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

Percentage Accurate: 98.4% → 98.4%

Time: 9.8s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% 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 98.8%

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

   1. +-commutative 98.8%

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

   2. fma-def 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 76.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+142}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-38}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-14} \lor \neg \left(z \leq 8.4 \cdot 10^{+58}\right) \land z \leq 7 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+142)
   (+ y x)
   (if (<= z -1.3e-38)
     (- x (* y (/ t z)))
     (if (or (<= z 1.02e-14) (and (not (<= z 8.4e+58)) (<= z 7e+125)))
       (+ x (* y (/ t a)))
       (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+142) {
		tmp = y + x;
	} else if (z <= -1.3e-38) {
		tmp = x - (y * (t / z));
	} else if ((z <= 1.02e-14) || (!(z <= 8.4e+58) && (z <= 7e+125))) {
		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) :: tmp
    if (z <= (-4.8d+142)) then
        tmp = y + x
    else if (z <= (-1.3d-38)) then
        tmp = x - (y * (t / z))
    else if ((z <= 1.02d-14) .or. (.not. (z <= 8.4d+58)) .and. (z <= 7d+125)) 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 tmp;
	if (z <= -4.8e+142) {
		tmp = y + x;
	} else if (z <= -1.3e-38) {
		tmp = x - (y * (t / z));
	} else if ((z <= 1.02e-14) || (!(z <= 8.4e+58) && (z <= 7e+125))) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e+142:
		tmp = y + x
	elif z <= -1.3e-38:
		tmp = x - (y * (t / z))
	elif (z <= 1.02e-14) or (not (z <= 8.4e+58) and (z <= 7e+125)):
		tmp = x + (y * (t / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+142)
		tmp = Float64(y + x);
	elseif (z <= -1.3e-38)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif ((z <= 1.02e-14) || (!(z <= 8.4e+58) && (z <= 7e+125)))
		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)
	tmp = 0.0;
	if (z <= -4.8e+142)
		tmp = y + x;
	elseif (z <= -1.3e-38)
		tmp = x - (y * (t / z));
	elseif ((z <= 1.02e-14) || (~((z <= 8.4e+58)) && (z <= 7e+125)))
		tmp = x + (y * (t / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+142], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.3e-38], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.02e-14], And[N[Not[LessEqual[z, 8.4e+58]], $MachinePrecision], LessEqual[z, 7e+125]]], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.7999999999999998e142 or 1.02e-14 < z < 8.40000000000000048e58 or 7.00000000000000023e125 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 87.1%

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

   if -4.7999999999999998e142 < z < -1.30000000000000005e-38

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0 82.8%

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

      1. +-commutative 82.8%

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

      2. *-commutative 82.8%

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

      3. associate-/l* 90.1%

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

   4. Simplified 90.1%

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

   5. Taylor expanded in z around 0 80.3%

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

      1. associate-*r/ 80.3%

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

      2. neg-mul-1 80.3%

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

   7. Simplified 80.3%

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

   8. Taylor expanded in y around 0 77.9%

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

      1. +-commutative 77.9%

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

      2. metadata-eval 77.9%

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

      3. associate-*r/ 80.2%

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

      4. cancel-sign-sub-inv 80.2%

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

      5. *-lft-identity 80.2%

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

   10. Simplified 80.2%

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

   if -1.30000000000000005e-38 < z < 1.02e-14 or 8.40000000000000048e58 < z < 7.00000000000000023e125

