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

Percentage Accurate: 85.4% → 98.0%

Time: 12.6s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.3%

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

   1. associate-/l* 98.6%

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

3. Simplified 98.6%

   \[\leadsto \color{blue}{x + y \cdot \frac{z - t}{a - t}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 77.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+156}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-33}:\\ \;\;\;\;x - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-26}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7e+156)
   (+ x y)
   (if (<= t -1.85e-33)
     (- x (/ z (/ t y)))
     (if (<= t 1.55e-26) (+ x (* z (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+156) {
		tmp = x + y;
	} else if (t <= -1.85e-33) {
		tmp = x - (z / (t / y));
	} else if (t <= 1.55e-26) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.7d+156)) then
        tmp = x + y
    else if (t <= (-1.85d-33)) then
        tmp = x - (z / (t / y))
    else if (t <= 1.55d-26) then
        tmp = x + (z * (y / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+156) {
		tmp = x + y;
	} else if (t <= -1.85e-33) {
		tmp = x - (z / (t / y));
	} else if (t <= 1.55e-26) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7e+156:
		tmp = x + y
	elif t <= -1.85e-33:
		tmp = x - (z / (t / y))
	elif t <= 1.55e-26:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7e+156)
		tmp = Float64(x + y);
	elseif (t <= -1.85e-33)
		tmp = Float64(x - Float64(z / Float64(t / y)));
	elseif (t <= 1.55e-26)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7e+156)
		tmp = x + y;
	elseif (t <= -1.85e-33)
		tmp = x - (z / (t / y));
	elseif (t <= 1.55e-26)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7e+156], N[(x + y), $MachinePrecision], If[LessEqual[t, -1.85e-33], N[(x - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e-26], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7e156 or 1.54999999999999992e-26 < t

   1. Initial program 71.0%

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

      1. +-commutative 71.0%

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

      2. *-commutative 71.0%

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

      3. associate-/l* 93.8%

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

      4. fma-define 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in t around inf 78.4%

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

      1. +-commutative 78.4%

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

   7. Simplified 78.4%

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

   if -2.7e156 < t < -1.85000000000000007e-33

   1. Initial program 82.9%

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

      1. +-commutative 82.9%

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

      2. *-commutative 82.9%

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

      3. associate-/l* 95.6%

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

      4. fma-define 95.6%

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

   3. Simplified 95.6%

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

      1. fma-undefine 95.6%

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

      2. clear-num 95.5%

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

      3. un-div-inv 95.6%

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in a around 0 80.2%

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

      1. neg-mul-1 80.2%

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

      2. distribute-neg-frac 80.2%

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

   9. Simplified 80.2%

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

   10. Taylor expanded in z around inf 72.4%

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

   if -1.85000000000000007e-33 < t < 1.54999999999999992e-26

   1. Initial program 95.8%

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

      1. +-commutative 95.8%

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

      2. *-commutative 95.8%

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

      3. associate-/l* 94.9%

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

      4. fma-define 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in t around 0 77.2%

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

      1. +-commutative 77.2%

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

      2. associate-/l* 77.0%

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

   7. Simplified 77.0%

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

      1. clear-num 76.9%

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

      2. un-div-inv 78.0%

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

   9. Applied egg-rr 78.0%

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

       1. associate-/r/ 78.2%

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

   11. Simplified 78.2%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+156}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-33}:\\ \;\;\;\;x - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-26}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+68}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-33}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-26}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.65e+68)
   (+ x y)
   (if (<= t -1.45e-33)
     (- x (/ (* y z) t))
     (if (<= t 2.35e-26) (+ x (* z (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.65e+68) {
		tmp = x + y;
	} else if (t <= -1.45e-33) {
		tmp = x - ((y * z) / t);
	} else if (t <= 2.35e-26) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.65d+68)) then
        tmp = x + y
    else if (t <= (-1.45d-33)) then
        tmp = x - ((y * z) / t)
    else if (t <= 2.35d-26) then
        tmp = x + (z * (y / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.65e+68) {
		tmp = x + y;
	} else if (t <= -1.45e-33) {
		tmp = x - ((y * z) / t);
	} else if (t <= 2.35e-26) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.65e+68:
		tmp = x + y
	elif t <= -1.45e-33:
		tmp = x - ((y * z) / t)
	elif t <= 2.35e-26:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.65e+68)
		tmp = Float64(x + y);
	elseif (t <= -1.45e-33)
		tmp = Float64(x - Float64(Float64(y * z) / t));
	elseif (t <= 2.35e-26)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.65e+68)
		tmp = x + y;
	elseif (t <= -1.45e-33)
		tmp = x - ((y * z) / t);
	elseif (t <= 2.35e-26)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.65e+68], N[(x + y), $MachinePrecision], If[LessEqual[t, -1.45e-33], N[(x - N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.35e-26], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.65e68 or 2.34999999999999995e-26 < t

