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

Percentage Accurate: 98.0% → 98.0%

Time: 12.1s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% 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 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-def 97.7%

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

3. Simplified 97.7%

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

4. Final simplification 97.7%

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

Alternative 2: 73.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+178}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+61}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+32}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 26500000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+16}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ y (- z a)))))
   (if (<= z -8.2e+178)
     (+ y x)
     (if (<= z -1.65e+61)
       (- x (/ y (/ z t)))
       (if (<= z -3.3e+32)
         (+ y x)
         (if (<= z -4.5e-133)
           t_1
           (if (<= z 2.9e-64)
             (+ x (/ y (/ a t)))
             (if (<= z 26500000.0)
               t_1
               (if (<= z 1.1e+16) (+ x (* y (/ t a))) (+ y x))))))))))

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 <= -8.2e+178) {
		tmp = y + x;
	} else if (z <= -1.65e+61) {
		tmp = x - (y / (z / t));
	} else if (z <= -3.3e+32) {
		tmp = y + x;
	} else if (z <= -4.5e-133) {
		tmp = t_1;
	} else if (z <= 2.9e-64) {
		tmp = x + (y / (a / t));
	} else if (z <= 26500000.0) {
		tmp = t_1;
	} else if (z <= 1.1e+16) {
		tmp = x + (y * (t / a));
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z - t) * (y / (z - a))
    if (z <= (-8.2d+178)) then
        tmp = y + x
    else if (z <= (-1.65d+61)) then
        tmp = x - (y / (z / t))
    else if (z <= (-3.3d+32)) then
        tmp = y + x
    else if (z <= (-4.5d-133)) then
        tmp = t_1
    else if (z <= 2.9d-64) then
        tmp = x + (y / (a / t))
    else if (z <= 26500000.0d0) then
        tmp = t_1
    else if (z <= 1.1d+16) then
        tmp = x + (y * (t / a))
    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 t_1 = (z - t) * (y / (z - a));
	double tmp;
	if (z <= -8.2e+178) {
		tmp = y + x;
	} else if (z <= -1.65e+61) {
		tmp = x - (y / (z / t));
	} else if (z <= -3.3e+32) {
		tmp = y + x;
	} else if (z <= -4.5e-133) {
		tmp = t_1;
	} else if (z <= 2.9e-64) {
		tmp = x + (y / (a / t));
	} else if (z <= 26500000.0) {
		tmp = t_1;
	} else if (z <= 1.1e+16) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * (y / (z - a))
	tmp = 0
	if z <= -8.2e+178:
		tmp = y + x
	elif z <= -1.65e+61:
		tmp = x - (y / (z / t))
	elif z <= -3.3e+32:
		tmp = y + x
	elif z <= -4.5e-133:
		tmp = t_1
	elif z <= 2.9e-64:
		tmp = x + (y / (a / t))
	elif z <= 26500000.0:
		tmp = t_1
	elif z <= 1.1e+16:
		tmp = x + (y * (t / a))
	else:
		tmp = y + x
	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 <= -8.2e+178)
		tmp = Float64(y + x);
	elseif (z <= -1.65e+61)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	elseif (z <= -3.3e+32)
		tmp = Float64(y + x);
	elseif (z <= -4.5e-133)
		tmp = t_1;
	elseif (z <= 2.9e-64)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 26500000.0)
		tmp = t_1;
	elseif (z <= 1.1e+16)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(y + x);
	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 <= -8.2e+178)
		tmp = y + x;
	elseif (z <= -1.65e+61)
		tmp = x - (y / (z / t));
	elseif (z <= -3.3e+32)
		tmp = y + x;
	elseif (z <= -4.5e-133)
		tmp = t_1;
	elseif (z <= 2.9e-64)
		tmp = x + (y / (a / t));
	elseif (z <= 26500000.0)
		tmp = t_1;
	elseif (z <= 1.1e+16)
		tmp = x + (y * (t / a));
	else
		tmp = y + x;
	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, -8.2e+178], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.65e+61], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e+32], N[(y + x), $MachinePrecision], If[LessEqual[z, -4.5e-133], t$95$1, If[LessEqual[z, 2.9e-64], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 26500000.0], t$95$1, If[LessEqual[z, 1.1e+16], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.19999999999999993e178 or -1.6499999999999999e61 < z < -3.3000000000000002e32 or 1.1e16 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 81.4%

