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

Percentage Accurate: 98.4% → 98.5%

Time: 7.4s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

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

Initial Program: 98.4% accurate, 1.0× speedup

Math

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

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

Alternative 1: 98.5% 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 98.8%

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

   1. associate-*r/ 82.9%

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

   2. associate-/l* 98.8%

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

3. Applied egg-rr 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 80.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{-61}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 0.007:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+61}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- z a))))))
   (if (<= z -5.4e-44)
     t_1
     (if (<= z 1.46e-61)
       (+ x (* y (/ t a)))
       (if (<= z 0.007)
         (- x (/ (* y t) z))
         (if (<= z 8.5e+49)
           (+ x (/ y (/ a t)))
           (if (<= z 3.2e+61) (- x (* t (/ y z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double tmp;
	if (z <= -5.4e-44) {
		tmp = t_1;
	} else if (z <= 1.46e-61) {
		tmp = x + (y * (t / a));
	} else if (z <= 0.007) {
		tmp = x - ((y * t) / z);
	} else if (z <= 8.5e+49) {
		tmp = x + (y / (a / t));
	} else if (z <= 3.2e+61) {
		tmp = x - (t * (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / (z - a)))
    if (z <= (-5.4d-44)) then
        tmp = t_1
    else if (z <= 1.46d-61) then
        tmp = x + (y * (t / a))
    else if (z <= 0.007d0) then
        tmp = x - ((y * t) / z)
    else if (z <= 8.5d+49) then
        tmp = x + (y / (a / t))
    else if (z <= 3.2d+61) then
        tmp = x - (t * (y / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double tmp;
	if (z <= -5.4e-44) {
		tmp = t_1;
	} else if (z <= 1.46e-61) {
		tmp = x + (y * (t / a));
	} else if (z <= 0.007) {
		tmp = x - ((y * t) / z);
	} else if (z <= 8.5e+49) {
		tmp = x + (y / (a / t));
	} else if (z <= 3.2e+61) {
		tmp = x - (t * (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (z - a)))
	tmp = 0
	if z <= -5.4e-44:
		tmp = t_1
	elif z <= 1.46e-61:
		tmp = x + (y * (t / a))
	elif z <= 0.007:
		tmp = x - ((y * t) / z)
	elif z <= 8.5e+49:
		tmp = x + (y / (a / t))
	elif z <= 3.2e+61:
		tmp = x - (t * (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(z - a))))
	tmp = 0.0
	if (z <= -5.4e-44)
		tmp = t_1;
	elseif (z <= 1.46e-61)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 0.007)
		tmp = Float64(x - Float64(Float64(y * t) / z));
	elseif (z <= 8.5e+49)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 3.2e+61)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / (z - a)));
	tmp = 0.0;
	if (z <= -5.4e-44)
		tmp = t_1;
	elseif (z <= 1.46e-61)
		tmp = x + (y * (t / a));
	elseif (z <= 0.007)
		tmp = x - ((y * t) / z);
	elseif (z <= 8.5e+49)
		tmp = x + (y / (a / t));
	elseif (z <= 3.2e+61)
		tmp = x - (t * (y / z));
	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[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e-44], t$95$1, If[LessEqual[z, 1.46e-61], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.007], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+49], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+61], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.3999999999999998e-44 or 3.1999999999999998e61 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 92.3%

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

   if -5.3999999999999998e-44 < z < 1.46e-61

   1. Initial program 96.8%

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

   2. Taylor expanded in z around 0 85.4%

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

   if 1.46e-61 < z < 0.00700000000000000015

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*r/ 99.9%

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

      3. associate-*l/ 99.7%

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

      4. *-commutative 99.7%

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

      5. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 78.1%

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

      1. associate-/l* 78.1%

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

   6. Simplified 78.1%

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

   7. Taylor expanded in z around 0 77.9%

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

      1. associate-*r/ 77.9%

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

      2. associate-*r* 77.9%

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

      3. neg-mul-1 77.9%

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

   9. Simplified 77.9%

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

   if 0.00700000000000000015 < z < 8.4999999999999996e49

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*r/ 93.6%

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

      3. associate-*l/ 99.8%

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

      4. *-commutative 99.8%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 76.7%

