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

Percentage Accurate: 85.1% → 97.9%

Time: 11.8s

Alternatives: 17

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: 85.1% 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: 97.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

   1. +-commutative 86.0%

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

   2. associate-/l* 98.8%

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

   3. fma-define 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. Add Preprocessing
5. Add Preprocessing

Alternative 2: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+119}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-55}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-158}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.8e+119)
   (+ x (* y (/ z (- z a))))
   (if (<= z -8.2e-55)
     (+ x (* y (/ (- z t) z)))
     (if (<= z 1.62e-158) (+ x (/ (* y t) a)) (+ x (* z (/ y (- z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+119) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= -8.2e-55) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 1.62e-158) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = x + (z * (y / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.8d+119)) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= (-8.2d-55)) then
        tmp = x + (y * ((z - t) / z))
    else if (z <= 1.62d-158) then
        tmp = x + ((y * t) / a)
    else
        tmp = x + (z * (y / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+119) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= -8.2e-55) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 1.62e-158) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = x + (z * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e+119:
		tmp = x + (y * (z / (z - a)))
	elif z <= -8.2e-55:
		tmp = x + (y * ((z - t) / z))
	elif z <= 1.62e-158:
		tmp = x + ((y * t) / a)
	else:
		tmp = x + (z * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e+119)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= -8.2e-55)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	elseif (z <= 1.62e-158)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.8e+119)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= -8.2e-55)
		tmp = x + (y * ((z - t) / z));
	elseif (z <= 1.62e-158)
		tmp = x + ((y * t) / a);
	else
		tmp = x + (z * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.8e+119], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.2e-55], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.62e-158], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.8000000000000005e119

   1. Initial program 54.6%

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

   3. Taylor expanded in t around 0 57.9%

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

      1. associate-/l* 91.9%

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

   5. Simplified 91.9%

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

   if -8.8000000000000005e119 < z < -8.1999999999999996e-55

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. associate-/l* 99.9%

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

      3. fma-define 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. Add Preprocessing

   5. Taylor expanded in a around 0 80.9%

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

      1. +-commutative 80.9%

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

      2. associate-/l* 83.6%

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

   7. Simplified 83.6%

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

   if -8.1999999999999996e-55 < z < 1.62000000000000002e-158

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 89.8%

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

   if 1.62000000000000002e-158 < z

   1. Initial program 85.0%

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

      1. +-commutative 85.0%

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

      2. associate-/l* 98.9%

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

      3. fma-define 98.9%

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

   3. Simplified 98.9%

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

      1. fma-undefine 98.9%

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

      2. associate-/l* 85.0%

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

      3. div-inv 84.9%

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

      4. *-commutative 84.9%

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

      5. associate-*r* 98.7%

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

      6. div-inv 98.8%

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

   6. Applied egg-rr 98.8%

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

   7. Taylor expanded in z around inf 80.2%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+119}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-55}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-158}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-55}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-158}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- z a))))))
   (if (<= z -1.15e+120)
     t_1
     (if (<= z -1.7e-55)
       (+ x (* y (/ (- z t) z)))
       (if (<= z 1.62e-158) (+ x (/ (* y t) a)) 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 <= -1.15e+120) {
		tmp = t_1;
	} else if (z <= -1.7e-55) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 1.62e-158) {
		tmp = x + ((y * t) / a);
	} 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 <= (-1.15d+120)) then
        tmp = t_1
    else if (z <= (-1.7d-55)) then
        tmp = x + (y * ((z - t) / z))
    else if (z <= 1.62d-158) then
        tmp = x + ((y * t) / a)
    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 <= -1.15e+120) {
		tmp = t_1;
	} else if (z <= -1.7e-55) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 1.62e-158) {
		tmp = x + ((y * t) / a);
	} 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 <= -1.15e+120:
		tmp = t_1
	elif z <= -1.7e-55:
		tmp = x + (y * ((z - t) / z))
	elif z <= 1.62e-158:
		tmp = x + ((y * t) / a)
	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 <= -1.15e+120)
		tmp = t_1;
	elseif (z <= -1.7e-55)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	elseif (z <= 1.62e-158)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	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 <= -1.15e+120)
		tmp = t_1;
	elseif (z <= -1.7e-55)
		tmp = x + (y * ((z - t) / z));
	elseif (z <= 1.62e-158)
		tmp = x + ((y * t) / a);
	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, -1.15e+120], t$95$1, If[LessEqual[z, -1.7e-55], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.62e-158], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.14999999999999996e120 or 1.62000000000000002e-158 < z