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

   if -8.19999999999999993e178 < z < -1.6499999999999999e61

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 86.4%

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

      1. neg-mul-1 86.4%

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

      2. distribute-neg-frac 86.4%

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

   4. Simplified 86.4%

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

   5. Taylor expanded in z around inf 65.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot t}{z} + x} \]
   6. 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%

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

   7. Simplified 81.9%

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

   if -3.3000000000000002e32 < z < -4.50000000000000009e-133 or 2.8999999999999999e-64 < z < 2.65e7

   1. Initial program 92.9%

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

      1. +-commutative 92.9%

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

      2. associate-*r/ 90.9%

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

      3. associate-*l/ 97.7%

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

      4. *-commutative 97.7%

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

      5. fma-def 97.7%

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

   3. Simplified 97.7%

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

      1. clear-num 97.4%

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

      2. associate-/r/ 97.6%

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

   5. Applied egg-rr 97.6%

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

   6. Taylor expanded in y around -inf 68.2%

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

      1. *-commutative 68.2%

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

      2. associate-*r/ 74.9%

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

   8. Simplified 74.9%

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

   if -4.50000000000000009e-133 < z < 2.8999999999999999e-64

   1. Initial program 96.9%

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

   2. Taylor expanded in z around 0 81.7%

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

      1. associate-/l* 85.5%

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

   4. Simplified 85.5%

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

   if 2.65e7 < z < 1.1e16

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+178}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+61}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+32}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-133}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 26500000:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+16}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 3: 76.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+166}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+68}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+42}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.28e+166)
   (+ y x)
   (if (<= z -3.7e+68)
     (- x (* y (/ t z)))
     (if (<= z -6e+42)
       (+ y x)
       (if (<= z 4.2e+16) (+ x (/ y (/ a t))) (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.28e+166) {
		tmp = y + x;
	} else if (z <= -3.7e+68) {
		tmp = x - (y * (t / z));
	} else if (z <= -6e+42) {
		tmp = y + x;
	} else if (z <= 4.2e+16) {
		tmp = x + (y / (a / t));
	} 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 <= (-1.28d+166)) then
        tmp = y + x
    else if (z <= (-3.7d+68)) then
        tmp = x - (y * (t / z))
    else if (z <= (-6d+42)) then
        tmp = y + x
    else if (z <= 4.2d+16) then
        tmp = x + (y / (a / t))
    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 <= -1.28e+166) {
		tmp = y + x;
	} else if (z <= -3.7e+68) {
		tmp = x - (y * (t / z));
	} else if (z <= -6e+42) {
		tmp = y + x;
	} else if (z <= 4.2e+16) {
		tmp = x + (y / (a / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.28e+166:
		tmp = y + x
	elif z <= -3.7e+68:
		tmp = x - (y * (t / z))
	elif z <= -6e+42:
		tmp = y + x
	elif z <= 4.2e+16:
		tmp = x + (y / (a / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.28e+166)
		tmp = Float64(y + x);
	elseif (z <= -3.7e+68)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (z <= -6e+42)
		tmp = Float64(y + x);
	elseif (z <= 4.2e+16)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.28e+166)
		tmp = y + x;
	elseif (z <= -3.7e+68)
		tmp = x - (y * (t / z));
	elseif (z <= -6e+42)
		tmp = y + x;
	elseif (z <= 4.2e+16)
		tmp = x + (y / (a / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.28e+166], N[(y + x), $MachinePrecision], If[LessEqual[z, -3.7e+68], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6e+42], N[(y + x), $MachinePrecision], If[LessEqual[z, 4.2e+16], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.28e166 or -3.69999999999999998e68 < z < -6.00000000000000058e42 or 4.2e16 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 81.8%