   1. Initial program 97.7%

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

   2. Taylor expanded in z around 0 77.5%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+142}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-38}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-14} \lor \neg \left(z \leq 8.4 \cdot 10^{+58}\right) \land z \leq 7 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 3: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+142}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-32}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-12} \lor \neg \left(z \leq 4.5 \cdot 10^{+57}\right) \land z \leq 7 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e+142)
   (+ y x)
   (if (<= z -2.7e-32)
     (- x (/ y (/ z t)))
     (if (or (<= z 1.75e-12) (and (not (<= z 4.5e+57)) (<= z 7e+125)))
       (+ x (* y (/ t a)))
       (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+142) {
		tmp = y + x;
	} else if (z <= -2.7e-32) {
		tmp = x - (y / (z / t));
	} else if ((z <= 1.75e-12) || (!(z <= 4.5e+57) && (z <= 7e+125))) {
		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) :: tmp
    if (z <= (-5.2d+142)) then
        tmp = y + x
    else if (z <= (-2.7d-32)) then
        tmp = x - (y / (z / t))
    else if ((z <= 1.75d-12) .or. (.not. (z <= 4.5d+57)) .and. (z <= 7d+125)) 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 tmp;
	if (z <= -5.2e+142) {
		tmp = y + x;
	} else if (z <= -2.7e-32) {
		tmp = x - (y / (z / t));
	} else if ((z <= 1.75e-12) || (!(z <= 4.5e+57) && (z <= 7e+125))) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e+142:
		tmp = y + x
	elif z <= -2.7e-32:
		tmp = x - (y / (z / t))
	elif (z <= 1.75e-12) or (not (z <= 4.5e+57) and (z <= 7e+125)):
		tmp = x + (y * (t / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e+142)
		tmp = Float64(y + x);
	elseif (z <= -2.7e-32)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	elseif ((z <= 1.75e-12) || (!(z <= 4.5e+57) && (z <= 7e+125)))
		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)
	tmp = 0.0;
	if (z <= -5.2e+142)
		tmp = y + x;
	elseif (z <= -2.7e-32)
		tmp = x - (y / (z / t));
	elseif ((z <= 1.75e-12) || (~((z <= 4.5e+57)) && (z <= 7e+125)))
		tmp = x + (y * (t / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e+142], N[(y + x), $MachinePrecision], If[LessEqual[z, -2.7e-32], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.75e-12], And[N[Not[LessEqual[z, 4.5e+57]], $MachinePrecision], LessEqual[z, 7e+125]]], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.20000000000000043e142 or 1.75e-12 < z < 4.49999999999999996e57 or 7.00000000000000023e125 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 87.1%

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

   if -5.20000000000000043e142 < z < -2.69999999999999981e-32

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0 82.8%

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

      1. +-commutative 82.8%

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

      2. *-commutative 82.8%

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

      3. associate-/l* 90.1%

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

   4. Simplified 90.1%

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

   5. Taylor expanded in z around 0 80.3%

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

      1. associate-*r/ 80.3%

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

      2. neg-mul-1 80.3%

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

   7. Simplified 80.3%

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

   8. Taylor expanded in y around 0 77.9%

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

      1. +-commutative 77.9%

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

      2. metadata-eval 77.9%

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

      3. associate-*r/ 80.2%

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

      4. cancel-sign-sub-inv 80.2%

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

      5. *-lft-identity 80.2%

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

      6. associate-*r/ 77.9%

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

      7. associate-/l* 80.3%

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

   10. Simplified 80.3%

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

   if -2.69999999999999981e-32 < z < 1.75e-12 or 4.49999999999999996e57 < z < 7.00000000000000023e125

   1. Initial program 97.7%

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

   2. Taylor expanded in z around 0 77.5%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+142}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-32}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-12} \lor \neg \left(z \leq 4.5 \cdot 10^{+57}\right) \land z \leq 7 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 4: 81.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{z}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-133}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-48}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 6.5128 \cdot 10^{-45}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) z)))))
   (if (<= z -2.6e-47)
     t_1
     (if (<= z 5.8e-133)
       (+ x (* y (/ t a)))
       (if (<= z 1.65e-48)
         (+ x (* y (/ z (- z a))))
         (if (<= z 6.5128e-45) (+ x (* t (/ y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -2.6e-47) {
		tmp = t_1;
	} else if (z <= 5.8e-133) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.65e-48) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 6.5128e-45) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / z))
    if (z <= (-2.6d-47)) then
        tmp = t_1
    else if (z <= 5.8d-133) then
        tmp = x + (y * (t / a))
    else if (z <= 1.65d-48) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= 6.5128d-45) then
        tmp = x + (t * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -2.6e-47) {
		tmp = t_1;
	} else if (z <= 5.8e-133) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.65e-48) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 6.5128e-45) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / z))
	tmp = 0
	if z <= -2.6e-47:
		tmp = t_1
	elif z <= 5.8e-133:
		tmp = x + (y * (t / a))
	elif z <= 1.65e-48:
		tmp = x + (y * (z / (z - a)))
	elif z <= 6.5128e-45:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / z)))
	tmp = 0.0
	if (z <= -2.6e-47)
		tmp = t_1;
	elseif (z <= 5.8e-133)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1.65e-48)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= 6.5128e-45)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / z));
	tmp = 0.0;
	if (z <= -2.6e-47)
		tmp = t_1;
	elseif (z <= 5.8e-133)
		tmp = x + (y * (t / a));
	elseif (z <= 1.65e-48)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= 6.5128e-45)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e-47], t$95$1, If[LessEqual[z, 5.8e-133], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-48], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5128e-45], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6e-47 or 6.5128000000000001e-45 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 89.7%