   1. Initial program 75.6%

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

   3. Taylor expanded in t around 0 63.8%

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

      1. associate-/l* 83.1%

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

   5. Simplified 83.1%

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

   if -1.14999999999999996e120 < z < -1.69999999999999986e-55

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. associate-/l* 99.9%

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

      3. fma-define 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. Add Preprocessing

   5. Taylor expanded in a around 0 80.9%

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

      1. +-commutative 80.9%

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

      2. associate-/l* 83.6%

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

   7. Simplified 83.6%

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

   if -1.69999999999999986e-55 < z < 1.62000000000000002e-158

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 89.8%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+120}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-55}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-158}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+160}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -4.25 \cdot 10^{-10}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.8e+160)
   (+ y x)
   (if (<= z -4.25e-10)
     (- x (* t (/ y z)))
     (if (<= z 1.7e+33) (+ x (/ t (/ a y))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+160) {
		tmp = y + x;
	} else if (z <= -4.25e-10) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.7e+33) {
		tmp = x + (t / (a / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.8d+160)) then
        tmp = y + x
    else if (z <= (-4.25d-10)) then
        tmp = x - (t * (y / z))
    else if (z <= 1.7d+33) then
        tmp = x + (t / (a / y))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+160) {
		tmp = y + x;
	} else if (z <= -4.25e-10) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.7e+33) {
		tmp = x + (t / (a / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e+160:
		tmp = y + x
	elif z <= -4.25e-10:
		tmp = x - (t * (y / z))
	elif z <= 1.7e+33:
		tmp = x + (t / (a / y))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e+160)
		tmp = Float64(y + x);
	elseif (z <= -4.25e-10)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 1.7e+33)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.8e+160)
		tmp = y + x;
	elseif (z <= -4.25e-10)
		tmp = x - (t * (y / z));
	elseif (z <= 1.7e+33)
		tmp = x + (t / (a / y));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.8e+160], N[(y + x), $MachinePrecision], If[LessEqual[z, -4.25e-10], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+33], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.79999999999999968e160 or 1.7e33 < z

   1. Initial program 70.3%

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

      1. +-commutative 70.3%

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

      2. associate-/l* 99.9%

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

      3. fma-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 84.6%

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative 84.6%

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

   7. Simplified 84.6%

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

   if -8.79999999999999968e160 < z < -4.2499999999999998e-10

   1. Initial program 78.7%

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

      1. +-commutative 78.7%

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

      2. associate-/l* 99.9%

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

      3. fma-define 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. Add Preprocessing

   5. Taylor expanded in a around 0 70.8%

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

      1. +-commutative 70.8%

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

      2. associate-/l* 79.6%

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

   7. Simplified 79.6%

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

   8. Taylor expanded in z around 0 70.4%

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

      1. mul-1-neg 70.4%

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

      2. associate-/l* 75.9%

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

      3. distribute-rgt-neg-in 75.9%

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

      4. distribute-neg-frac2 75.9%

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

   10. Simplified 75.9%

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

   if -4.2499999999999998e-10 < z < 1.7e33

   1. Initial program 97.4%

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

      1. +-commutative 97.4%

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

      2. associate-/l* 97.9%

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

      3. fma-define 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around 0 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-/l* 76.8%