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

   if -1.28e166 < z < -3.69999999999999998e68

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 86.4%

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

      1. neg-mul-1 86.4%

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

      2. distribute-neg-frac 86.4%

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

   4. Simplified 86.4%

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

   5. Taylor expanded in x around 0 69.6%

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

      1. +-commutative 69.6%

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

      2. mul-1-neg 69.6%

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

      3. associate-*r/ 86.4%

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

      4. sub-neg 86.4%

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

      5. associate-*r/ 69.6%

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

   7. Simplified 69.6%

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

   8. Taylor expanded in z around inf 65.1%

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

      1. associate-*r/ 81.9%

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

   10. Simplified 81.9%

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

   if -6.00000000000000058e42 < z < 4.2e16

   1. Initial program 95.8%

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

   2. Taylor expanded in z around 0 70.3%

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

      1. associate-/l* 74.8%

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

   4. Simplified 74.8%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+166}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+68}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+42}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 4: 76.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+169}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+60}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+44}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.85e+169)
   (+ y x)
   (if (<= z -1.7e+60)
     (- x (/ y (/ z t)))
     (if (<= z -2.3e+44)
       (+ y x)
       (if (<= z 4.1e+16) (+ x (/ y (/ a t))) (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.85e+169) {
		tmp = y + x;
	} else if (z <= -1.7e+60) {
		tmp = x - (y / (z / t));
	} else if (z <= -2.3e+44) {
		tmp = y + x;
	} else if (z <= 4.1e+16) {
		tmp = x + (y / (a / t));
	} 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 <= (-1.85d+169)) then
        tmp = y + x
    else if (z <= (-1.7d+60)) then
        tmp = x - (y / (z / t))
    else if (z <= (-2.3d+44)) then
        tmp = y + x
    else if (z <= 4.1d+16) then
        tmp = x + (y / (a / t))
    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 <= -1.85e+169) {
		tmp = y + x;
	} else if (z <= -1.7e+60) {
		tmp = x - (y / (z / t));
	} else if (z <= -2.3e+44) {
		tmp = y + x;
	} else if (z <= 4.1e+16) {
		tmp = x + (y / (a / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.85e+169:
		tmp = y + x
	elif z <= -1.7e+60:
		tmp = x - (y / (z / t))
	elif z <= -2.3e+44:
		tmp = y + x
	elif z <= 4.1e+16:
		tmp = x + (y / (a / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.85e+169)
		tmp = Float64(y + x);
	elseif (z <= -1.7e+60)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	elseif (z <= -2.3e+44)
		tmp = Float64(y + x);
	elseif (z <= 4.1e+16)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.85e+169)
		tmp = y + x;
	elseif (z <= -1.7e+60)
		tmp = x - (y / (z / t));
	elseif (z <= -2.3e+44)
		tmp = y + x;
	elseif (z <= 4.1e+16)
		tmp = x + (y / (a / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.85e+169], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.7e+60], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e+44], N[(y + x), $MachinePrecision], If[LessEqual[z, 4.1e+16], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.85e169 or -1.7e60 < z < -2.30000000000000004e44 or 4.1e16 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 81.8%

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

   if -1.85e169 < z < -1.7e60

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 86.4%

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

      1. neg-mul-1 86.4%

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

      2. distribute-neg-frac 86.4%

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

   4. Simplified 86.4%

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

   5. Taylor expanded in z around inf 65.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot t}{z} + x} \]
   6. 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%

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

   7. Simplified 81.9%

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

   if -2.30000000000000004e44 < z < 4.1e16

   1. Initial program 95.8%

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

   2. Taylor expanded in z around 0 70.3%

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

      1. associate-/l* 74.8%

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

   4. Simplified 74.8%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+169}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+60}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+44}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5: 80.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-133}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-43}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ t z))))))
   (if (<= z -1.5e-31)
     t_1
     (if (<= z -3.8e-133)
       (* (- z t) (/ y (- z a)))
       (if (<= z 1.65e-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 <= -1.5e-31) {
		tmp = t_1;
	} else if (z <= -3.8e-133) {
		tmp = (z - t) * (y / (z - a));
	} else if (z <= 1.65e-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 <= (-1.5d-31)) then
        tmp = t_1
    else if (z <= (-3.8d-133)) then
        tmp = (z - t) * (y / (z - a))
    else if (z <= 1.65d-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 <= -1.5e-31) {
		tmp = t_1;
	} else if (z <= -3.8e-133) {
		tmp = (z - t) * (y / (z - a));
	} else if (z <= 1.65e-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 <= -1.5e-31:
		tmp = t_1
	elif z <= -3.8e-133:
		tmp = (z - t) * (y / (z - a))
	elif z <= 1.65e-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 <= -1.5e-31)
		tmp = t_1;
	elseif (z <= -3.8e-133)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	elseif (z <= 1.65e-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 <= -1.5e-31)
		tmp = t_1;
	elseif (z <= -3.8e-133)
		tmp = (z - t) * (y / (z - a));
	elseif (z <= 1.65e-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, -1.5e-31], t$95$1, If[LessEqual[z, -3.8e-133], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-43], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.49999999999999991e-31 or 1.65000000000000008e-43 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 84.4%