   1. Initial program 70.8%

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

      1. +-commutative 70.8%

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

      2. *-commutative 70.8%

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

      3. associate-/l* 94.1%

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

      4. fma-define 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in t around inf 77.1%

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

      1. +-commutative 77.1%

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

   7. Simplified 77.1%

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

   if -1.65e68 < t < -1.45000000000000001e-33

   1. Initial program 95.7%

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

      1. +-commutative 95.7%

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

      2. *-commutative 95.7%

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

      3. associate-/l* 95.5%

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

      4. fma-define 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in a around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

      3. associate-/l* 77.5%

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

      4. div-sub 77.4%

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

      5. sub-neg 77.4%

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

      6. *-inverses 77.4%

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

      7. metadata-eval 77.4%

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

   7. Simplified 77.4%

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

   8. Taylor expanded in z around inf 70.3%

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

   if -1.45000000000000001e-33 < t < 2.34999999999999995e-26

   1. Initial program 95.8%

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

      1. +-commutative 95.8%

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

      2. *-commutative 95.8%

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

      3. associate-/l* 94.9%

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

      4. fma-define 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in t around 0 77.2%

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

      1. +-commutative 77.2%

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

      2. associate-/l* 77.0%

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

   7. Simplified 77.0%

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

      1. clear-num 76.9%

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

      2. un-div-inv 78.0%

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

   9. Applied egg-rr 78.0%

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

       1. associate-/r/ 78.2%

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

   11. Simplified 78.2%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+68}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-33}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-26}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+34}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-34}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-26}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.9e+34)
   (+ x y)
   (if (<= t -5.6e-34)
     (* y (/ z (- a t)))
     (if (<= t 2e-26) (+ x (* z (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.9e+34) {
		tmp = x + y;
	} else if (t <= -5.6e-34) {
		tmp = y * (z / (a - t));
	} else if (t <= 2e-26) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.9d+34)) then
        tmp = x + y
    else if (t <= (-5.6d-34)) then
        tmp = y * (z / (a - t))
    else if (t <= 2d-26) then
        tmp = x + (z * (y / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.9e+34) {
		tmp = x + y;
	} else if (t <= -5.6e-34) {
		tmp = y * (z / (a - t));
	} else if (t <= 2e-26) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.9e+34:
		tmp = x + y
	elif t <= -5.6e-34:
		tmp = y * (z / (a - t))
	elif t <= 2e-26:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.9e+34)
		tmp = Float64(x + y);
	elseif (t <= -5.6e-34)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 2e-26)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.9e+34)
		tmp = x + y;
	elseif (t <= -5.6e-34)
		tmp = y * (z / (a - t));
	elseif (t <= 2e-26)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.9e+34], N[(x + y), $MachinePrecision], If[LessEqual[t, -5.6e-34], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-26], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.90000000000000019e34 or 2.0000000000000001e-26 < t

   1. Initial program 72.4%

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

      1. +-commutative 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-/l* 93.7%

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

      4. fma-define 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in t around inf 76.4%

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

      1. +-commutative 76.4%

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

   7. Simplified 76.4%

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

   if -3.90000000000000019e34 < t < -5.59999999999999994e-34

   1. Initial program 93.8%

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

      1. +-commutative 93.8%

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

      2. *-commutative 93.8%

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

      3. associate-/l* 99.9%

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

      4. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 99.9%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. div-sub 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in z around inf 65.2%

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

       1. div-sub 65.2%

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

       2. associate-/r/ 64.9%

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

   11. Simplified 64.9%

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

   if -5.59999999999999994e-34 < t < 2.0000000000000001e-26

   1. Initial program 95.8%

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

      1. +-commutative 95.8%

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

      2. *-commutative 95.8%

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

      3. associate-/l* 94.8%

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

      4. fma-define 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in t around 0 78.0%