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

      1. associate-/l* 83.1%

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

   6. Simplified 83.1%

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

   if 8.4999999999999996e49 < z < 3.1999999999999998e61

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*r/ 99.7%

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

      3. associate-*l/ 100.0%

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

      4. *-commutative 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 99.7%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around 0 99.7%

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

      1. associate-*r/ 99.7%

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

      2. mul-1-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. associate-*l/ 100.0%

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

      5. *-commutative 100.0%

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

      6. distribute-lft-neg-out 100.0%

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

      7. distribute-rgt-neg-in 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-44}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{-61}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 0.007:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+61}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 3: 76.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-37}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-61}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 0.0152:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.6e-37)
   (+ x y)
   (if (<= z 4e-61)
     (+ x (* y (/ t a)))
     (if (<= z 0.0152)
       (- x (* t (/ y z)))
       (if (<= z 7.6e+61) (+ x (/ y (/ a t))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e-37) {
		tmp = x + y;
	} else if (z <= 4e-61) {
		tmp = x + (y * (t / a));
	} else if (z <= 0.0152) {
		tmp = x - (t * (y / z));
	} else if (z <= 7.6e+61) {
		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 <= (-3.6d-37)) then
        tmp = x + y
    else if (z <= 4d-61) then
        tmp = x + (y * (t / a))
    else if (z <= 0.0152d0) then
        tmp = x - (t * (y / z))
    else if (z <= 7.6d+61) 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 <= -3.6e-37) {
		tmp = x + y;
	} else if (z <= 4e-61) {
		tmp = x + (y * (t / a));
	} else if (z <= 0.0152) {
		tmp = x - (t * (y / z));
	} else if (z <= 7.6e+61) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.6e-37:
		tmp = x + y
	elif z <= 4e-61:
		tmp = x + (y * (t / a))
	elif z <= 0.0152:
		tmp = x - (t * (y / z))
	elif z <= 7.6e+61:
		tmp = x + (y / (a / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.6e-37)
		tmp = Float64(x + y);
	elseif (z <= 4e-61)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 0.0152)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 7.6e+61)
		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 <= -3.6e-37)
		tmp = x + y;
	elseif (z <= 4e-61)
		tmp = x + (y * (t / a));
	elseif (z <= 0.0152)
		tmp = x - (t * (y / z));
	elseif (z <= 7.6e+61)
		tmp = x + (y / (a / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.6e-37], N[(x + y), $MachinePrecision], If[LessEqual[z, 4e-61], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0152], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e+61], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.60000000000000007e-37 or 7.5999999999999999e61 < z

