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

Percentage Accurate: 84.8% → 98.4%

Time: 9.1s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.1%

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

   1. associate-/l* 99.4%

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

3. Simplified 99.4%

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

4. Final simplification 99.4%

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

Alternative 2: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+44}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+74}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+95}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+126}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.4e+44)
   (+ x y)
   (if (<= z 1.05e+32)
     (+ x (/ y (/ a t)))
     (if (<= z 2.3e+74)
       (- x (* t (/ y z)))
       (if (<= z 1.45e+95)
         (+ x (* y (/ t a)))
         (if (<= z 5.3e+126) (* (- z t) (/ y z)) (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.4e+44) {
		tmp = x + y;
	} else if (z <= 1.05e+32) {
		tmp = x + (y / (a / t));
	} else if (z <= 2.3e+74) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.45e+95) {
		tmp = x + (y * (t / a));
	} else if (z <= 5.3e+126) {
		tmp = (z - t) * (y / 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 (z <= (-6.4d+44)) then
        tmp = x + y
    else if (z <= 1.05d+32) then
        tmp = x + (y / (a / t))
    else if (z <= 2.3d+74) then
        tmp = x - (t * (y / z))
    else if (z <= 1.45d+95) then
        tmp = x + (y * (t / a))
    else if (z <= 5.3d+126) then
        tmp = (z - t) * (y / 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 (z <= -6.4e+44) {
		tmp = x + y;
	} else if (z <= 1.05e+32) {
		tmp = x + (y / (a / t));
	} else if (z <= 2.3e+74) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.45e+95) {
		tmp = x + (y * (t / a));
	} else if (z <= 5.3e+126) {
		tmp = (z - t) * (y / z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.4e+44:
		tmp = x + y
	elif z <= 1.05e+32:
		tmp = x + (y / (a / t))
	elif z <= 2.3e+74:
		tmp = x - (t * (y / z))
	elif z <= 1.45e+95:
		tmp = x + (y * (t / a))
	elif z <= 5.3e+126:
		tmp = (z - t) * (y / z)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.4e+44)
		tmp = Float64(x + y);
	elseif (z <= 1.05e+32)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 2.3e+74)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 1.45e+95)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 5.3e+126)
		tmp = Float64(Float64(z - t) * Float64(y / z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.4e+44)
		tmp = x + y;
	elseif (z <= 1.05e+32)
		tmp = x + (y / (a / t));
	elseif (z <= 2.3e+74)
		tmp = x - (t * (y / z));
	elseif (z <= 1.45e+95)
		tmp = x + (y * (t / a));
	elseif (z <= 5.3e+126)
		tmp = (z - t) * (y / z);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.4e+44], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.05e+32], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+74], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+95], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e+126], N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.40000000000000009e44 or 5.30000000000000028e126 < z

