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

Percentage Accurate: 85.5% → 98.2%

Time: 12.7s

Alternatives: 16

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: 85.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% 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]

Derivation

1. Initial program 84.0%

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

   1. associate-/l* 97.9%

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

3. Simplified 97.9%

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

4. Final simplification 97.9%

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

Alternative 2: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+169}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+65}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{+30}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+67}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ y (- z a)))))
   (if (<= z -1.85e+169)
     (+ x y)
     (if (<= z -5e+65)
       (- x (* t (/ y z)))
       (if (<= z -1.66e+30)
         (+ x y)
         (if (<= z -4.5e-133)
           t_1
           (if (<= z 1.9e-64)
             (+ x (/ y (/ a t)))
             (if (<= z 3.2e+19)
               t_1
               (if (<= z 8.6e+67) (- x (/ y (/ a z))) (+ x y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (z - a));
	double tmp;
	if (z <= -1.85e+169) {
		tmp = x + y;
	} else if (z <= -5e+65) {
		tmp = x - (t * (y / z));
	} else if (z <= -1.66e+30) {
		tmp = x + y;
	} else if (z <= -4.5e-133) {
		tmp = t_1;
	} else if (z <= 1.9e-64) {
		tmp = x + (y / (a / t));
	} else if (z <= 3.2e+19) {
		tmp = t_1;
	} else if (z <= 8.6e+67) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) * (y / (z - a))
    if (z <= (-1.85d+169)) then
        tmp = x + y
    else if (z <= (-5d+65)) then
        tmp = x - (t * (y / z))
    else if (z <= (-1.66d+30)) then
        tmp = x + y
    else if (z <= (-4.5d-133)) then
        tmp = t_1
    else if (z <= 1.9d-64) then
        tmp = x + (y / (a / t))
    else if (z <= 3.2d+19) then
        tmp = t_1
    else if (z <= 8.6d+67) then
        tmp = x - (y / (a / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (z - a));
	double tmp;
	if (z <= -1.85e+169) {
		tmp = x + y;
	} else if (z <= -5e+65) {
		tmp = x - (t * (y / z));
	} else if (z <= -1.66e+30) {
		tmp = x + y;
	} else if (z <= -4.5e-133) {
		tmp = t_1;
	} else if (z <= 1.9e-64) {
		tmp = x + (y / (a / t));
	} else if (z <= 3.2e+19) {
		tmp = t_1;
	} else if (z <= 8.6e+67) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * (y / (z - a))
	tmp = 0
	if z <= -1.85e+169:
		tmp = x + y
	elif z <= -5e+65:
		tmp = x - (t * (y / z))
	elif z <= -1.66e+30:
		tmp = x + y
	elif z <= -4.5e-133:
		tmp = t_1
	elif z <= 1.9e-64:
		tmp = x + (y / (a / t))
	elif z <= 3.2e+19:
		tmp = t_1
	elif z <= 8.6e+67:
		tmp = x - (y / (a / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * Float64(y / Float64(z - a)))
	tmp = 0.0
	if (z <= -1.85e+169)
		tmp = Float64(x + y);
	elseif (z <= -5e+65)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= -1.66e+30)
		tmp = Float64(x + y);
	elseif (z <= -4.5e-133)
		tmp = t_1;
	elseif (z <= 1.9e-64)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 3.2e+19)
		tmp = t_1;
	elseif (z <= 8.6e+67)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * (y / (z - a));
	tmp = 0.0;
	if (z <= -1.85e+169)
		tmp = x + y;
	elseif (z <= -5e+65)
		tmp = x - (t * (y / z));
	elseif (z <= -1.66e+30)
		tmp = x + y;
	elseif (z <= -4.5e-133)
		tmp = t_1;
	elseif (z <= 1.9e-64)
		tmp = x + (y / (a / t));
	elseif (z <= 3.2e+19)
		tmp = t_1;
	elseif (z <= 8.6e+67)
		tmp = x - (y / (a / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e+169], N[(x + y), $MachinePrecision], If[LessEqual[z, -5e+65], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.66e+30], N[(x + y), $MachinePrecision], If[LessEqual[z, -4.5e-133], t$95$1, If[LessEqual[z, 1.9e-64], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+19], t$95$1, If[LessEqual[z, 8.6e+67], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.85e169 or -4.99999999999999973e65 < z < -1.66e30 or 8.6000000000000002e67 < z