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*r/ 68.9%

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

      3. associate-*l/ 97.6%

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

      4. *-commutative 97.6%

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

      5. fma-def 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around inf 85.3%

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

   if -3.60000000000000007e-37 < z < 4.0000000000000002e-61

   1. Initial program 96.8%

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

   2. Taylor expanded in z around 0 85.4%

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

   if 4.0000000000000002e-61 < z < 0.0152

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*r/ 99.9%

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

      3. associate-*l/ 99.7%

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

      4. *-commutative 99.7%

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

      5. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 78.1%

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

      1. associate-/l* 78.1%

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

   6. Simplified 78.1%

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

   7. Taylor expanded in z around 0 77.9%

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

      1. associate-*r/ 77.9%

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

      2. mul-1-neg 77.9%

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

      3. distribute-rgt-neg-in 77.9%

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

      4. associate-*l/ 77.8%

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

      5. *-commutative 77.8%

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

      6. distribute-lft-neg-out 77.8%

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

      7. distribute-rgt-neg-in 77.8%

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

   9. Simplified 77.8%

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

   if 0.0152 < z < 7.5999999999999999e61

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*r/ 91.3%

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

      3. associate-*l/ 99.9%

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

      4. *-commutative 99.9%

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

      5. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 66.6%

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

      1. associate-/l* 75.2%

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

   6. Simplified 75.2%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}} + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-37}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-61}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 0.0152:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 76.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-37}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-61}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 0.0075:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e-37)
   (+ x y)
   (if (<= z 1.5e-61)
     (+ x (* y (/ t a)))
     (if (<= z 0.0075)
       (+ x (/ y (/ (- z) t)))
       (if (<= z 9.4e+61) (+ x (/ y (/ a t))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e-37) {
		tmp = x + y;
	} else if (z <= 1.5e-61) {
		tmp = x + (y * (t / a));
	} else if (z <= 0.0075) {
		tmp = x + (y / (-z / t));
	} else if (z <= 9.4e+61) {
		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 <= (-4.8d-37)) then
        tmp = x + y
    else if (z <= 1.5d-61) then
        tmp = x + (y * (t / a))
    else if (z <= 0.0075d0) then
        tmp = x + (y / (-z / t))
    else if (z <= 9.4d+61) 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 <= -4.8e-37) {
		tmp = x + y;
	} else if (z <= 1.5e-61) {
		tmp = x + (y * (t / a));
	} else if (z <= 0.0075) {
		tmp = x + (y / (-z / t));
	} else if (z <= 9.4e+61) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e-37:
		tmp = x + y
	elif z <= 1.5e-61:
		tmp = x + (y * (t / a))
	elif z <= 0.0075:
		tmp = x + (y / (-z / t))
	elif z <= 9.4e+61:
		tmp = x + (y / (a / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e-37)
		tmp = Float64(x + y);
	elseif (z <= 1.5e-61)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 0.0075)
		tmp = Float64(x + Float64(y / Float64(Float64(-z) / t)));
	elseif (z <= 9.4e+61)
		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 <= -4.8e-37)
		tmp = x + y;
	elseif (z <= 1.5e-61)
		tmp = x + (y * (t / a));
	elseif (z <= 0.0075)
		tmp = x + (y / (-z / t));
	elseif (z <= 9.4e+61)
		tmp = x + (y / (a / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e-37], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.5e-61], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0075], N[(x + N[(y / N[((-z) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.4e+61], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.79999999999999982e-37 or 9.3999999999999997e61 < z