   1. Initial program 73.8%

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

      1. +-commutative 73.8%

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

      2. associate-*r/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 84.1%

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

   if -6.40000000000000009e44 < z < 1.05e32

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. associate-*r/ 98.6%

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

      3. fma-def 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around 0 78.6%

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

      1. associate-/l* 80.2%

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

   6. Simplified 80.2%

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

   if 1.05e32 < z < 2.2999999999999999e74

   1. Initial program 63.7%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 80.1%

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

      1. associate-*r/ 80.1%

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

      2. neg-mul-1 80.1%

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

      3. sub-neg 80.1%

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

      4. mul-1-neg 80.1%

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

      5. distribute-neg-in 80.1%

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

      6. mul-1-neg 80.1%

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

      7. remove-double-neg 80.1%

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

   6. Simplified 80.1%

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

   7. Taylor expanded in z around inf 61.9%

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

      1. +-commutative 61.9%

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

      2. mul-1-neg 61.9%

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

      3. unsub-neg 61.9%

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

      4. *-commutative 61.9%

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

      5. associate-*r/ 80.1%

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

   9. Simplified 80.1%

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

   if 2.2999999999999999e74 < z < 1.45000000000000007e95

   1. Initial program 61.5%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 81.0%

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

      1. associate-*r/ 81.0%

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

      2. neg-mul-1 81.0%

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

      3. sub-neg 81.0%

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

      4. mul-1-neg 81.0%

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

      5. distribute-neg-in 81.0%

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

      6. mul-1-neg 81.0%

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

      7. remove-double-neg 81.0%

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

   6. Simplified 81.0%

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

   7. Taylor expanded in z around 0 61.6%

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

      1. associate-*r/ 81.0%

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

   9. Simplified 81.0%

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

   if 1.45000000000000007e95 < z < 5.30000000000000028e126

   1. Initial program 81.3%

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

      1. +-commutative 81.3%

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

      2. associate-*r/ 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 81.3%

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

   5. Taylor expanded in a around 0 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-/l* 100.0%

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

      3. associate-/r/ 99.7%

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

   7. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot \left(z - t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+44}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+74}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+95}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+126}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 76.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+44}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+89}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+93}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.6e+44)
   (+ x y)
   (if (<= z 1.6e+32)
     (+ x (/ y (/ a t)))
     (if (<= z 1.8e+89)
       (- x (* t (/ y z)))
       (if (<= z 2.5e+93) (* (/ y a) (- t z)) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+44) {
		tmp = x + y;
	} else if (z <= 1.6e+32) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.8e+89) {
		tmp = x - (t * (y / z));
	} else if (z <= 2.5e+93) {
		tmp = (y / a) * (t - 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 (z <= (-4.6d+44)) then
        tmp = x + y
    else if (z <= 1.6d+32) then
        tmp = x + (y / (a / t))
    else if (z <= 1.8d+89) then
        tmp = x - (t * (y / z))
    else if (z <= 2.5d+93) then
        tmp = (y / a) * (t - 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 (z <= -4.6e+44) {
		tmp = x + y;
	} else if (z <= 1.6e+32) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.8e+89) {
		tmp = x - (t * (y / z));
	} else if (z <= 2.5e+93) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.6e+44:
		tmp = x + y
	elif z <= 1.6e+32:
		tmp = x + (y / (a / t))
	elif z <= 1.8e+89:
		tmp = x - (t * (y / z))
	elif z <= 2.5e+93:
		tmp = (y / a) * (t - z)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e+44)
		tmp = Float64(x + y);
	elseif (z <= 1.6e+32)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 1.8e+89)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 2.5e+93)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.6e+44)
		tmp = x + y;
	elseif (z <= 1.6e+32)
		tmp = x + (y / (a / t));
	elseif (z <= 1.8e+89)
		tmp = x - (t * (y / z));
	elseif (z <= 2.5e+93)
		tmp = (y / a) * (t - z);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.6e+44], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.6e+32], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+89], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+93], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.60000000000000009e44 or 2.5000000000000001e93 < z

   1. Initial program 74.2%

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

      1. +-commutative 74.2%

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

      2. associate-*r/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 83.0%

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

   if -4.60000000000000009e44 < z < 1.5999999999999999e32

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. associate-*r/ 98.6%

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

      3. fma-def 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around 0 78.6%

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

      1. associate-/l* 80.2%

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

   6. Simplified 80.2%

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

   if 1.5999999999999999e32 < z < 1.8e89

   1. Initial program 72.1%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 84.7%

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

      1. associate-*r/ 84.7%

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

      2. neg-mul-1 84.7%

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

      3. sub-neg 84.7%

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

      4. mul-1-neg 84.7%

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

      5. distribute-neg-in 84.7%

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

      6. mul-1-neg 84.7%

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

      7. remove-double-neg 84.7%

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

   6. Simplified 84.7%

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

   7. Taylor expanded in z around inf 65.8%

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

      1. +-commutative 65.8%

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

      2. mul-1-neg 65.8%

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

      3. unsub-neg 65.8%

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

      4. *-commutative 65.8%

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

      5. associate-*r/ 79.8%

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

   9. Simplified 79.8%

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

   if 1.8e89 < z < 2.5000000000000001e93

   1. Initial program 3.9%

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

      1. +-commutative 3.9%

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

      2. associate-*r/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around inf 3.9%