   1. Initial program 70.5%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in z around inf 82.8%

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

   if -1.85e169 < z < -4.99999999999999973e65

   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-*r/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around inf 86.4%

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

      1. neg-mul-1 86.4%

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

      2. distribute-neg-frac 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in z around inf 65.1%

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

      1. +-commutative 65.1%

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

      2. mul-1-neg 65.1%

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

      3. unsub-neg 65.1%

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

      4. associate-/l* 81.9%

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

      5. associate-/r/ 81.9%

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

   9. Simplified 81.9%

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

   if -1.66e30 < z < -4.50000000000000009e-133 or 1.9000000000000001e-64 < z < 3.2e19

   1. Initial program 91.5%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in x around 0 68.1%

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

      1. *-un-lft-identity 68.1%

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

      2. times-frac 74.3%

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

      3. clear-num 74.2%

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

      4. times-frac 72.1%

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

      5. *-un-lft-identity 72.1%

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

      6. associate-/l/ 74.1%

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

      7. associate-/r/ 74.3%

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

      8. /-rgt-identity 74.3%

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

   6. Applied egg-rr 74.3%

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

   if -4.50000000000000009e-133 < z < 1.9000000000000001e-64

   1. Initial program 95.8%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around 0 81.7%

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

      1. associate-/l* 85.5%

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

   6. Simplified 85.5%

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

   if 3.2e19 < z < 8.6000000000000002e67

   1. Initial program 88.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 88.2%

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

   5. Taylor expanded in z around 0 76.2%

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

      1. +-commutative 76.2%

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

      2. mul-1-neg 76.2%

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

      3. unsub-neg 76.2%

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

      4. associate-/l* 76.2%

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

   7. Simplified 76.2%

      \[\leadsto \color{blue}{x - \frac{y}{\frac{a}{z}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+169}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+65}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{+30}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-133}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+19}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+67}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 76.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+166}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+63}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{+38} \lor \neg \left(z \leq 1.9 \cdot 10^{+16}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+166)
   (+ x y)
   (if (<= z -5.2e+63)
     (- x (* t (/ y z)))
     (if (or (<= z -1.46e+38) (not (<= z 1.9e+16)))
       (+ x y)
       (+ x (/ y (/ a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+166) {
		tmp = x + y;
	} else if (z <= -5.2e+63) {
		tmp = x - (t * (y / z));
	} else if ((z <= -1.46e+38) || !(z <= 1.9e+16)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.15d+166)) then
        tmp = x + y
    else if (z <= (-5.2d+63)) then
        tmp = x - (t * (y / z))
    else if ((z <= (-1.46d+38)) .or. (.not. (z <= 1.9d+16))) then
        tmp = x + y
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+166) {
		tmp = x + y;
	} else if (z <= -5.2e+63) {
		tmp = x - (t * (y / z));
	} else if ((z <= -1.46e+38) || !(z <= 1.9e+16)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e+166:
		tmp = x + y
	elif z <= -5.2e+63:
		tmp = x - (t * (y / z))
	elif (z <= -1.46e+38) or not (z <= 1.9e+16):
		tmp = x + y
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+166)
		tmp = Float64(x + y);
	elseif (z <= -5.2e+63)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif ((z <= -1.46e+38) || !(z <= 1.9e+16))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e+166)
		tmp = x + y;
	elseif (z <= -5.2e+63)
		tmp = x - (t * (y / z));
	elseif ((z <= -1.46e+38) || ~((z <= 1.9e+16)))
		tmp = x + y;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+166], N[(x + y), $MachinePrecision], If[LessEqual[z, -5.2e+63], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.46e+38], N[Not[LessEqual[z, 1.9e+16]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15000000000000004e166 or -5.2000000000000002e63 < z < -1.46000000000000008e38 or 1.9e16 < z

   1. Initial program 72.5%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in z around inf 81.8%

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

   if -1.15000000000000004e166 < z < -5.2000000000000002e63

   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-*r/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around inf 86.4%

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

      1. neg-mul-1 86.4%

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

      2. distribute-neg-frac 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in z around inf 65.1%