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*r/ 68.9%

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

      3. associate-*l/ 97.6%

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

      4. *-commutative 97.6%

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

      5. fma-def 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around inf 85.3%

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

   if -4.79999999999999982e-37 < z < 1.50000000000000006e-61

   1. Initial program 96.8%

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

   2. Taylor expanded in z around 0 85.4%

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

   if 1.50000000000000006e-61 < z < 0.0074999999999999997

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*r/ 99.9%

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

      3. associate-*l/ 99.7%

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

      4. *-commutative 99.7%

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

      5. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 78.1%

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

      1. associate-/l* 78.1%

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

   6. Simplified 78.1%

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

   7. Taylor expanded in z around 0 77.8%

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

      1. associate-*r/ 77.8%

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

      2. neg-mul-1 77.8%

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

   9. Simplified 77.8%

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

   if 0.0074999999999999997 < z < 9.3999999999999997e61

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*r/ 91.3%

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

      3. associate-*l/ 99.9%

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

      4. *-commutative 99.9%

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

      5. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 66.6%

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

      1. associate-/l* 75.2%

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

   6. Simplified 75.2%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}} + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-37}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-61}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 0.0075:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 76.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-59}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 0.145:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.6e-38)
   (+ x y)
   (if (<= z 8.8e-59)
     (+ x (* y (/ t a)))
     (if (<= z 0.145)
       (- x (/ (* y t) z))
       (if (<= z 5.5e+61) (+ x (/ y (/ a t))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e-38) {
		tmp = x + y;
	} else if (z <= 8.8e-59) {
		tmp = x + (y * (t / a));
	} else if (z <= 0.145) {
		tmp = x - ((y * t) / z);
	} else if (z <= 5.5e+61) {
		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 <= (-4.6d-38)) then
        tmp = x + y
    else if (z <= 8.8d-59) then
        tmp = x + (y * (t / a))
    else if (z <= 0.145d0) then
        tmp = x - ((y * t) / z)
    else if (z <= 5.5d+61) 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 <= -4.6e-38) {
		tmp = x + y;
	} else if (z <= 8.8e-59) {
		tmp = x + (y * (t / a));
	} else if (z <= 0.145) {
		tmp = x - ((y * t) / z);
	} else if (z <= 5.5e+61) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.6e-38:
		tmp = x + y
	elif z <= 8.8e-59:
		tmp = x + (y * (t / a))
	elif z <= 0.145:
		tmp = x - ((y * t) / z)
	elif z <= 5.5e+61:
		tmp = x + (y / (a / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e-38)
		tmp = Float64(x + y);
	elseif (z <= 8.8e-59)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 0.145)
		tmp = Float64(x - Float64(Float64(y * t) / z));
	elseif (z <= 5.5e+61)
		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 <= -4.6e-38)
		tmp = x + y;
	elseif (z <= 8.8e-59)
		tmp = x + (y * (t / a));
	elseif (z <= 0.145)
		tmp = x - ((y * t) / z);
	elseif (z <= 5.5e+61)
		tmp = x + (y / (a / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.6e-38], N[(x + y), $MachinePrecision], If[LessEqual[z, 8.8e-59], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.145], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+61], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.60000000000000003e-38 or 5.50000000000000036e61 < z

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*r/ 68.9%

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

      3. associate-*l/ 97.6%

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

      4. *-commutative 97.6%

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

      5. fma-def 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around inf 85.3%

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

   if -4.60000000000000003e-38 < z < 8.7999999999999995e-59

   1. Initial program 96.8%

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

   2. Taylor expanded in z around 0 85.4%

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

   if 8.7999999999999995e-59 < z < 0.14499999999999999

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*r/ 99.9%

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

      3. associate-*l/ 99.7%

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

      4. *-commutative 99.7%

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

      5. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 78.1%

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

      1. associate-/l* 78.1%

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

   6. Simplified 78.1%

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

   7. Taylor expanded in z around 0 77.9%

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

      1. associate-*r/ 77.9%

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

      2. associate-*r* 77.9%

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

      3. neg-mul-1 77.9%

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

   9. Simplified 77.9%

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

   if 0.14499999999999999 < z < 5.50000000000000036e61

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*r/ 91.3%

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

      3. associate-*l/ 99.9%

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

      4. *-commutative 99.9%

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

      5. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 66.6%

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

      1. associate-/l* 75.2%

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

   6. Simplified 75.2%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}} + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-59}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 0.145:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+65} \lor \neg \left(z \leq 2.6 \cdot 10^{+62}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.8e+65) (not (<= z 2.6e+62)))
   (+ x (* y (/ z (- z a))))
   (+ x (/ y (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.8e+65) || !(z <= 2.6e+62)) {
		tmp = x + (y * (z / (z - a)));
	} 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 <= (-1.8d+65)) .or. (.not. (z <= 2.6d+62))) then
        tmp = x + (y * (z / (z - a)))
    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 <= -1.8e+65) || !(z <= 2.6e+62)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.8e+65) or not (z <= 2.6e+62):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + (y / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.8e+65) || !(z <= 2.6e+62))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	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 <= -1.8e+65) || ~((z <= 2.6e+62)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + (y / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.8e+65], N[Not[LessEqual[z, 2.6e+62]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $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 < -1.79999999999999989e65 or 2.59999999999999984e62 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 94.9%