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

   7. Simplified 76.8%

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

      1. clear-num 76.7%

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

      2. un-div-inv 78.3%

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

   9. Applied egg-rr 78.3%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+160}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -4.25 \cdot 10^{-10}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+160}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-10}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.4e+160)
   (+ y x)
   (if (<= z -1.36e-10)
     (- x (* y (/ t z)))
     (if (<= z 3.6e+33) (+ x (/ t (/ a y))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+160) {
		tmp = y + x;
	} else if (z <= -1.36e-10) {
		tmp = x - (y * (t / z));
	} else if (z <= 3.6e+33) {
		tmp = x + (t / (a / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.4d+160)) then
        tmp = y + x
    else if (z <= (-1.36d-10)) then
        tmp = x - (y * (t / z))
    else if (z <= 3.6d+33) then
        tmp = x + (t / (a / y))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+160) {
		tmp = y + x;
	} else if (z <= -1.36e-10) {
		tmp = x - (y * (t / z));
	} else if (z <= 3.6e+33) {
		tmp = x + (t / (a / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.4e+160:
		tmp = y + x
	elif z <= -1.36e-10:
		tmp = x - (y * (t / z))
	elif z <= 3.6e+33:
		tmp = x + (t / (a / y))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.4e+160)
		tmp = Float64(y + x);
	elseif (z <= -1.36e-10)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (z <= 3.6e+33)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.4e+160)
		tmp = y + x;
	elseif (z <= -1.36e-10)
		tmp = x - (y * (t / z));
	elseif (z <= 3.6e+33)
		tmp = x + (t / (a / y));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.4e+160], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.36e-10], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+33], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4e160 or 3.6000000000000003e33 < z

   1. Initial program 70.3%

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

      1. +-commutative 70.3%

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

      2. associate-/l* 99.9%

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

      3. fma-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 84.6%

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative 84.6%

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

   7. Simplified 84.6%

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

   if -5.4e160 < z < -1.36e-10

   1. Initial program 78.7%

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

      1. +-commutative 78.7%

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

      2. associate-/l* 99.9%

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

      3. fma-define 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. Add Preprocessing

   5. Taylor expanded in a around 0 70.8%

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

      1. +-commutative 70.8%

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

      2. associate-/l* 79.6%

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

   7. Simplified 79.6%

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

   8. Taylor expanded in z around 0 75.8%

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

      1. neg-mul-1 75.8%

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

   10. Simplified 75.8%

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

   11. Taylor expanded in y around 0 70.4%

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

       1. mul-1-neg 70.4%

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

       2. *-commutative 70.4%

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

       3. associate-*r/ 75.8%

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

       4. sub-neg 75.8%

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

   13. Simplified 75.8%

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

   if -1.36e-10 < z < 3.6000000000000003e33

   1. Initial program 97.4%

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

      1. +-commutative 97.4%

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

      2. associate-/l* 97.9%

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

      3. fma-define 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around 0 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-/l* 76.8%

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

   7. Simplified 76.8%

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

      1. clear-num 76.7%

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

      2. un-div-inv 78.3%

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

   9. Applied egg-rr 78.3%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+160}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-10}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+121} \lor \neg \left(z \leq 2.45 \cdot 10^{+129}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.1e+121) (not (<= z 2.45e+129)))
   (+ x (* y (/ z (- z a))))
   (+ x (/ (* y (- z t)) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e+121) || !(z <= 2.45e+129)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + ((y * (z - t)) / (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 <= (-2.1d+121)) .or. (.not. (z <= 2.45d+129))) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + ((y * (z - t)) / (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 <= -2.1e+121) || !(z <= 2.45e+129)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + ((y * (z - t)) / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.1e+121) or not (z <= 2.45e+129):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + ((y * (z - t)) / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.1e+121) || !(z <= 2.45e+129))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.1e+121) || ~((z <= 2.45e+129)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + ((y * (z - t)) / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.1e+121], N[Not[LessEqual[z, 2.45e+129]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1000000000000002e121 or 2.45e129 < z

   1. Initial program 58.4%

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

   3. Taylor expanded in t around 0 59.0%

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

      1. associate-/l* 94.1%

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

   5. Simplified 94.1%

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

   if -2.1000000000000002e121 < z < 2.45e129

   1. Initial program 96.6%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+121} \lor \neg \left(z \leq 2.45 \cdot 10^{+129}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -250000000 \lor \neg \left(t \leq 6.8 \cdot 10^{-78}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -250000000.0) (not (<= t 6.8e-78)))
   (+ x (* t (/ y (- a z))))
   (+ x (* y (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -250000000.0) || !(t <= 6.8e-78)) {
		tmp = x + (t * (y / (a - z)));
	} 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 ((t <= (-250000000.0d0)) .or. (.not. (t <= 6.8d-78))) then
        tmp = x + (t * (y / (a - z)))
    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 ((t <= -250000000.0) || !(t <= 6.8e-78)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -250000000.0) or not (t <= 6.8e-78):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -250000000.0) || !(t <= 6.8e-78))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	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 ((t <= -250000000.0) || ~((t <= 6.8e-78)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -250000000.0], N[Not[LessEqual[t, 6.8e-78]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5e8 or 6.80000000000000023e-78 < t

