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

Percentage Accurate: 98.0% → 98.0%

Time: 9.7s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.0% accurate, 1.0× speedup

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.8%

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

2. Final simplification 98.8%

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

Alternative 2: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+36}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+102}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \frac{-y}{a - t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+142}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.02e+36)
   (+ x y)
   (if (<= t 4.8e-55)
     (+ x (/ y (/ a z)))
     (if (<= t 4.8e-24)
       (* y (/ (- t) (- a t)))
       (if (<= t 6e+102)
         (+ x (/ (* y z) a))
         (if (<= t 5e+118)
           (* t (/ (- y) (- a t)))
           (if (<= t 3.5e+142) (+ x (* z (/ y a))) (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.02e+36) {
		tmp = x + y;
	} else if (t <= 4.8e-55) {
		tmp = x + (y / (a / z));
	} else if (t <= 4.8e-24) {
		tmp = y * (-t / (a - t));
	} else if (t <= 6e+102) {
		tmp = x + ((y * z) / a);
	} else if (t <= 5e+118) {
		tmp = t * (-y / (a - t));
	} else if (t <= 3.5e+142) {
		tmp = x + (z * (y / a));
	} 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 <= (-1.02d+36)) then
        tmp = x + y
    else if (t <= 4.8d-55) then
        tmp = x + (y / (a / z))
    else if (t <= 4.8d-24) then
        tmp = y * (-t / (a - t))
    else if (t <= 6d+102) then
        tmp = x + ((y * z) / a)
    else if (t <= 5d+118) then
        tmp = t * (-y / (a - t))
    else if (t <= 3.5d+142) then
        tmp = x + (z * (y / a))
    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 <= -1.02e+36) {
		tmp = x + y;
	} else if (t <= 4.8e-55) {
		tmp = x + (y / (a / z));
	} else if (t <= 4.8e-24) {
		tmp = y * (-t / (a - t));
	} else if (t <= 6e+102) {
		tmp = x + ((y * z) / a);
	} else if (t <= 5e+118) {
		tmp = t * (-y / (a - t));
	} else if (t <= 3.5e+142) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.02e+36:
		tmp = x + y
	elif t <= 4.8e-55:
		tmp = x + (y / (a / z))
	elif t <= 4.8e-24:
		tmp = y * (-t / (a - t))
	elif t <= 6e+102:
		tmp = x + ((y * z) / a)
	elif t <= 5e+118:
		tmp = t * (-y / (a - t))
	elif t <= 3.5e+142:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.02e+36)
		tmp = Float64(x + y);
	elseif (t <= 4.8e-55)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 4.8e-24)
		tmp = Float64(y * Float64(Float64(-t) / Float64(a - t)));
	elseif (t <= 6e+102)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 5e+118)
		tmp = Float64(t * Float64(Float64(-y) / Float64(a - t)));
	elseif (t <= 3.5e+142)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.02e+36)
		tmp = x + y;
	elseif (t <= 4.8e-55)
		tmp = x + (y / (a / z));
	elseif (t <= 4.8e-24)
		tmp = y * (-t / (a - t));
	elseif (t <= 6e+102)
		tmp = x + ((y * z) / a);
	elseif (t <= 5e+118)
		tmp = t * (-y / (a - t));
	elseif (t <= 3.5e+142)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.02e+36], N[(x + y), $MachinePrecision], If[LessEqual[t, 4.8e-55], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-24], N[(y * N[((-t) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+102], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+118], N[(t * N[((-y) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+142], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.02000000000000003e36 or 3.49999999999999997e142 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 85.6%

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

   if -1.02000000000000003e36 < t < 4.79999999999999983e-55

   1. Initial program 97.5%

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

   2. Taylor expanded in t around 0 85.1%

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

      1. associate-/l* 86.0%

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

   4. Simplified 86.0%

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

   if 4.79999999999999983e-55 < t < 4.7999999999999996e-24

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. associate-/l* 58.1%

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

      3. distribute-neg-frac 58.1%

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

   4. Simplified 58.1%

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

   5. Taylor expanded in x around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. unsub-neg 67.9%

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

      3. associate-/l* 58.1%

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

   7. Simplified 58.1%

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

   8. Taylor expanded in x around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. associate-*l/ 67.7%

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

      3. *-commutative 67.7%

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

      4. distribute-lft-neg-in 67.7%

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

   10. Simplified 67.7%

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

   if 4.7999999999999996e-24 < t < 5.9999999999999996e102

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 65.6%

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

   if 5.9999999999999996e102 < t < 4.99999999999999972e118

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 84.8%

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

      1. mul-1-neg 84.8%

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

      2. associate-/l* 99.7%

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

      3. distribute-neg-frac 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in x around 0 84.8%