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

      1. +-commutative 3.9%

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

      2. *-commutative 3.9%

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

      3. mul-1-neg 3.9%

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

      4. unsub-neg 3.9%

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

      5. *-commutative 3.9%

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

      6. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around 0 3.9%

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

      1. associate-/l* 100.0%

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

      2. associate-*r/ 100.0%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

      5. distribute-neg-frac 100.0%

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

      6. distribute-lft-neg-in 100.0%

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

      7. distribute-rgt-neg-in 100.0%

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

      8. associate-/r/ 100.0%

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

      9. associate-*l/ 100.0%

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

      10. *-lft-identity 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+44}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+89}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+93}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.03 \cdot 10^{+158} \lor \neg \left(z \leq 4.4 \cdot 10^{+104}\right):\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.03e+158) (not (<= z 4.4e+104)))
   (+ x (/ y (- 1.0 (/ a z))))
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.03e+158) || !(z <= 4.4e+104)) {
		tmp = x + (y / (1.0 - (a / z)));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.03d+158)) .or. (.not. (z <= 4.4d+104))) then
        tmp = x + (y / (1.0d0 - (a / z)))
    else
        tmp = x + (t * (y / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.03e+158) || !(z <= 4.4e+104)) {
		tmp = x + (y / (1.0 - (a / z)));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.03e+158) or not (z <= 4.4e+104):
		tmp = x + (y / (1.0 - (a / z)))
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.03e+158) || !(z <= 4.4e+104))
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.03e+158) || ~((z <= 4.4e+104)))
		tmp = x + (y / (1.0 - (a / z)));
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.03e+158], N[Not[LessEqual[z, 4.4e+104]], $MachinePrecision]], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.03000000000000002e158 or 4.40000000000000001e104 < z

   1. Initial program 65.8%

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

      1. associate-*l/ 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in t around 0 60.5%

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

      1. associate-/l* 91.7%

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

      2. div-sub 91.7%

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

      3. *-inverses 91.7%

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

   6. Simplified 91.7%

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

   if -1.03000000000000002e158 < z < 4.40000000000000001e104

   1. Initial program 94.3%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in t around inf 91.3%

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

      1. associate-*r/ 91.3%

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

      2. neg-mul-1 91.3%

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

      3. sub-neg 91.3%

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

      4. mul-1-neg 91.3%

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

      5. distribute-neg-in 91.3%

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

      6. mul-1-neg 91.3%

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

      7. remove-double-neg 91.3%

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

   6. Simplified 91.3%

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

   7. Taylor expanded in x around 0 87.9%

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

      1. associate-/l* 91.3%

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

      2. associate-/r/ 90.9%

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

   9. Simplified 90.9%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.03 \cdot 10^{+158} \lor \neg \left(z \leq 4.4 \cdot 10^{+104}\right):\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 5: 87.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+44} \lor \neg \left(z \leq 2.15 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.2e+44) (not (<= z 2.15e+32)))
   (+ x (/ y (/ z (- z t))))
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+44) || !(z <= 2.15e+32)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.2d+44)) .or. (.not. (z <= 2.15d+32))) then
        tmp = x + (y / (z / (z - t)))
    else
        tmp = x + (t * (y / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+44) || !(z <= 2.15e+32)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.2e+44) or not (z <= 2.15e+32):
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.2e+44) || !(z <= 2.15e+32))
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.2e+44) || ~((z <= 2.15e+32)))
		tmp = x + (y / (z / (z - t)));
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.2e+44], N[Not[LessEqual[z, 2.15e+32]], $MachinePrecision]], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999974e44 or 2.1499999999999999e32 < z

   1. Initial program 72.7%

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

      1. +-commutative 72.7%

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

      2. associate-*r/ 100.0%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 67.2%

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

      1. +-commutative 67.2%

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

      2. *-commutative 67.2%

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

      3. associate-/l* 91.2%

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

   6. Simplified 91.2%

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

   if -4.19999999999999974e44 < z < 2.1499999999999999e32

   1. Initial program 96.6%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in t around inf 94.3%

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

      1. associate-*r/ 94.3%

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

      2. neg-mul-1 94.3%

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

      3. sub-neg 94.3%

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

      4. mul-1-neg 94.3%

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

      5. distribute-neg-in 94.3%

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

      6. mul-1-neg 94.3%

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

      7. remove-double-neg 94.3%

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

   6. Simplified 94.3%

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

   7. Taylor expanded in x around 0 91.9%

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

      1. associate-/l* 94.3%

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

      2. associate-/r/ 93.8%

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

   9. Simplified 93.8%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+44} \lor \neg \left(z \leq 2.15 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 6: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+44} \lor \neg \left(z \leq 1.15 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.5e+44) (not (<= z 1.15e+32)))
   (+ x (/ y (/ z (- z t))))
   (+ x (/ y (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.5e+44) || !(z <= 1.15e+32)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-7.5d+44)) .or. (.not. (z <= 1.15d+32))) then
        tmp = x + (y / (z / (z - t)))
    else
        tmp = x + (y / ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.5e+44) || !(z <= 1.15e+32)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.5e+44) or not (z <= 1.15e+32):
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = x + (y / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.5e+44) || !(z <= 1.15e+32))
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.5e+44) || ~((z <= 1.15e+32)))
		tmp = x + (y / (z / (z - t)));
	else
		tmp = x + (y / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.5e+44], N[Not[LessEqual[z, 1.15e+32]], $MachinePrecision]], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.50000000000000027e44 or 1.15e32 < z