   1. Initial program 84.2%

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

   3. Taylor expanded in t around inf 82.6%

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

      1. mul-1-neg 82.6%

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

      2. associate-/l* 89.5%

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

      3. distribute-rgt-neg-in 89.5%

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

      4. distribute-frac-neg2 89.5%

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

   5. Simplified 89.5%

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

   if -2.5e8 < t < 6.80000000000000023e-78

   1. Initial program 88.1%

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

   3. Taylor expanded in t around 0 81.5%

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

      1. associate-/l* 92.7%

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

   5. Simplified 92.7%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -250000000 \lor \neg \left(t \leq 6.8 \cdot 10^{-78}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -960000 \lor \neg \left(a \leq 14000000000\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -960000.0) (not (<= a 14000000000.0)))
   (+ x (* y (/ (- t z) a)))
   (+ x (* y (/ (- z t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -960000.0) || !(a <= 14000000000.0)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + (y * ((z - t) / 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 ((a <= (-960000.0d0)) .or. (.not. (a <= 14000000000.0d0))) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x + (y * ((z - t) / 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 ((a <= -960000.0) || !(a <= 14000000000.0)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -960000.0) or not (a <= 14000000000.0):
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -960000.0) || !(a <= 14000000000.0))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -960000.0) || ~((a <= 14000000000.0)))
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -960000.0], N[Not[LessEqual[a, 14000000000.0]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.6e5 or 1.4e10 < a

   1. Initial program 85.2%

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

      1. +-commutative 85.2%

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

      2. associate-/l* 99.9%

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

      3. fma-define 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. Add Preprocessing

   5. Taylor expanded in a around inf 81.8%

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

      1. mul-1-neg 81.8%

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

      2. unsub-neg 81.8%

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

      3. associate-/l* 89.8%

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

   7. Simplified 89.8%

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

   if -9.6e5 < a < 1.4e10

   1. Initial program 86.7%

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

      1. +-commutative 86.7%

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

      2. associate-/l* 97.8%

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

      3. fma-define 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in a around 0 70.2%

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

      1. +-commutative 70.2%

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

      2. associate-/l* 82.0%

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

   7. Simplified 82.0%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -960000 \lor \neg \left(a \leq 14000000000\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-55} \lor \neg \left(z \leq 1.5 \cdot 10^{-158}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.65e-55) (not (<= z 1.5e-158)))
   (+ x (* y (/ z (- z a))))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e-55) || !(z <= 1.5e-158)) {
		tmp = x + (y * (z / (z - a)));
	} 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 <= (-1.65d-55)) .or. (.not. (z <= 1.5d-158))) then
        tmp = x + (y * (z / (z - a)))
    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 <= -1.65e-55) || !(z <= 1.5e-158)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.65e-55) or not (z <= 1.5e-158):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.65e-55) || !(z <= 1.5e-158))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.65e-55) || ~((z <= 1.5e-158)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.65e-55], N[Not[LessEqual[z, 1.5e-158]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e-55 or 1.5e-158 < z

   1. Initial program 79.0%

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

   3. Taylor expanded in t around 0 65.2%

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

      1. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

   if -1.65e-55 < z < 1.5e-158

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 89.8%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-55} \lor \neg \left(z \leq 1.5 \cdot 10^{-158}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+154} \lor \neg \left(z \leq 4.5 \cdot 10^{+32}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.75e+154) (not (<= z 4.5e+32))) (+ y x) (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.75e+154) || !(z <= 4.5e+32)) {
		tmp = y + x;
	} else {
		tmp = x + (t / (a / 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 <= (-1.75d+154)) .or. (.not. (z <= 4.5d+32))) then
        tmp = y + x
    else
        tmp = x + (t / (a / 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 <= -1.75e+154) || !(z <= 4.5e+32)) {
		tmp = y + x;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.75e+154) or not (z <= 4.5e+32):
		tmp = y + x
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.75e+154) || !(z <= 4.5e+32))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.75e+154) || ~((z <= 4.5e+32)))
		tmp = y + x;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.75e+154], N[Not[LessEqual[z, 4.5e+32]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7500000000000001e154 or 4.5000000000000003e32 < z