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

      1. mul-1-neg 84.8%

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

      2. unsub-neg 84.8%

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

      3. associate-/l* 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around 0 84.8%

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

      1. mul-1-neg 84.8%

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

      2. associate-*r/ 99.7%

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

      3. distribute-rgt-neg-out 99.7%

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

      4. distribute-neg-frac 99.7%

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

   10. Simplified 99.7%

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

   if 4.99999999999999972e118 < t < 3.49999999999999997e142

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

      1. associate-/r/ 100.0%

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

   6. Applied egg-rr 100.0%

      \[\leadsto x + \color{blue}{\frac{y}{a} \cdot z} \]
3. Recombined 6 regimes into one program.

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+36}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+102}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \frac{-y}{a - t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+142}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+36} \lor \neg \left(z \leq 16500000000000\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.7e+36) (not (<= z 16500000000000.0)))
   (+ x (* y (/ z (- a t))))
   (+ x (* t (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.7e+36) || !(z <= 16500000000000.0)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (t * (y / (t - 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 ((z <= (-3.7d+36)) .or. (.not. (z <= 16500000000000.0d0))) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = x + (t * (y / (t - 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 ((z <= -3.7e+36) || !(z <= 16500000000000.0)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (t * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.7e+36) or not (z <= 16500000000000.0):
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + (t * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.7e+36) || !(z <= 16500000000000.0))
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.7e+36) || ~((z <= 16500000000000.0)))
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x + (t * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.7e+36], N[Not[LessEqual[z, 16500000000000.0]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.70000000000000029e36 or 1.65e13 < z

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 84.8%

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

   if -3.70000000000000029e36 < z < 1.65e13

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. associate-/l* 93.3%

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

      3. distribute-neg-frac 93.3%

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

   4. Simplified 93.3%

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

      1. frac-2neg 93.3%

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

      2. div-inv 93.2%

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

      3. remove-double-neg 93.2%

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

      4. distribute-neg-frac 93.2%

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

      5. sub-neg 93.2%

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

      6. distribute-neg-in 93.2%

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

      7. remove-double-neg 93.2%

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

   6. Applied egg-rr 93.2%

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

      1. associate-/r/ 93.8%

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

      2. associate-*l/ 93.9%

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

      3. *-lft-identity 93.9%

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

      4. +-commutative 93.9%

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

      5. unsub-neg 93.9%

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

   8. Simplified 93.9%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+36} \lor \neg \left(z \leq 16500000000000\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \]

Alternative 4: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+39} \lor \neg \left(z \leq 1.9 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.25e+39) (not (<= z 1.9e+15)))
   (+ x (/ y (/ (- a t) z)))
   (+ x (* t (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.25e+39) || !(z <= 1.9e+15)) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x + (t * (y / (t - 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 ((z <= (-2.25d+39)) .or. (.not. (z <= 1.9d+15))) then
        tmp = x + (y / ((a - t) / z))
    else
        tmp = x + (t * (y / (t - 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 ((z <= -2.25e+39) || !(z <= 1.9e+15)) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x + (t * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.25e+39) or not (z <= 1.9e+15):
		tmp = x + (y / ((a - t) / z))
	else:
		tmp = x + (t * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.25e+39) || !(z <= 1.9e+15))
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.25e+39) || ~((z <= 1.9e+15)))
		tmp = x + (y / ((a - t) / z));
	else
		tmp = x + (t * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.25e+39], N[Not[LessEqual[z, 1.9e+15]], $MachinePrecision]], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.24999999999999998e39 or 1.9e15 < z