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

   if -2.6e-47 < z < 5.7999999999999997e-133

   1. Initial program 97.7%

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

   2. Taylor expanded in z around 0 82.2%

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

   if 5.7999999999999997e-133 < z < 1.65e-48

   1. Initial program 95.5%

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

   2. Taylor expanded in t around 0 81.6%

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

   if 1.65e-48 < z < 6.5128000000000001e-45

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 79.1%

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

      1. div-inv 79.1%

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

      2. *-commutative 79.1%

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

      3. associate-*l* 79.1%

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

      4. div-inv 79.1%

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

   4. Applied egg-rr 79.1%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-47}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-133}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-48}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 6.5128 \cdot 10^{-45}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]

Alternative 5: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-135}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-47}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 6.5128 \cdot 10^{-45}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ z (- z t))))))
   (if (<= z -3.7e-47)
     t_1
     (if (<= z 9.2e-135)
       (+ x (* y (/ t a)))
       (if (<= z 1.55e-47)
         (+ x (* y (/ z (- z a))))
         (if (<= z 6.5128e-45) (+ x (* t (/ y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (z / (z - t)));
	double tmp;
	if (z <= -3.7e-47) {
		tmp = t_1;
	} else if (z <= 9.2e-135) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.55e-47) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 6.5128e-45) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (z / (z - t)))
    if (z <= (-3.7d-47)) then
        tmp = t_1
    else if (z <= 9.2d-135) then
        tmp = x + (y * (t / a))
    else if (z <= 1.55d-47) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= 6.5128d-45) then
        tmp = x + (t * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (z / (z - t)));
	double tmp;
	if (z <= -3.7e-47) {
		tmp = t_1;
	} else if (z <= 9.2e-135) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.55e-47) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 6.5128e-45) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (z / (z - t)))
	tmp = 0
	if z <= -3.7e-47:
		tmp = t_1
	elif z <= 9.2e-135:
		tmp = x + (y * (t / a))
	elif z <= 1.55e-47:
		tmp = x + (y * (z / (z - a)))
	elif z <= 6.5128e-45:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(z / Float64(z - t))))
	tmp = 0.0
	if (z <= -3.7e-47)
		tmp = t_1;
	elseif (z <= 9.2e-135)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1.55e-47)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= 6.5128e-45)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (z / (z - t)));
	tmp = 0.0;
	if (z <= -3.7e-47)
		tmp = t_1;
	elseif (z <= 9.2e-135)
		tmp = x + (y * (t / a));
	elseif (z <= 1.55e-47)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= 6.5128e-45)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e-47], t$95$1, If[LessEqual[z, 9.2e-135], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-47], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5128e-45], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.7e-47 or 6.5128000000000001e-45 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 69.2%