   1. Initial program 69.4%

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

      1. +-commutative 69.4%

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

      2. associate-/l* 99.9%

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

      3. fma-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 84.7%

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative 84.7%

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

   7. Simplified 84.7%

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

   if -1.7500000000000001e154 < z < 4.5000000000000003e32

   1. Initial program 94.1%

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

      1. +-commutative 94.1%

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

      2. associate-/l* 98.3%

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

      3. fma-define 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in z around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. associate-/l* 73.9%

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

   7. Simplified 73.9%

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

      1. clear-num 73.8%

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

      2. un-div-inv 75.1%

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

   9. Applied egg-rr 75.1%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+154} \lor \neg \left(z \leq 4.5 \cdot 10^{+32}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+154} \lor \neg \left(z \leq 1.3 \cdot 10^{+34}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.75e+154) (not (<= z 1.3e+34))) (+ y x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.75e+154) || !(z <= 1.3e+34)) {
		tmp = y + x;
	} 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 <= (-1.75d+154)) .or. (.not. (z <= 1.3d+34))) then
        tmp = y + x
    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 <= -1.75e+154) || !(z <= 1.3e+34)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.75e+154) or not (z <= 1.3e+34):
		tmp = y + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.75e+154) || !(z <= 1.3e+34))
		tmp = Float64(y + x);
	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 <= -1.75e+154) || ~((z <= 1.3e+34)))
		tmp = y + x;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.75e+154], N[Not[LessEqual[z, 1.3e+34]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7500000000000001e154 or 1.29999999999999999e34 < z

   1. Initial program 69.4%

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

      1. +-commutative 69.4%

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

      2. associate-/l* 99.9%

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

      3. fma-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 84.7%

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative 84.7%

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

   7. Simplified 84.7%

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

   if -1.7500000000000001e154 < z < 1.29999999999999999e34

   1. Initial program 94.1%

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

      1. +-commutative 94.1%

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

      2. associate-/l* 98.3%

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

      3. fma-define 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in z around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. associate-/l* 73.9%

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

   7. Simplified 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-*l/ 72.4%

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

   9. Applied egg-rr 72.4%

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

       1. associate-/l* 74.5%

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

   11. Applied egg-rr 74.5%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+154} \lor \neg \left(z \leq 1.3 \cdot 10^{+34}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-55} \lor \neg \left(z \leq 3.3 \cdot 10^{+33}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.3e-55) (not (<= z 3.3e+33))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.3e-55) || !(z <= 3.3e+33)) {
		tmp = y + x;
	} 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 <= (-3.3d-55)) .or. (.not. (z <= 3.3d+33))) then
        tmp = y + x
    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 <= -3.3e-55) || !(z <= 3.3e+33)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.3e-55) or not (z <= 3.3e+33):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.3e-55) || !(z <= 3.3e+33))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.3e-55) || ~((z <= 3.3e+33)))
		tmp = y + x;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.3e-55], N[Not[LessEqual[z, 3.3e+33]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999999e-55 or 3.29999999999999976e33 < z

   1. Initial program 73.4%

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

      1. +-commutative 73.4%

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

      2. associate-/l* 99.9%

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

      3. fma-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 76.6%

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative 76.6%

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

   7. Simplified 76.6%

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

   if -3.2999999999999999e-55 < z < 3.29999999999999976e33

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0 78.4%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-55} \lor \neg \left(z \leq 3.3 \cdot 10^{+33}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-55} \lor \neg \left(z \leq 1.5 \cdot 10^{+72}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3e-55) (not (<= z 1.5e+72))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3e-55) || !(z <= 1.5e+72)) {
		tmp = y + x;
	} 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 ((z <= (-3d-55)) .or. (.not. (z <= 1.5d+72))) then
        tmp = y + x
    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 ((z <= -3e-55) || !(z <= 1.5e+72)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3e-55) or not (z <= 1.5e+72):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3e-55) || !(z <= 1.5e+72))
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3e-55) || ~((z <= 1.5e+72)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3e-55], N[Not[LessEqual[z, 1.5e+72]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.00000000000000016e-55 or 1.50000000000000001e72 < z