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 82.3%

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

      1. associate-/l* 85.7%

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

   4. Simplified 85.7%

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

   if -2.24999999999999998e39 < z < 1.9e15

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. associate-/l* 93.3%

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

      3. distribute-neg-frac 93.3%

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

   4. Simplified 93.3%

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

      1. frac-2neg 93.3%

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

      2. div-inv 93.2%

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

      3. remove-double-neg 93.2%

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

      4. distribute-neg-frac 93.2%

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

      5. sub-neg 93.2%

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

      6. distribute-neg-in 93.2%

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

      7. remove-double-neg 93.2%

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

   6. Applied egg-rr 93.2%

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

      1. associate-/r/ 93.8%

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

      2. associate-*l/ 93.9%

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

      3. *-lft-identity 93.9%

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

      4. +-commutative 93.9%

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

      5. unsub-neg 93.9%

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

   8. Simplified 93.9%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+39} \lor \neg \left(z \leq 1.9 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \]

Alternative 5: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+40} \lor \neg \left(z \leq 4.9 \cdot 10^{+38}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.8e+40) (not (<= z 4.9e+38)))
   (+ x (/ y (/ (- a t) z)))
   (- x (* y (/ t (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e+40) || !(z <= 4.9e+38)) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x - (y * (t / (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 <= (-4.8d+40)) .or. (.not. (z <= 4.9d+38))) then
        tmp = x + (y / ((a - t) / z))
    else
        tmp = x - (y * (t / (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 <= -4.8e+40) || !(z <= 4.9e+38)) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x - (y * (t / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.8e+40) or not (z <= 4.9e+38):
		tmp = x + (y / ((a - t) / z))
	else:
		tmp = x - (y * (t / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.8e+40) || !(z <= 4.9e+38))
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.8e+40) || ~((z <= 4.9e+38)))
		tmp = x + (y / ((a - t) / z));
	else
		tmp = x - (y * (t / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.8e+40], N[Not[LessEqual[z, 4.9e+38]], $MachinePrecision]], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e40 or 4.90000000000000002e38 < z

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf 82.5%

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

      1. associate-/l* 86.1%

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

   4. Simplified 86.1%

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

   if -4.8e40 < z < 4.90000000000000002e38

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 95.4%

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

      1. neg-mul-1 95.4%

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

      2. distribute-neg-frac 95.4%

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

   4. Simplified 95.4%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+40} \lor \neg \left(z \leq 4.9 \cdot 10^{+38}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \]

Alternative 6: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+151}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+173}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+151)
   (+ x (/ (* y z) a))
   (if (<= z 1.4e+173) (+ x (* t (/ y (- t a)))) (+ x (* z (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+151) {
		tmp = x + ((y * z) / a);
	} else if (z <= 1.4e+173) {
		tmp = x + (t * (y / (t - a)));
	} else {
		tmp = x + (z * (y / 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 (z <= (-5.5d+151)) then
        tmp = x + ((y * z) / a)
    else if (z <= 1.4d+173) then
        tmp = x + (t * (y / (t - a)))
    else
        tmp = x + (z * (y / 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 (z <= -5.5e+151) {
		tmp = x + ((y * z) / a);
	} else if (z <= 1.4e+173) {
		tmp = x + (t * (y / (t - a)));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+151:
		tmp = x + ((y * z) / a)
	elif z <= 1.4e+173:
		tmp = x + (t * (y / (t - a)))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+151)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (z <= 1.4e+173)
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e+151)
		tmp = x + ((y * z) / a);
	elseif (z <= 1.4e+173)
		tmp = x + (t * (y / (t - a)));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+151], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+173], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4999999999999994e151

