)) then
        tmp = x + y
    else if (t <= 2.9d+23) then
        tmp = x
    else
        tmp = x + y
    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 <= -5.2e-84) {
		tmp = x + y;
	} else if (t <= 2.9e+23) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.2e-84:
		tmp = x + y
	elif t <= 2.9e+23:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.2e-84)
		tmp = Float64(x + y);
	elseif (t <= 2.9e+23)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.2e-84)
		tmp = x + y;
	elseif (t <= 2.9e+23)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.2e-84], N[(x + y), $MachinePrecision], If[LessEqual[t, 2.9e+23], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.2e-84 or 2.90000000000000013e23 < t

   1. Initial program 78.2%

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

   2. Taylor expanded in t around inf 76.1%

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

   if -5.2e-84 < t < 2.90000000000000013e23

   1. Initial program 94.9%

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

   2. Taylor expanded in x around inf 60.0%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-84}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12: 52.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{-251}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-288}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.12e-251) x (if (<= x 4.2e-288) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.12e-251) {
		tmp = x;
	} else if (x <= 4.2e-288) {
		tmp = y;
	} 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 (x <= (-1.12d-251)) then
        tmp = x
    else if (x <= 4.2d-288) then
        tmp = y
    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 (x <= -1.12e-251) {
		tmp = x;
	} else if (x <= 4.2e-288) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.12e-251:
		tmp = x
	elif x <= 4.2e-288:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.12e-251)
		tmp = x;
	elseif (x <= 4.2e-288)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.12e-251)
		tmp = x;
	elseif (x <= 4.2e-288)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.12e-251], x, If[LessEqual[x, 4.2e-288], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.12000000000000007e-251 or 4.19999999999999991e-288 < x

   1. Initial program 87.1%

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

   2. Taylor expanded in x around inf 62.8%

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

   if -1.12000000000000007e-251 < x < 4.19999999999999991e-288

   1. Initial program 73.3%

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

      1. +-commutative 73.3%

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

      2. associate-*l/ 93.4%

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

      3. fma-def 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in x around 0 62.8%

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

   5. Taylor expanded in z around 0 31.4%

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

      1. mul-1-neg 31.4%

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

      2. distribute-rgt-neg-out 31.4%

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

   7. Simplified 31.4%

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

   8. Taylor expanded in t around inf 54.1%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{-251}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-288}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 50.9% 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 85.7%

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

2. Taylor expanded in x around inf 57.8%

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

3. Final simplification 57.8%

   \[\leadsto x \]

Developer target: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / ((a - t) / (z - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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