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

      1. +-commutative 65.1%

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

      2. mul-1-neg 65.1%

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

      3. unsub-neg 65.1%

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

      4. associate-/l* 81.9%

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

      5. associate-/r/ 81.9%

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

   9. Simplified 81.9%

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

   if -1.46000000000000008e38 < z < 1.9e16

   1. Initial program 93.8%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in z around 0 70.3%

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

      1. associate-/l* 74.8%

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

   6. Simplified 74.8%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+166}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+63}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{+38} \lor \neg \left(z \leq 1.9 \cdot 10^{+16}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 4: 80.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-134}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-43}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ t z))))))
   (if (<= z -3e-30)
     t_1
     (if (<= z -4.5e-134)
       (* (- z t) (/ y (- z a)))
       (if (<= z 1.25e-43) (+ x (/ y (/ a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -3e-30) {
		tmp = t_1;
	} else if (z <= -4.5e-134) {
		tmp = (z - t) * (y / (z - a));
	} else if (z <= 1.25e-43) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (1.0d0 - (t / z)))
    if (z <= (-3d-30)) then
        tmp = t_1
    else if (z <= (-4.5d-134)) then
        tmp = (z - t) * (y / (z - a))
    else if (z <= 1.25d-43) then
        tmp = x + (y / (a / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -3e-30) {
		tmp = t_1;
	} else if (z <= -4.5e-134) {
		tmp = (z - t) * (y / (z - a));
	} else if (z <= 1.25e-43) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (t / z)))
	tmp = 0
	if z <= -3e-30:
		tmp = t_1
	elif z <= -4.5e-134:
		tmp = (z - t) * (y / (z - a))
	elif z <= 1.25e-43:
		tmp = x + (y / (a / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	tmp = 0.0
	if (z <= -3e-30)
		tmp = t_1;
	elseif (z <= -4.5e-134)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	elseif (z <= 1.25e-43)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (1.0 - (t / z)));
	tmp = 0.0;
	if (z <= -3e-30)
		tmp = t_1;
	elseif (z <= -4.5e-134)
		tmp = (z - t) * (y / (z - a));
	elseif (z <= 1.25e-43)
		tmp = x + (y / (a / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e-30], t$95$1, If[LessEqual[z, -4.5e-134], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-43], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9999999999999999e-30 or 1.25000000000000005e-43 < z

   1. Initial program 76.4%

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

      1. +-commutative 76.4%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around 0 84.4%

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

      1. div-sub 84.4%

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

      2. *-inverses 84.4%

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

   8. Simplified 84.4%

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

   if -2.9999999999999999e-30 < z < -4.5000000000000005e-134

   1. Initial program 84.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 70.1%

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

      1. *-un-lft-identity 70.1%

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

      2. times-frac 84.9%

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

      3. clear-num 84.8%

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

      4. times-frac 74.6%

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

      5. *-un-lft-identity 74.6%

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

      6. associate-/l/ 84.6%

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

      7. associate-/r/ 84.9%

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

      8. /-rgt-identity 84.9%

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

   6. Applied egg-rr 84.9%

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

   if -4.5000000000000005e-134 < z < 1.25000000000000005e-43

   1. Initial program 95.0%

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

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in z around 0 80.4%

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

      1. associate-/l* 85.0%

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

   6. Simplified 85.0%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-30}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-134}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-43}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]

Alternative 5: 80.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-123} \lor \neg \left(z \leq 1.45 \cdot 10^{-43}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e-123) (not (<= z 1.45e-43)))
   (+ x (* (- z t) (/ y z)))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e-123) || !(z <= 1.45e-43)) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.2d-123)) .or. (.not. (z <= 1.45d-43))) then
        tmp = x + ((z - t) * (y / z))
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e-123) || !(z <= 1.45e-43)) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e-123) or not (z <= 1.45e-43):
		tmp = x + ((z - t) * (y / z))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e-123) || !(z <= 1.45e-43))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.2e-123) || ~((z <= 1.45e-43)))
		tmp = x + ((z - t) * (y / z));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e-123], N[Not[LessEqual[z, 1.45e-43]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e-123 or 1.4500000000000001e-43 < z