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

      1. +-commutative 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-/l* 89.7%

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

   4. Simplified 89.7%

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

   if -3.7e-47 < z < 9.1999999999999996e-135

   1. Initial program 97.7%

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

   2. Taylor expanded in z around 0 82.2%

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

   if 9.1999999999999996e-135 < z < 1.5499999999999999e-47

   1. Initial program 95.5%

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

   2. Taylor expanded in t around 0 81.6%

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

   if 1.5499999999999999e-47 < z < 6.5128000000000001e-45

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 79.1%

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

      1. div-inv 79.1%

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

      2. *-commutative 79.1%

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

      3. associate-*l* 79.1%

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

      4. div-inv 79.1%

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

   4. Applied egg-rr 79.1%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-135}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-47}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 6.5128 \cdot 10^{-45}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 6: 76.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-14} \lor \neg \left(z \leq 1.88 \cdot 10^{+59}\right) \land z \leq 7 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.1e-47)
   (+ y x)
   (if (or (<= z 9.2e-14) (and (not (<= z 1.88e+59)) (<= z 7e+125)))
     (+ x (* y (/ t a)))
     (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e-47) {
		tmp = y + x;
	} else if ((z <= 9.2e-14) || (!(z <= 1.88e+59) && (z <= 7e+125))) {
		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) :: tmp
    if (z <= (-3.1d-47)) then
        tmp = y + x
    else if ((z <= 9.2d-14) .or. (.not. (z <= 1.88d+59)) .and. (z <= 7d+125)) 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 tmp;
	if (z <= -3.1e-47) {
		tmp = y + x;
	} else if ((z <= 9.2e-14) || (!(z <= 1.88e+59) && (z <= 7e+125))) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.1e-47:
		tmp = y + x
	elif (z <= 9.2e-14) or (not (z <= 1.88e+59) and (z <= 7e+125)):
		tmp = x + (y * (t / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.1e-47)
		tmp = Float64(y + x);
	elseif ((z <= 9.2e-14) || (!(z <= 1.88e+59) && (z <= 7e+125)))
		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)
	tmp = 0.0;
	if (z <= -3.1e-47)
		tmp = y + x;
	elseif ((z <= 9.2e-14) || (~((z <= 1.88e+59)) && (z <= 7e+125)))
		tmp = x + (y * (t / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.1e-47], N[(y + x), $MachinePrecision], If[Or[LessEqual[z, 9.2e-14], And[N[Not[LessEqual[z, 1.88e+59]], $MachinePrecision], LessEqual[z, 7e+125]]], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0999999999999998e-47 or 9.19999999999999993e-14 < z < 1.87999999999999989e59 or 7.00000000000000023e125 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 80.7%

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

   if -3.0999999999999998e-47 < z < 9.19999999999999993e-14 or 1.87999999999999989e59 < z < 7.00000000000000023e125

   1. Initial program 97.6%

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

   2. Taylor expanded in z around 0 78.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-14} \lor \neg \left(z \leq 1.88 \cdot 10^{+59}\right) \land z \leq 7 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7: 80.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-48} \lor \neg \left(z \leq 1.1 \cdot 10^{-134}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e-48) (not (<= z 1.1e-134)))
   (+ x (* y (/ z (- z a))))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e-48) || !(z <= 1.1e-134)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.5d-48)) .or. (.not. (z <= 1.1d-134))) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e-48) || !(z <= 1.1e-134)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.5e-48) or not (z <= 1.1e-134):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.5e-48) || !(z <= 1.1e-134))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	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 <= -3.5e-48) || ~((z <= 1.1e-134)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.5e-48], N[Not[LessEqual[z, 1.1e-134]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.49999999999999991e-48 or 1.1e-134 < z

   1. Initial program 99.4%

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

   2. Taylor expanded in t around 0 82.1%

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

   if -3.49999999999999991e-48 < z < 1.1e-134

   1. Initial program 97.7%

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

   2. Taylor expanded in z around 0 82.2%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-48} \lor \neg \left(z \leq 1.1 \cdot 10^{-134}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 8: 82.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-149} \lor \neg \left(z \leq 3.8 \cdot 10^{-15}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.7e-149) (not (<= z 3.8e-15)))
   (+ x (/ y (/ z (- z t))))
   (+ x (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e-149) || !(z <= 3.8e-15)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.7d-149)) .or. (.not. (z <= 3.8d-15))) then
        tmp = x + (y / (z / (z - t)))
    else
        tmp = x + ((y / a) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e-149) || !(z <= 3.8e-15)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.7e-149) or not (z <= 3.8e-15):
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = x + ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.7e-149) || !(z <= 3.8e-15))
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	else
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.7e-149) || ~((z <= 3.8e-15)))
		tmp = x + (y / (z / (z - t)));
	else
		tmp = x + ((y / a) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.7e-149], N[Not[LessEqual[z, 3.8e-15]], $MachinePrecision]], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6999999999999999e-149 or 3.8000000000000002e-15 < z