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

   if -1.79999999999999989e65 < z < 2.59999999999999984e62

   1. Initial program 98.0%

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

      1. associate-*r/ 95.5%

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

      2. associate-/l* 98.0%

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

   3. Applied egg-rr 98.0%

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

   4. Taylor expanded in t around inf 89.8%

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

      1. associate-*r/ 89.8%

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

      2. neg-mul-1 89.8%

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

      3. neg-sub0 89.8%

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

      4. associate--r- 89.8%

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

      5. neg-sub0 89.8%

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

   6. Simplified 89.8%

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

   7. Taylor expanded in z around 0 89.8%

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

      1. mul-1-neg 89.8%

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

      2. sub-neg 89.8%

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

      3. div-sub 89.8%

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

   9. Simplified 89.8%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+65} \lor \neg \left(z \leq 2.6 \cdot 10^{+62}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 7: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+65}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.8e+65)
   (+ x (/ y (- 1.0 (/ a z))))
   (if (<= z 1.2e+62) (+ x (/ y (/ (- a z) t))) (+ x (* y (/ z (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.8e+65) {
		tmp = x + (y / (1.0 - (a / z)));
	} else if (z <= 1.2e+62) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.8d+65)) then
        tmp = x + (y / (1.0d0 - (a / z)))
    else if (z <= 1.2d+62) then
        tmp = x + (y / ((a - z) / t))
    else
        tmp = x + (y * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.8e+65) {
		tmp = x + (y / (1.0 - (a / z)));
	} else if (z <= 1.2e+62) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.8e+65:
		tmp = x + (y / (1.0 - (a / z)))
	elif z <= 1.2e+62:
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.8e+65)
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	elseif (z <= 1.2e+62)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.8e+65)
		tmp = x + (y / (1.0 - (a / z)));
	elseif (z <= 1.2e+62)
		tmp = x + (y / ((a - z) / t));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.8e+65], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+62], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8000000000000001e65

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 64.8%

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

      3. associate-*l/ 96.6%

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

      4. *-commutative 96.6%

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

      5. fma-def 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in t around 0 62.2%

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

      1. associate-/l* 96.8%

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

      2. div-sub 96.8%

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

      3. *-inverses 96.8%

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

   6. Simplified 96.8%

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

   if -5.8000000000000001e65 < z < 1.2e62

   1. Initial program 98.0%

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

      1. associate-*r/ 95.5%

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

      2. associate-/l* 98.0%

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

   3. Applied egg-rr 98.0%

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

   4. Taylor expanded in t around inf 89.8%

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

      1. associate-*r/ 89.8%

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

      2. neg-mul-1 89.8%

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

      3. neg-sub0 89.8%

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

      4. associate--r- 89.8%

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

      5. neg-sub0 89.8%

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

   6. Simplified 89.8%

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

   7. Taylor expanded in z around 0 89.8%

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

      1. mul-1-neg 89.8%

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

      2. sub-neg 89.8%

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

      3. div-sub 89.8%

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

   9. Simplified 89.8%

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

   if 1.2e62 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 93.1%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+65}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 8: 76.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{-43} \lor \neg \left(z \leq 1.2 \cdot 10^{+62}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.52e-43) (not (<= z 1.2e+62))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.52e-43) || !(z <= 1.2e+62)) {
		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 <= (-1.52d-43)) .or. (.not. (z <= 1.2d+62))) 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 <= -1.52e-43) || !(z <= 1.2e+62)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.52e-43) or not (z <= 1.2e+62):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.52e-43) || !(z <= 1.2e+62))
		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 <= -1.52e-43) || ~((z <= 1.2e+62)))
		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, -1.52e-43], N[Not[LessEqual[z, 1.2e+62]], $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 < -1.52e-43 or 1.2e62 < z

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*r/ 68.9%

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

      3. associate-*l/ 97.6%

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

      4. *-commutative 97.6%

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

      5. fma-def 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around inf 85.3%

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

   if -1.52e-43 < z < 1.2e62

   1. Initial program 97.7%

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

   2. Taylor expanded in z around 0 78.1%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{-43} \lor \neg \left(z \leq 1.2 \cdot 10^{+62}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 9: 98.4% accurate, 1.0× speedup