   1. Initial program 77.2%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in z around inf 78.1%

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

   if -1.2e-123 < z < 1.4500000000000001e-43

   1. Initial program 95.0%

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

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in z around 0 79.6%

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

      1. associate-/l* 84.2%

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

   6. Simplified 84.2%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-123} \lor \neg \left(z \leq 1.45 \cdot 10^{-43}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 6: 80.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-125}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.6e-125)
   (+ x (* (- z t) (/ y z)))
   (if (<= z 3.1e-30) (+ x (/ y (/ a t))) (+ x (/ y (/ (- z a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e-125) {
		tmp = x + ((z - t) * (y / z));
	} else if (z <= 3.1e-30) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.6d-125)) then
        tmp = x + ((z - t) * (y / z))
    else if (z <= 3.1d-30) then
        tmp = x + (y / (a / t))
    else
        tmp = x + (y / ((z - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e-125) {
		tmp = x + ((z - t) * (y / z));
	} else if (z <= 3.1e-30) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.6e-125:
		tmp = x + ((z - t) * (y / z))
	elif z <= 3.1e-30:
		tmp = x + (y / (a / t))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.6e-125)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / z)));
	elseif (z <= 3.1e-30)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.6e-125)
		tmp = x + ((z - t) * (y / z));
	elseif (z <= 3.1e-30)
		tmp = x + (y / (a / t));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.6e-125], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-30], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5999999999999999e-125

   1. Initial program 78.1%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around inf 76.7%

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

   if -1.5999999999999999e-125 < z < 3.09999999999999991e-30

   1. Initial program 95.2%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in z around 0 78.4%

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

      1. associate-/l* 82.8%

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

   6. Simplified 82.8%

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

   if 3.09999999999999991e-30 < z

   1. Initial program 75.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 85.5%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-125}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 7: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-47}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+16}:\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e-47)
   (+ x (* y (- 1.0 (/ t z))))
   (if (<= z 7.5e+16) (- x (/ (* y t) (- z a))) (+ x (/ y (/ (- z a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-47) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 7.5e+16) {
		tmp = x - ((y * t) / (z - a));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.5d-47)) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else if (z <= 7.5d+16) then
        tmp = x - ((y * t) / (z - a))
    else
        tmp = x + (y / ((z - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-47) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 7.5e+16) {
		tmp = x - ((y * t) / (z - a));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e-47:
		tmp = x + (y * (1.0 - (t / z)))
	elif z <= 7.5e+16:
		tmp = x - ((y * t) / (z - a))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e-47)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	elseif (z <= 7.5e+16)
		tmp = Float64(x - Float64(Float64(y * t) / Float64(z - a)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e-47)
		tmp = x + (y * (1.0 - (t / z)));
	elseif (z <= 7.5e+16)
		tmp = x - ((y * t) / (z - a));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e-47], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+16], N[(x - N[(N[(y * t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5000000000000002e-47

   1. Initial program 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around 0 82.8%

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

      1. div-sub 82.8%

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

      2. *-inverses 82.8%

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

   8. Simplified 82.8%

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

   if -5.5000000000000002e-47 < z < 7.5e16

   1. Initial program 94.4%

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

      1. +-commutative 94.4%

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

      2. associate-*r/ 95.1%

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

      3. fma-def 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in t around inf 90.5%

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

      1. neg-mul-1 90.5%

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

      2. distribute-neg-frac 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in y around 0 88.9%

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

      1. +-commutative 88.9%

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

      2. mul-1-neg 88.9%

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

      3. associate-*r/ 90.4%

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

      4. distribute-lft-neg-in 90.4%

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

      5. cancel-sign-sub-inv 90.4%

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

      6. associate-*r/ 88.9%

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

   9. Simplified 88.9%

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

   if 7.5e16 < z

   1. Initial program 71.9%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 89.5%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-47}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+16}:\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 8: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+45}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e+45)
   (+ x (* y (- 1.0 (/ t z))))
   (if (<= z 9.8e+16) (+ x (/ y (/ (- a z) t))) (+ x (/ y (/ (- z a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+45) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 9.8e+16) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.35d+45)) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else if (z <= 9.8d+16) then
        tmp = x + (y / ((a - z) / t))
    else
        tmp = x + (y / ((z - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+45) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 9.8e+16) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e+45:
		tmp = x + (y * (1.0 - (t / z)))
	elif z <= 9.8e+16:
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e+45)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	elseif (z <= 9.8e+16)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e+45)
		tmp = x + (y * (1.0 - (t / z)));
	elseif (z <= 9.8e+16)
		tmp = x + (y / ((a - z) / t));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e+45], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e+16], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.34999999999999992e45