   1. Initial program 71.3%

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

      1. +-commutative 71.3%

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

      2. associate-/l* 99.9%

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

      3. fma-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 78.1%

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative 78.1%

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

   7. Simplified 78.1%

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

   if -3.00000000000000016e-55 < z < 1.50000000000000001e72

   1. Initial program 98.1%

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

      1. +-commutative 98.1%

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

      2. associate-/l* 97.9%

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

      3. fma-define 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in y around 0 47.5%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-55} \lor \neg \left(z \leq 1.5 \cdot 10^{+72}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 97.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x - \frac{\frac{t - z}{z - a}}{\frac{1}{y}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (/ (- t z) (- z a)) (/ 1.0 y))))

C

double code(double x, double y, double z, double t, double a) {
	return x - (((t - z) / (z - a)) / (1.0 / y));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - (((t - z) / (z - a)) / (1.0d0 / y))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - (((t - z) / (z - a)) / (1.0 / y));
}

Python

def code(x, y, z, t, a):
	return x - (((t - z) / (z - a)) / (1.0 / y))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(Float64(t - z) / Float64(z - a)) / Float64(1.0 / y)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - (((t - z) / (z - a)) / (1.0 / y));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(N[(t - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] / N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.0%

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

   1. +-commutative 86.0%

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

   2. associate-/l* 98.8%

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

   3. fma-define 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. Add Preprocessing
5. Step-by-step derivation

   1. fma-undefine 98.8%

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

   2. associate-/l* 86.0%

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

   3. div-inv 85.9%

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

   4. *-commutative 85.9%

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

   5. associate-*r* 96.5%

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

   6. div-inv 96.6%

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

6. Applied egg-rr 96.6%

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

   1. clear-num 96.2%

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

   2. div-inv 96.7%

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

   3. div-inv 96.6%

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

   4. associate-/r* 98.7%

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

8. Applied egg-rr 98.7%

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

9. Final simplification 98.7%

   \[\leadsto x - \frac{\frac{t - z}{z - a}}{\frac{1}{y}} \]
10. Add Preprocessing

Alternative 15: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

   1. +-commutative 86.0%

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

   2. associate-/l* 98.8%

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

   3. fma-define 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. Add Preprocessing
5. Step-by-step derivation

   1. fma-undefine 98.8%

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

   2. associate-/l* 86.0%

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

   3. div-inv 85.9%

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

   4. *-commutative 85.9%

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

   5. associate-*r* 96.5%

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

   6. div-inv 96.6%

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

6. Applied egg-rr 96.6%

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

   1. clear-num 96.2%

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

   2. div-inv 96.7%

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

8. Applied egg-rr 96.7%

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

9. Final simplification 96.7%

   \[\leadsto x + \frac{z - t}{\frac{z - a}{y}} \]
10. Add Preprocessing

Alternative 16: 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 86.0%

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

   1. +-commutative 86.0%

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

   2. associate-/l* 98.8%

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

   3. fma-define 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. Add Preprocessing
5. Step-by-step derivation

   1. fma-undefine 98.8%

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

   2. associate-/l* 86.0%

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

   3. div-inv 85.9%

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

   4. *-commutative 85.9%

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

   5. associate-*r* 96.5%

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

   6. div-inv 96.6%

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

6. Applied egg-rr 96.6%

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

7. Final simplification 96.6%

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

Alternative 17: 49.6% 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 86.0%

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

   1. +-commutative 86.0%

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

   2. associate-/l* 98.8%

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

   3. fma-define 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. Add Preprocessing

5. Taylor expanded in y around 0 50.4%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 98.2% 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 2024170 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- z a) (- z t)))))

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