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

      1. div-sub 84.4%

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

      2. *-inverses 84.4%

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

   4. Simplified 84.4%

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

   if -1.49999999999999991e-31 < z < -3.8000000000000003e-133

   1. Initial program 84.6%

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

      1. +-commutative 84.6%

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

      2. associate-*r/ 84.9%

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

      3. associate-*l/ 99.9%

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

      4. *-commutative 99.9%

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

      5. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around -inf 70.1%

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

      1. *-commutative 70.1%

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

      2. associate-*r/ 84.9%

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

   8. Simplified 84.9%

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

   if -3.8000000000000003e-133 < z < 1.65000000000000008e-43

   1. Initial program 96.9%

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

   2. Taylor expanded in z around 0 80.4%

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

      1. associate-/l* 85.0%

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

   4. Simplified 85.0%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-31}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-133}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-43}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]

Alternative 6: 80.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3e-30)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	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 = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3e-30], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.9999999999999999e-30

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 84.3%

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

      1. div-sub 84.3%

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

      2. *-inverses 84.3%

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

   4. Simplified 84.3%

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

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

   1. Initial program 84.6%

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

      1. +-commutative 84.6%

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

      2. associate-*r/ 84.9%

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

      3. associate-*l/ 99.9%

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

      4. *-commutative 99.9%

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

      5. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around -inf 70.1%

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

      1. *-commutative 70.1%

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

      2. associate-*r/ 84.9%

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

   8. Simplified 84.9%

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

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

   1. Initial program 96.9%

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

   2. Taylor expanded in z around 0 80.4%

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

      1. associate-/l* 85.0%

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

   4. Simplified 85.0%

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

   if 1.25000000000000005e-43 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 65.8%

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

      1. +-commutative 65.8%

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

      2. *-commutative 65.8%

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

      3. associate-/l* 84.5%

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

   4. Simplified 84.5%

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

4. Final simplification 84.6%

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

Alternative 7: 86.8% accurate, 0.8× speedup

Math

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

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 (- z a)))))))

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 / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.5d-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 / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-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 / (z - a)));
	}
	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 / (z - a)))
	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(z / Float64(z - a))));
	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 / (z - a)));
	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[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5000000000000002e-47

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 82.8%

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

      1. div-sub 82.8%

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

      2. *-inverses 82.8%

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

   4. Simplified 82.8%

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

   if -5.5000000000000002e-47 < z < 7.5e16

   1. Initial program 95.1%

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

   2. Taylor expanded in t around inf 90.4%

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

      1. neg-mul-1 90.4%

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

      2. distribute-neg-frac 90.4%

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

   4. Simplified 90.4%

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

   5. Taylor expanded in x around 0 88.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot t}{z - a} + x} \]
   6. 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. sub-neg 90.4%

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

      5. associate-*r/ 88.9%

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

   7. Simplified 88.9%

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

   if 7.5e16 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 89.5%

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

4. Final simplification 87.4%

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

Alternative 8: 87.4% accurate, 0.8× speedup

Math

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

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

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 * (t / (z - a)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Fortran

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

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+45) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 9.8e+16) {
		tmp = x - (y * (t / (z - a)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	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 * (t / (z - a)))
	else:
		tmp = x + (y * (z / (z - a)))
	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(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

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

Derivation

1. Split input into 3 regimes

2. if z < -1.34999999999999992e45

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 87.7%

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

      1. div-sub 87.7%

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

      2. *-inverses 87.7%

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

   4. Simplified 87.7%

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

   if -1.34999999999999992e45 < z < 9.8e16

   1. Initial program 95.8%

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

   2. Taylor expanded in t around inf 88.5%

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

      1. neg-mul-1 88.5%

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

      2. distribute-neg-frac 88.5%

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

   4. Simplified 88.5%

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

   if 9.8e16 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 89.5%

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

4. Final simplification 88.6%

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

Alternative 9: 77.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+39} \lor \neg \left(z \leq 3.2 \cdot 10^{+16}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2e+39) (not (<= z 3.2e+16))) (+ y x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e+39) || !(z <= 3.2e+16)) {
		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 <= (-2d+39)) .or. (.not. (z <= 3.2d+16))) 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 <= -2e+39) || !(z <= 3.2e+16)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2e+39) or not (z <= 3.2e+16):
		tmp = y + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2e+39) || !(z <= 3.2e+16))
		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 <= -2e+39) || ~((z <= 3.2e+16)))
		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, -2e+39], N[Not[LessEqual[z, 3.2e+16]], $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 < -1.99999999999999988e39 or 3.2e16 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 77.9%