Math

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

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

Derivation

1. Initial program 98.8%

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

2. Final simplification 98.8%

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

Alternative 10: 51.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+232}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+135}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{+45}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3e+232)
   y
   (if (<= y -5.5e+135) x (if (<= y -1.36e+45) y (if (<= y 5.3e+129) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3e+232) {
		tmp = y;
	} else if (y <= -5.5e+135) {
		tmp = x;
	} else if (y <= -1.36e+45) {
		tmp = y;
	} else if (y <= 5.3e+129) {
		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 <= (-3d+232)) then
        tmp = y
    else if (y <= (-5.5d+135)) then
        tmp = x
    else if (y <= (-1.36d+45)) then
        tmp = y
    else if (y <= 5.3d+129) 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 <= -3e+232) {
		tmp = y;
	} else if (y <= -5.5e+135) {
		tmp = x;
	} else if (y <= -1.36e+45) {
		tmp = y;
	} else if (y <= 5.3e+129) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3e+232:
		tmp = y
	elif y <= -5.5e+135:
		tmp = x
	elif y <= -1.36e+45:
		tmp = y
	elif y <= 5.3e+129:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3e+232)
		tmp = y;
	elseif (y <= -5.5e+135)
		tmp = x;
	elseif (y <= -1.36e+45)
		tmp = y;
	elseif (y <= 5.3e+129)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3e+232)
		tmp = y;
	elseif (y <= -5.5e+135)
		tmp = x;
	elseif (y <= -1.36e+45)
		tmp = y;
	elseif (y <= 5.3e+129)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3e+232], y, If[LessEqual[y, -5.5e+135], x, If[LessEqual[y, -1.36e+45], y, If[LessEqual[y, 5.3e+129], x, y]]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.00000000000000003e232 or -5.4999999999999999e135 < y < -1.36e45 or 5.2999999999999999e129 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*r/ 55.7%

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

      3. associate-*l/ 97.1%

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

      4. *-commutative 97.1%

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

      5. fma-def 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in t around 0 26.5%

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

      1. associate-/l* 62.9%

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

      2. div-sub 62.9%

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

      3. *-inverses 62.9%

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

   6. Simplified 62.9%

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

   7. Taylor expanded in y around inf 52.6%

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

   8. Taylor expanded in a around 0 45.7%

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

   if -3.00000000000000003e232 < y < -5.4999999999999999e135 or -1.36e45 < y < 5.2999999999999999e129

   1. Initial program 98.4%

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

      1. +-commutative 98.4%

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

      2. associate-*r/ 93.2%

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

      3. associate-*l/ 97.0%

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

      4. *-commutative 97.0%

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

      5. fma-def 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in y around 0 73.7%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+232}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+135}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{+45}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 11: 63.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+152}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+182}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.5e+152) x (if (<= a 6.5e+182) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e+152) {
		tmp = x;
	} else if (a <= 6.5e+182) {
		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 (a <= (-5.5d+152)) then
        tmp = x
    else if (a <= 6.5d+182) 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 (a <= -5.5e+152) {
		tmp = x;
	} else if (a <= 6.5e+182) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.5e+152:
		tmp = x
	elif a <= 6.5e+182:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.5e+152)
		tmp = x;
	elseif (a <= 6.5e+182)
		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 (a <= -5.5e+152)
		tmp = x;
	elseif (a <= 6.5e+182)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.5e+152], x, If[LessEqual[a, 6.5e+182], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.4999999999999999e152 or 6.4999999999999998e182 < a

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 87.3%

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

      3. associate-*l/ 94.0%

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

      4. *-commutative 94.0%

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

      5. fma-def 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in y around 0 73.7%

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

   if -5.4999999999999999e152 < a < 6.4999999999999998e182

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      2. associate-*r/ 81.6%

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

      3. associate-*l/ 97.9%

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

      4. *-commutative 97.9%

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

      5. fma-def 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in z around inf 72.3%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+152}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+182}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 50.6% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. +-commutative 98.8%

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

   2. associate-*r/ 82.9%

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

   3. associate-*l/ 97.0%

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

   4. *-commutative 97.0%

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

   5. fma-def 97.0%

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

3. Simplified 97.0%

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

4. Taylor expanded in y around 0 56.6%

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

5. Final simplification 56.6%

   \[\leadsto x \]

Developer target: 98.5% 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 2023257 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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