   1. Initial program 99.3%

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

   2. Taylor expanded in a around 0 69.1%

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

      1. +-commutative 69.1%

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

      2. *-commutative 69.1%

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

      3. associate-/l* 87.1%

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

   4. Simplified 87.1%

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

   if -1.6999999999999999e-149 < z < 3.8000000000000002e-15

   1. Initial program 97.9%

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

      1. clear-num 97.8%

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

      2. associate-/r/ 97.9%

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

   3. Applied egg-rr 97.9%

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

   4. Taylor expanded in a around inf 85.8%

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

      1. +-commutative 85.8%

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

      2. mul-1-neg 85.8%

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

      3. associate-*r/ 84.3%

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

      4. *-rgt-identity 84.3%

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

      5. distribute-lft-neg-in 84.3%

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

      6. cancel-sign-sub-inv 84.3%

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

      7. *-commutative 84.3%

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

      8. *-lft-identity 84.3%

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

   6. Simplified 84.3%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-149} \lor \neg \left(z \leq 3.8 \cdot 10^{-15}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 9: 87.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+41} \lor \neg \left(t \leq 70000000000\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.6e+41) (not (<= t 70000000000.0)))
   (- 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 ((t <= -2.6e+41) || !(t <= 70000000000.0)) {
		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 ((t <= (-2.6d+41)) .or. (.not. (t <= 70000000000.0d0))) 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 ((t <= -2.6e+41) || !(t <= 70000000000.0)) {
		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 (t <= -2.6e+41) or not (t <= 70000000000.0):
		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 ((t <= -2.6e+41) || !(t <= 70000000000.0))
		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 ((t <= -2.6e+41) || ~((t <= 70000000000.0)))
		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[Or[LessEqual[t, -2.6e+41], N[Not[LessEqual[t, 70000000000.0]], $MachinePrecision]], 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 2 regimes

2. if t < -2.6000000000000001e41 or 7e10 < t

   1. Initial program 97.2%

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

      1. clear-num 97.2%

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

      2. associate-/r/ 97.2%

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

   3. Applied egg-rr 97.2%

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

   4. Taylor expanded in t around inf 83.8%

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

      1. associate-*r/ 83.8%

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

      2. mul-1-neg 83.8%

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

      3. distribute-rgt-neg-out 83.8%

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

      4. associate-*l/ 87.2%

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

   6. Simplified 87.2%

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

   7. Taylor expanded in x around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. mul-1-neg 83.8%

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

      3. *-commutative 83.8%

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

      4. associate-/l* 87.1%

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

      5. sub-neg 87.1%

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

      6. associate-/r/ 88.1%

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

   9. Simplified 88.1%

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

   if -2.6000000000000001e41 < t < 7e10

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 95.6%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+41} \lor \neg \left(t \leq 70000000000\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 10: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+44}:\\ \;\;\;\;x - \frac{t}{\frac{z - a}{y}}\\ \mathbf{elif}\;t \leq 4600000000:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.4e+44)
   (- x (/ t (/ (- z a) y)))
   (if (<= t 4600000000.0)
     (+ x (* y (/ z (- z a))))
     (- x (* y (/ t (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.4e+44) {
		tmp = x - (t / ((z - a) / y));
	} else if (t <= 4600000000.0) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x - (y * (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.4d+44)) then
        tmp = x - (t / ((z - a) / y))
    else if (t <= 4600000000.0d0) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x - (y * (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.4e+44) {
		tmp = x - (t / ((z - a) / y));
	} else if (t <= 4600000000.0) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x - (y * (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.4e+44:
		tmp = x - (t / ((z - a) / y))
	elif t <= 4600000000.0:
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x - (y * (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.4e+44)
		tmp = Float64(x - Float64(t / Float64(Float64(z - a) / y)));
	elseif (t <= 4600000000.0)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.4e+44)
		tmp = x - (t / ((z - a) / y));
	elseif (t <= 4600000000.0)
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x - (y * (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.4e+44], N[(x - N[(t / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4600000000.0], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.39999999999999991e44