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

   if -1.99999999999999988e39 < z < 3.2e16

   1. Initial program 95.8%

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

   2. Taylor expanded in z around 0 74.3%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+39} \lor \neg \left(z \leq 3.2 \cdot 10^{+16}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 10: 77.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+42}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.6e+42) (+ y x) (if (<= z 5.5e+16) (+ x (/ y (/ a t))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e+42) {
		tmp = y + x;
	} else if (z <= 5.5e+16) {
		tmp = x + (y / (a / t));
	} 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 <= (-1.6d+42)) then
        tmp = y + x
    else if (z <= 5.5d+16) then
        tmp = x + (y / (a / t))
    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 <= -1.6e+42) {
		tmp = y + x;
	} else if (z <= 5.5e+16) {
		tmp = x + (y / (a / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.6e+42:
		tmp = y + x
	elif z <= 5.5e+16:
		tmp = x + (y / (a / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.6e+42)
		tmp = Float64(y + x);
	elseif (z <= 5.5e+16)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.6e+42)
		tmp = y + x;
	elseif (z <= 5.5e+16)
		tmp = x + (y / (a / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.6e+42], N[(y + x), $MachinePrecision], If[LessEqual[z, 5.5e+16], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000001e42 or 5.5e16 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 77.9%

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

   if -1.60000000000000001e42 < z < 5.5e16

   1. Initial program 95.8%

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

   2. Taylor expanded in z around 0 70.3%

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

      1. associate-/l* 74.8%

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

   4. Simplified 74.8%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+42}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 11: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

2. Final simplification 97.6%

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

Alternative 12: 61.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+216} \lor \neg \left(t \leq 7 \cdot 10^{+200}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.45e+216) (not (<= t 7e+200))) (* y (/ t a)) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.45e+216) || !(t <= 7e+200)) {
		tmp = y * (t / a);
	} 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 ((t <= (-2.45d+216)) .or. (.not. (t <= 7d+200))) then
        tmp = y * (t / a)
    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 ((t <= -2.45e+216) || !(t <= 7e+200)) {
		tmp = y * (t / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.45e+216) or not (t <= 7e+200):
		tmp = y * (t / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.45e+216) || !(t <= 7e+200))
		tmp = Float64(y * Float64(t / a));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.45e+216) || ~((t <= 7e+200)))
		tmp = y * (t / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.45e+216], N[Not[LessEqual[t, 7e+200]], $MachinePrecision]], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.45000000000000007e216 or 7.00000000000000013e200 < t

   1. Initial program 91.2%

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

   2. Taylor expanded in x around 0 60.9%

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

   3. Taylor expanded in z around 0 47.5%

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

      1. associate-/l* 56.1%

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

   5. Simplified 56.1%

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

      1. clear-num 56.0%

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

      2. inv-pow 56.0%

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

   7. Applied egg-rr 56.0%

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

      1. unpow-1 56.0%

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

      2. associate-/l/ 47.6%

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

   9. Simplified 47.6%

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

   10. Taylor expanded in a around 0 47.5%

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

       1. associate-*r/ 56.1%

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

   12. Simplified 56.1%

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

   if -2.45000000000000007e216 < t < 7.00000000000000013e200

   1. Initial program 99.0%

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

   2. 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+216} \lor \neg \left(t \leq 7 \cdot 10^{+200}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 13: 61.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+215}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 1.38 \cdot 10^{+200}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.4e+215)
   (/ y (/ a t))
   (if (<= t 1.38e+200) (+ y x) (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.4e+215) {
		tmp = y / (a / t);
	} else if (t <= 1.38e+200) {
		tmp = y + x;
	} else {
		tmp = 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 (t <= (-6.4d+215)) then
        tmp = y / (a / t)
    else if (t <= 1.38d+200) then
        tmp = y + x
    else
        tmp = 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 (t <= -6.4e+215) {
		tmp = y / (a / t);
	} else if (t <= 1.38e+200) {
		tmp = y + x;
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.4e+215:
		tmp = y / (a / t)
	elif t <= 1.38e+200:
		tmp = y + x
	else:
		tmp = y * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.4e+215)
		tmp = Float64(y / Float64(a / t));
	elseif (t <= 1.38e+200)
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.4e+215)
		tmp = y / (a / t);
	elseif (t <= 1.38e+200)
		tmp = y + x;
	else
		tmp = y * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.4e+215], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.38e+200], N[(y + x), $MachinePrecision], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.3999999999999997e215