   1. Initial program 93.6%

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

   2. Taylor expanded in t around 0 73.0%

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

   if -5.4999999999999994e151 < z < 1.39999999999999991e173

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. associate-/l* 85.2%

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

      3. distribute-neg-frac 85.2%

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

   4. Simplified 85.2%

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

      1. frac-2neg 85.2%

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

      2. div-inv 85.0%

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

      3. remove-double-neg 85.0%

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

      4. distribute-neg-frac 85.0%

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

      5. sub-neg 85.0%

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

      6. distribute-neg-in 85.0%

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

      7. remove-double-neg 85.0%

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

   6. Applied egg-rr 85.0%

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

      1. associate-/r/ 85.5%

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

      2. associate-*l/ 85.5%

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

      3. *-lft-identity 85.5%

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

      4. +-commutative 85.5%

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

      5. unsub-neg 85.5%

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

   8. Simplified 85.5%

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

   if 1.39999999999999991e173 < z

   1. Initial program 96.6%

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

   2. Taylor expanded in t around 0 70.8%

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

      1. associate-/l* 77.6%

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

   4. Simplified 77.6%

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

      1. associate-/r/ 81.0%

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

   6. Applied egg-rr 81.0%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+151}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+173}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7: 76.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+31} \lor \neg \left(t \leq 1.95 \cdot 10^{+101}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.4e+31) (not (<= t 1.95e+101))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.4e+31) || !(t <= 1.95e+101)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / 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 <= (-1.4d+31)) .or. (.not. (t <= 1.95d+101))) then
        tmp = x + y
    else
        tmp = x + (z * (y / 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 <= -1.4e+31) || !(t <= 1.95e+101)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.4e+31) or not (t <= 1.95e+101):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.4e+31) || !(t <= 1.95e+101))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.4e+31) || ~((t <= 1.95e+101)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.4e+31], N[Not[LessEqual[t, 1.95e+101]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.40000000000000008e31 or 1.95e101 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 82.0%

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

   if -1.40000000000000008e31 < t < 1.95e101

   1. Initial program 98.0%

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

   2. Taylor expanded in t around 0 76.9%

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

      1. associate-/l* 77.6%

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

   4. Simplified 77.6%

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

      1. associate-/r/ 76.6%

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

   6. Applied egg-rr 76.6%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+31} \lor \neg \left(t \leq 1.95 \cdot 10^{+101}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 70.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.02 \lor \neg \left(a \leq 1.15 \cdot 10^{+91}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.02) (not (<= a 1.15e+91))) (+ x (/ y (/ a z))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.02) || !(a <= 1.15e+91)) {
		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 ((a <= (-1.02d0)) .or. (.not. (a <= 1.15d+91))) 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 ((a <= -1.02) || !(a <= 1.15e+91)) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.02) or not (a <= 1.15e+91):
		tmp = x + (y / (a / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.02) || !(a <= 1.15e+91))
		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 ((a <= -1.02) || ~((a <= 1.15e+91)))
		tmp = x + (y / (a / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.02], N[Not[LessEqual[a, 1.15e+91]], $MachinePrecision]], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.02 or 1.14999999999999996e91 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 79.9%

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

      1. associate-/l* 82.8%

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

   4. Simplified 82.8%

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

   if -1.02 < a < 1.14999999999999996e91

   1. Initial program 97.8%

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

   2. Taylor expanded in t around inf 71.9%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \lor \neg \left(a \leq 1.15 \cdot 10^{+91}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9: 64.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{-104} \lor \neg \left(t \leq 1.7 \cdot 10^{-101}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.4e-104) (not (<= t 1.7e-101))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.4e-104) || !(t <= 1.7e-101)) {
		tmp = x + 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 ((t <= (-8.4d-104)) .or. (.not. (t <= 1.7d-101))) then
        tmp = x + 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 ((t <= -8.4e-104) || !(t <= 1.7e-101)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.4e-104) or not (t <= 1.7e-101):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.4e-104) || !(t <= 1.7e-101))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.4e-104) || ~((t <= 1.7e-101)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.4e-104], N[Not[LessEqual[t, 1.7e-101]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -8.39999999999999994e-104 or 1.69999999999999995e-101 < t

   1. Initial program 99.4%

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

   2. Taylor expanded in t around inf 69.9%

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

   if -8.39999999999999994e-104 < t < 1.69999999999999995e-101

   1. Initial program 97.5%

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

   2. Taylor expanded in z around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. associate-/l* 76.2%

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

      3. distribute-neg-frac 76.2%

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

   4. Simplified 76.2%

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

   5. Taylor expanded in x around inf 72.5%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{-104} \lor \neg \left(t \leq 1.7 \cdot 10^{-101}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 51.5% 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 98.8%

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

2. Taylor expanded in z around 0 69.1%

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

   1. mul-1-neg 69.1%

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

   2. associate-/l* 76.4%

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

   3. distribute-neg-frac 76.4%

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

4. Simplified 76.4%

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

5. Taylor expanded in x around inf 52.9%

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

6. Final simplification 52.9%

   \[\leadsto x \]

Developer target: 99.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} 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 - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    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 - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023322 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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