   1. Initial program 72.7%

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

      1. +-commutative 72.7%

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

      2. associate-*r/ 100.0%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 67.2%

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

      1. +-commutative 67.2%

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

      2. *-commutative 67.2%

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

      3. associate-/l* 91.2%

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

   6. Simplified 91.2%

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

   if -7.50000000000000027e44 < z < 1.15e32

   1. Initial program 96.6%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in t around inf 94.3%

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

      1. associate-*r/ 94.3%

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

      2. neg-mul-1 94.3%

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

      3. sub-neg 94.3%

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

      4. mul-1-neg 94.3%

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

      5. distribute-neg-in 94.3%

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

      6. mul-1-neg 94.3%

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

      7. remove-double-neg 94.3%

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

   6. Simplified 94.3%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+44} \lor \neg \left(z \leq 1.15 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 7: 76.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+56}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-146}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.2e+56)
   (+ x (* t (/ y a)))
   (if (<= a 2.1e-146) (+ x (* (- z t) (/ y z))) (+ x (/ y (/ a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.2e+56) {
		tmp = x + (t * (y / a));
	} else if (a <= 2.1e-146) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7.2d+56)) then
        tmp = x + (t * (y / a))
    else if (a <= 2.1d-146) then
        tmp = x + ((z - t) * (y / z))
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.2e+56) {
		tmp = x + (t * (y / a));
	} else if (a <= 2.1e-146) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.2e+56:
		tmp = x + (t * (y / a))
	elif a <= 2.1e-146:
		tmp = x + ((z - t) * (y / z))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.2e+56)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (a <= 2.1e-146)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.2e+56)
		tmp = x + (t * (y / a));
	elseif (a <= 2.1e-146)
		tmp = x + ((z - t) * (y / z));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.2e+56], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e-146], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.19999999999999996e56

   1. Initial program 88.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 84.0%

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

      1. associate-*r/ 84.0%

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

      2. neg-mul-1 84.0%

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

      3. sub-neg 84.0%

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

      4. mul-1-neg 84.0%

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

      5. distribute-neg-in 84.0%

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

      6. mul-1-neg 84.0%

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

      7. remove-double-neg 84.0%

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

   6. Simplified 84.0%

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

   7. Taylor expanded in x around 0 78.3%

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

      1. associate-/l* 84.0%

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

      2. associate-/r/ 82.9%

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

   9. Simplified 82.9%

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

   10. Taylor expanded in a around inf 82.2%

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

   if -7.19999999999999996e56 < a < 2.0999999999999999e-146

   1. Initial program 87.2%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around inf 92.4%

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

   if 2.0999999999999999e-146 < a

   1. Initial program 83.4%

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

      1. +-commutative 83.4%

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

      2. associate-*r/ 98.8%

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

      3. fma-def 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around 0 71.6%

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

      1. associate-/l* 75.3%

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

   6. Simplified 75.3%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+56}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-146}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 8: 77.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+44} \lor \neg \left(z \leq 2 \cdot 10^{+42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.2e+44) (not (<= z 2e+42))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.2e+44) || !(z <= 2e+42)) {
		tmp = x + y;
	} else {
		tmp = x + (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 <= (-8.2d+44)) .or. (.not. (z <= 2d+42))) then
        tmp = x + y
    else
        tmp = x + (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 <= -8.2e+44) || !(z <= 2e+42)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.2e+44) or not (z <= 2e+42):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.2e+44) || !(z <= 2e+42))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.2e+44) || ~((z <= 2e+42)))
		tmp = x + y;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.2e+44], N[Not[LessEqual[z, 2e+42]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.1999999999999993e44 or 2.00000000000000009e42 < z

   1. Initial program 72.2%

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

      1. +-commutative 72.2%

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

      2. associate-*r/ 100.0%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 80.5%