   1. Initial program 85.7%

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

   2. Taylor expanded in x around 0 61.2%

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

   3. Taylor expanded in z around 0 42.5%

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

      1. associate-/l* 52.9%

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

   5. Simplified 52.9%

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

   if -6.3999999999999997e215 < t < 1.38000000000000005e200

   1. Initial program 99.0%

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

   2. Taylor expanded in z around inf 62.0%

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

   if 1.38000000000000005e200 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 60.2%

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

   3. Taylor expanded in z around 0 55.6%

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

      1. associate-/l* 61.1%

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

   5. Simplified 61.1%

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

      1. clear-num 61.0%

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

      2. inv-pow 61.0%

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

   7. Applied egg-rr 61.0%

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

      1. unpow-1 61.0%

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

      2. associate-/l/ 55.5%

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

   9. Simplified 55.5%

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

   10. Taylor expanded in a around 0 55.6%

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

       1. associate-*r/ 61.2%

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

   12. Simplified 61.2%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+215}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 1.38 \cdot 10^{+200}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 14: 60.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+193}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+201}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e+193)
   (* t (/ (- y) z))
   (if (<= t 1.45e+201) (+ y x) (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e+193) {
		tmp = t * (-y / z);
	} else if (t <= 1.45e+201) {
		tmp = y + x;
	} else {
		tmp = 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 (t <= (-1.15d+193)) then
        tmp = t * (-y / z)
    else if (t <= 1.45d+201) then
        tmp = y + x
    else
        tmp = 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 (t <= -1.15e+193) {
		tmp = t * (-y / z);
	} else if (t <= 1.45e+201) {
		tmp = y + x;
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e+193:
		tmp = t * (-y / z)
	elif t <= 1.45e+201:
		tmp = y + x
	else:
		tmp = y * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e+193)
		tmp = Float64(t * Float64(Float64(-y) / z));
	elseif (t <= 1.45e+201)
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.15e+193)
		tmp = t * (-y / z);
	elseif (t <= 1.45e+201)
		tmp = y + x;
	else
		tmp = y * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e+193], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+201], N[(y + x), $MachinePrecision], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15000000000000007e193

   1. Initial program 88.6%

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

      1. +-commutative 88.6%

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

      2. associate-*r/ 75.3%

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

      3. associate-*l/ 91.5%

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

      4. *-commutative 91.5%

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

      5. fma-def 91.5%

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

   3. Simplified 91.5%

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

      1. clear-num 91.3%

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

      2. associate-/r/ 91.4%

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

   5. Applied egg-rr 91.4%

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

   6. Taylor expanded in t around inf 53.0%

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

      1. associate-*r/ 53.0%

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

      2. mul-1-neg 53.0%

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

      3. distribute-rgt-neg-in 53.0%

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

   8. Simplified 53.0%

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

   9. Taylor expanded in z around inf 36.0%

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

       1. associate-*r/ 36.0%

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

       2. associate-*r* 36.0%

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

       3. neg-mul-1 36.0%

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

   11. Simplified 36.0%

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

   12. Taylor expanded in y around 0 36.0%

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

       1. mul-1-neg 36.0%

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

       2. associate-*l/ 49.4%

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

       3. distribute-rgt-neg-in 49.4%

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

   14. Simplified 49.4%

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

   if -1.15000000000000007e193 < t < 1.4500000000000001e201

   1. Initial program 99.0%

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

   2. Taylor expanded in z around inf 63.0%

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

   if 1.4500000000000001e201 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 60.2%

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

   3. Taylor expanded in z around 0 55.6%

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

      1. associate-/l* 61.1%

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

   5. Simplified 61.1%

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

      1. clear-num 61.0%

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

      2. inv-pow 61.0%

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

   7. Applied egg-rr 61.0%

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

      1. unpow-1 61.0%

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

      2. associate-/l/ 55.5%

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

   9. Simplified 55.5%

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

   10. Taylor expanded in a around 0 55.6%

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

       1. associate-*r/ 61.2%

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

   12. Simplified 61.2%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+193}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+201}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 15: 60.9% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

2. Taylor expanded in z around inf 56.0%

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

3. Final simplification 56.0%

   \[\leadsto y + x \]

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 97.6%

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

2. Taylor expanded in x around inf 47.1%

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

3. 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:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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