   1. Initial program 95.4%

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

      1. clear-num 95.4%

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

      2. associate-/r/ 95.5%

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

   3. Applied egg-rr 95.5%

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

   4. Taylor expanded in t around inf 83.6%

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

      1. associate-*r/ 83.6%

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

      2. mul-1-neg 83.6%

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

      3. distribute-rgt-neg-out 83.6%

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

      4. associate-*l/ 86.1%

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

   6. Simplified 86.1%

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

      1. distribute-rgt-neg-out 86.1%

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

      2. unsub-neg 86.1%

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

      3. clear-num 86.0%

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

      4. associate-*l/ 86.0%

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

      5. *-un-lft-identity 86.0%

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

   8. Applied egg-rr 86.0%

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

   if -4.39999999999999991e44 < t < 4.6e9

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 95.6%

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

   if 4.6e9 < t

   1. Initial program 98.3%

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

      1. clear-num 98.3%

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

      2. associate-/r/ 98.3%

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

   3. Applied egg-rr 98.3%

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

   4. Taylor expanded in t around inf 84.0%

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

      1. associate-*r/ 84.0%

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

      2. mul-1-neg 84.0%

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

      3. distribute-rgt-neg-out 84.0%

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

      4. associate-*l/ 87.8%

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

   6. Simplified 87.8%

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

   7. Taylor expanded in x around 0 84.0%

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

      1. +-commutative 84.0%

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

      2. mul-1-neg 84.0%

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

      3. *-commutative 84.0%

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

      4. associate-/l* 87.8%

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

      5. sub-neg 87.8%

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

      6. associate-/r/ 90.7%

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

   9. Simplified 90.7%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+44}:\\ \;\;\;\;x - \frac{t}{\frac{z - a}{y}}\\ \mathbf{elif}\;t \leq 4600000000:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \]

Alternative 11: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+40}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e+40)
   (- x (* t (/ y (- z a))))
   (if (<= t 6.2e+17) (+ x (* y (/ z (- z a)))) (- x (* y (/ t (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e+40) {
		tmp = x - (t * (y / (z - a)));
	} else if (t <= 6.2e+17) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x - (y * (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.15d+40)) then
        tmp = x - (t * (y / (z - a)))
    else if (t <= 6.2d+17) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x - (y * (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e+40) {
		tmp = x - (t * (y / (z - a)));
	} else if (t <= 6.2e+17) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x - (y * (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e+40:
		tmp = x - (t * (y / (z - a)))
	elif t <= 6.2e+17:
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x - (y * (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e+40)
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	elseif (t <= 6.2e+17)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.15e+40)
		tmp = x - (t * (y / (z - a)));
	elseif (t <= 6.2e+17)
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x - (y * (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e+40], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+17], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.14999999999999997e40

   1. Initial program 95.4%

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

      1. clear-num 95.4%

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

      2. associate-/r/ 95.5%

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

   3. Applied egg-rr 95.5%

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

   4. Taylor expanded in t around inf 83.6%

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

      1. associate-*r/ 83.6%

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

      2. mul-1-neg 83.6%

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

      3. distribute-rgt-neg-out 83.6%

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

      4. associate-*l/ 86.1%

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

   6. Simplified 86.1%

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

   if -1.14999999999999997e40 < t < 6.2e17

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 95.6%

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

   if 6.2e17 < t

   1. Initial program 98.3%

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

      1. clear-num 98.3%

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

      2. associate-/r/ 98.3%

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

   3. Applied egg-rr 98.3%

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

   4. Taylor expanded in t around inf 84.0%

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

      1. associate-*r/ 84.0%

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

      2. mul-1-neg 84.0%

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

      3. distribute-rgt-neg-out 84.0%

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

      4. associate-*l/ 87.8%

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

   6. Simplified 87.8%

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

   7. Taylor expanded in x around 0 84.0%

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

      1. +-commutative 84.0%

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

      2. mul-1-neg 84.0%

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

      3. *-commutative 84.0%

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

      4. associate-/l* 87.8%

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

      5. sub-neg 87.8%

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

      6. associate-/r/ 90.7%

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

   9. Simplified 90.7%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+40}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \]

Alternative 12: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

2. Final simplification 98.8%

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

Alternative 13: 63.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+175}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+116}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.5e+175) x (if (<= a 1.65e+116) (+ y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e+175) {
		tmp = x;
	} else if (a <= 1.65e+116) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.5d+175)) then
        tmp = x
    else if (a <= 1.65d+116) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e+175) {
		tmp = x;
	} else if (a <= 1.65e+116) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.5e+175:
		tmp = x
	elif a <= 1.65e+116:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.5e+175)
		tmp = x;
	elseif (a <= 1.65e+116)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.5e+175)
		tmp = x;
	elseif (a <= 1.65e+116)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.5e+175], x, If[LessEqual[a, 1.65e+116], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.49999999999999989e175 or 1.6499999999999999e116 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 74.4%

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

   if -4.49999999999999989e175 < a < 1.6499999999999999e116

   1. Initial program 98.5%

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

   2. Taylor expanded in z around inf 64.1%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+175}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+116}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 50.9% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

2. Taylor expanded in x around inf 48.8%

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

3. Final simplification 48.8%

   \[\leadsto x \]

Developer target: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023240 
(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)))))