   1. Initial program 72.3%

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

      1. +-commutative 72.3%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around 0 87.7%

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

      1. div-sub 87.7%

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

      2. *-inverses 87.7%

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

   8. Simplified 87.7%

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

   if -1.34999999999999992e45 < z < 9.8e16

   1. Initial program 93.8%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in t around inf 89.1%

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

      1. associate-*r/ 89.1%

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

      2. neg-mul-1 89.1%

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

      3. sub-neg 89.1%

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

      4. mul-1-neg 89.1%

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

      5. distribute-neg-in 89.1%

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

      6. mul-1-neg 89.1%

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

      7. remove-double-neg 89.1%

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

   6. Simplified 89.1%

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

   if 9.8e16 < z

   1. Initial program 71.9%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 89.5%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+45}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 9: 77.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+38} \lor \neg \left(z \leq 8.5 \cdot 10^{+16}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e+38) (not (<= z 8.5e+16))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+38) || !(z <= 8.5e+16)) {
		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 <= (-1.45d+38)) .or. (.not. (z <= 8.5d+16))) 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 <= -1.45e+38) || !(z <= 8.5e+16)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e+38) or not (z <= 8.5e+16):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e+38) || !(z <= 8.5e+16))
		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 <= -1.45e+38) || ~((z <= 8.5e+16)))
		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, -1.45e+38], N[Not[LessEqual[z, 8.5e+16]], $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 < -1.45000000000000003e38 or 8.5e16 < z

   1. Initial program 72.1%

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

      1. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in z around inf 77.9%

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

   if -1.45000000000000003e38 < z < 8.5e16

   1. Initial program 93.8%

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

      1. +-commutative 93.8%

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

      2. associate-*r/ 95.8%

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

      3. fma-def 95.8%

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

   3. Simplified 95.8%

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

      1. fma-udef 95.8%

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

   5. Applied egg-rr 95.8%

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

   6. Taylor expanded in z around 0 74.3%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+38} \lor \neg \left(z \leq 8.5 \cdot 10^{+16}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 10: 77.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+42}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+16}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.8e+42) (+ x y) (if (<= z 7.5e+16) (+ x (* t (/ y a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+42) {
		tmp = x + y;
	} else if (z <= 7.5e+16) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.8d+42)) then
        tmp = x + y
    else if (z <= 7.5d+16) then
        tmp = x + (t * (y / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+42) {
		tmp = x + y;
	} else if (z <= 7.5e+16) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e+42:
		tmp = x + y
	elif z <= 7.5e+16:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e+42)
		tmp = Float64(x + y);
	elseif (z <= 7.5e+16)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.8e+42)
		tmp = x + y;
	elseif (z <= 7.5e+16)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.8e+42], N[(x + y), $MachinePrecision], If[LessEqual[z, 7.5e+16], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8000000000000005e42 or 7.5e16 < z

   1. Initial program 72.1%

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

      1. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in z around inf 77.9%

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

   if -8.8000000000000005e42 < z < 7.5e16

   1. Initial program 93.8%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

      1. associate-/l* 93.8%

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

      2. clear-num 93.8%

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

      3. associate-/r/ 93.8%

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

   5. Applied egg-rr 93.8%

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

   6. Taylor expanded in z around 0 70.3%

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

      1. associate-/l* 74.8%

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

      2. associate-/r/ 72.3%

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

   8. Simplified 72.3%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+42}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+16}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 77.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+43}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e+43) (+ x y) (if (<= z 5.6e+16) (+ x (/ y (/ a t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+43) {
		tmp = x + y;
	} else if (z <= 5.6e+16) {
		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 <= (-2.8d+43)) then
        tmp = x + y
    else if (z <= 5.6d+16) 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 <= -2.8e+43) {
		tmp = x + y;
	} else if (z <= 5.6e+16) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8e+43:
		tmp = x + y
	elif z <= 5.6e+16:
		tmp = x + (y / (a / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e+43)
		tmp = Float64(x + y);
	elseif (z <= 5.6e+16)
		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 <= -2.8e+43)
		tmp = x + y;
	elseif (z <= 5.6e+16)
		tmp = x + (y / (a / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e+43], N[(x + y), $MachinePrecision], If[LessEqual[z, 5.6e+16], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.80000000000000019e43 or 5.6e16 < z