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

   if -8.1999999999999993e44 < z < 2.00000000000000009e42

   1. Initial program 96.7%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in t around inf 94.4%

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

      1. associate-*r/ 94.4%

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

      2. neg-mul-1 94.4%

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

      3. sub-neg 94.4%

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

      4. mul-1-neg 94.4%

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

      5. distribute-neg-in 94.4%

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

      6. mul-1-neg 94.4%

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

      7. remove-double-neg 94.4%

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

   6. Simplified 94.4%

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

   7. Taylor expanded in z around 0 77.7%

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

      1. associate-*r/ 79.2%

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

   9. Simplified 79.2%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+44} \lor \neg \left(z \leq 2 \cdot 10^{+42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 9: 77.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+44}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.4e+44) (+ x y) (if (<= z 4.4e+42) (+ x (/ y (/ a t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e+44) {
		tmp = x + y;
	} else if (z <= 4.4e+42) {
		tmp = x + (y / (a / t));
	} 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 (z <= (-3.4d+44)) then
        tmp = x + y
    else if (z <= 4.4d+42) then
        tmp = x + (y / (a / t))
    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 (z <= -3.4e+44) {
		tmp = x + y;
	} else if (z <= 4.4e+42) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.4e+44:
		tmp = x + y
	elif z <= 4.4e+42:
		tmp = x + (y / (a / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.4e+44)
		tmp = Float64(x + y);
	elseif (z <= 4.4e+42)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.4e+44)
		tmp = x + y;
	elseif (z <= 4.4e+42)
		tmp = x + (y / (a / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.4e+44], N[(x + y), $MachinePrecision], If[LessEqual[z, 4.4e+42], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4e44 or 4.4000000000000003e42 < z

   1. Initial program 72.2%

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

      1. +-commutative 72.2%

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

      2. associate-*r/ 100.0%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 80.5%

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

   if -3.4e44 < z < 4.4000000000000003e42

   1. Initial program 96.7%

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

      1. +-commutative 96.7%

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

      2. associate-*r/ 98.6%

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

      3. fma-def 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around 0 77.7%

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

      1. associate-/l* 79.2%

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

   6. Simplified 79.2%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+44}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * (y / (z - a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.1%

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

   1. associate-*l/ 95.9%

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

3. Simplified 95.9%

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

4. Final simplification 95.9%

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

Alternative 11: 62.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+60}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e+60) (+ x y) (if (<= z 1.4e+37) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+60) {
		tmp = x + y;
	} else if (z <= 1.4e+37) {
		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 (z <= (-5.2d+60)) then
        tmp = x + y
    else if (z <= 1.4d+37) 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 (z <= -5.2e+60) {
		tmp = x + y;
	} else if (z <= 1.4e+37) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e+60:
		tmp = x + y
	elif z <= 1.4e+37:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e+60)
		tmp = Float64(x + y);
	elseif (z <= 1.4e+37)
		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 (z <= -5.2e+60)
		tmp = x + y;
	elseif (z <= 1.4e+37)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e+60], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.4e+37], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.20000000000000016e60 or 1.3999999999999999e37 < z

   1. Initial program 71.4%

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

      1. +-commutative 71.4%

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

      2. associate-*r/ 100.0%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 80.7%

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

   if -5.20000000000000016e60 < z < 1.3999999999999999e37

   1. Initial program 96.7%

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

      1. +-commutative 96.7%

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

      2. associate-*r/ 98.6%

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

      3. fma-def 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in y around 0 55.1%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+60}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12: 51.6% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.02 \cdot 10^{+114}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= y 1.02e+114) x y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.02e+114) {
		tmp = x;
	} else {
		tmp = 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 (y <= 1.02d+114) then
        tmp = x
    else
        tmp = 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 (y <= 1.02e+114) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.02e+114:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.02e+114)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.02e+114)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.02e+114], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.01999999999999999e114

   1. Initial program 89.6%

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

      1. +-commutative 89.6%

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

      2. associate-*r/ 99.1%

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

      3. fma-def 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 56.9%

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

   if 1.01999999999999999e114 < y

   1. Initial program 65.1%

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

      1. +-commutative 65.1%

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

      2. associate-*r/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 54.9%

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

   5. Taylor expanded in z around inf 38.1%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.02 \cdot 10^{+114}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 13: 50.5% 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 86.1%

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

   1. +-commutative 86.1%

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

   2. associate-*r/ 99.2%

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

   3. fma-def 99.2%

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

3. Simplified 99.2%

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

4. Taylor expanded in y around 0 50.5%

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

5. Final simplification 50.5%

   \[\leadsto x \]

Developer target: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023200 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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