   1. Initial program 72.1%

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

      1. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in z around inf 77.9%

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

   if -2.80000000000000019e43 < z < 5.6e16

   1. Initial program 93.8%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in z around 0 70.3%

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

      1. associate-/l* 74.8%

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

   6. Simplified 74.8%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+43}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12: 96.1% 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 84.0%

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

   1. associate-*l/ 94.3%

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

3. Simplified 94.3%

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

4. Final simplification 94.3%

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

Alternative 13: 61.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+216} \lor \neg \left(t \leq 4 \cdot 10^{+199}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.3e+216) (not (<= t 4e+199))) (* t (/ y a)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.3e+216) || !(t <= 4e+199)) {
		tmp = t * (y / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.3d+216)) .or. (.not. (t <= 4d+199))) then
        tmp = t * (y / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.3e+216) || !(t <= 4e+199)) {
		tmp = t * (y / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.3e+216) or not (t <= 4e+199):
		tmp = t * (y / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.3e+216) || !(t <= 4e+199))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.3e+216) || ~((t <= 4e+199)))
		tmp = t * (y / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.3e+216], N[Not[LessEqual[t, 4e+199]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.29999999999999996e216 or 4.00000000000000039e199 < t

   1. Initial program 82.8%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in x around 0 60.9%

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

   5. Taylor expanded in z around 0 58.8%

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

      1. mul-1-neg 58.8%

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

      2. distribute-rgt-neg-out 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in z around 0 47.5%

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

      1. associate-*l/ 51.9%

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

      2. *-commutative 51.9%

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

   10. Simplified 51.9%

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

   if -2.29999999999999996e216 < t < 4.00000000000000039e199

   1. Initial program 84.3%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around inf 62.0%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+216} \lor \neg \left(t \leq 4 \cdot 10^{+199}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 14: 61.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+215} \lor \neg \left(t \leq 7.8 \cdot 10^{+199}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.8e+215) (not (<= t 7.8e+199))) (* y (/ t a)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e+215) || !(t <= 7.8e+199)) {
		tmp = y * (t / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.8d+215)) .or. (.not. (t <= 7.8d+199))) then
        tmp = y * (t / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e+215) || !(t <= 7.8e+199)) {
		tmp = y * (t / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.8e+215) or not (t <= 7.8e+199):
		tmp = y * (t / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.8e+215) || !(t <= 7.8e+199))
		tmp = Float64(y * Float64(t / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.8e+215) || ~((t <= 7.8e+199)))
		tmp = y * (t / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.8e+215], N[Not[LessEqual[t, 7.8e+199]], $MachinePrecision]], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.8000000000000002e215 or 7.8000000000000004e199 < t

   1. Initial program 82.8%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in x around 0 60.9%

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

   5. Taylor expanded in z around 0 58.8%

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

      1. mul-1-neg 58.8%

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

      2. distribute-rgt-neg-out 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in z around 0 47.5%

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

      1. associate-*r/ 56.1%

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

   10. Simplified 56.1%

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

   if -4.8000000000000002e215 < t < 7.8000000000000004e199

   1. Initial program 84.3%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around inf 62.0%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+215} \lor \neg \left(t \leq 7.8 \cdot 10^{+199}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 15: 60.9% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 84.0%

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

   1. associate-*l/ 94.3%

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

3. Simplified 94.3%

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

4. Taylor expanded in z around inf 56.0%

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

5. Final simplification 56.0%

   \[\leadsto x + y \]

Alternative 16: 50.7% 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 84.0%

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

   1. associate-*l/ 94.3%

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

3. Simplified 94.3%

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

4. Taylor expanded in x around inf 47.1%

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

5. Final simplification 47.1%

   \[\leadsto x \]

Developer target: 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 2023192 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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