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

      1. +-commutative 78.0%

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

      2. associate-/l* 77.8%

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

   7. Simplified 77.8%

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

      1. clear-num 77.7%

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

      2. un-div-inv 78.8%

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

   9. Applied egg-rr 78.8%

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

       1. associate-/r/ 79.0%

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

   11. Simplified 79.0%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+34}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-34}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-26}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+34}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-34}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4e+34)
   (+ x y)
   (if (<= t -5.6e-34)
     (* y (/ z (- a t)))
     (if (<= t 2.3e-49) (+ x (/ (* y z) a)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+34) {
		tmp = x + y;
	} else if (t <= -5.6e-34) {
		tmp = y * (z / (a - t));
	} else if (t <= 2.3e-49) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4d+34)) then
        tmp = x + y
    else if (t <= (-5.6d-34)) then
        tmp = y * (z / (a - t))
    else if (t <= 2.3d-49) then
        tmp = x + ((y * z) / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+34) {
		tmp = x + y;
	} else if (t <= -5.6e-34) {
		tmp = y * (z / (a - t));
	} else if (t <= 2.3e-49) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4e+34:
		tmp = x + y
	elif t <= -5.6e-34:
		tmp = y * (z / (a - t))
	elif t <= 2.3e-49:
		tmp = x + ((y * z) / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4e+34)
		tmp = Float64(x + y);
	elseif (t <= -5.6e-34)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 2.3e-49)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4e+34)
		tmp = x + y;
	elseif (t <= -5.6e-34)
		tmp = y * (z / (a - t));
	elseif (t <= 2.3e-49)
		tmp = x + ((y * z) / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4e+34], N[(x + y), $MachinePrecision], If[LessEqual[t, -5.6e-34], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e-49], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.99999999999999978e34 or 2.2999999999999999e-49 < t

   1. Initial program 72.5%

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

      1. +-commutative 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-/l* 93.9%

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

      4. fma-define 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in t around inf 76.1%

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

      1. +-commutative 76.1%

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

   7. Simplified 76.1%

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

   if -3.99999999999999978e34 < t < -5.59999999999999994e-34

   1. Initial program 93.8%

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

      1. +-commutative 93.8%

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

      2. *-commutative 93.8%

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

      3. associate-/l* 99.9%

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

      4. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 99.9%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. div-sub 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in z around inf 65.2%

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

       1. div-sub 65.2%

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

       2. associate-/r/ 64.9%

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

   11. Simplified 64.9%

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

   if -5.59999999999999994e-34 < t < 2.2999999999999999e-49

   1. Initial program 96.7%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in t around 0 79.2%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+34}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-34}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.35 \cdot 10^{-9} \lor \neg \left(z \leq 7.5 \cdot 10^{-21}\right):\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.35e-9) (not (<= z 7.5e-21)))
   (+ x (/ z (/ (- a t) y)))
   (+ x (* t (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.35e-9) || !(z <= 7.5e-21)) {
		tmp = x + (z / ((a - t) / y));
	} else {
		tmp = x + (t * (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 <= (-3.35d-9)) .or. (.not. (z <= 7.5d-21))) then
        tmp = x + (z / ((a - t) / y))
    else
        tmp = x + (t * (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 <= -3.35e-9) || !(z <= 7.5e-21)) {
		tmp = x + (z / ((a - t) / y));
	} else {
		tmp = x + (t * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.35e-9) or not (z <= 7.5e-21):
		tmp = x + (z / ((a - t) / y))
	else:
		tmp = x + (t * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.35e-9) || !(z <= 7.5e-21))
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.35e-9) || ~((z <= 7.5e-21)))
		tmp = x + (z / ((a - t) / y));
	else
		tmp = x + (t * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.35e-9], N[Not[LessEqual[z, 7.5e-21]], $MachinePrecision]], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.34999999999999981e-9 or 7.50000000000000072e-21 < z

   1. Initial program 78.4%

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

      1. +-commutative 78.4%

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

      2. *-commutative 78.4%

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

      3. associate-/l* 94.4%

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

      4. fma-define 94.4%

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

   3. Simplified 94.4%

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

      1. fma-undefine 94.4%

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

      2. clear-num 94.1%

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

      3. un-div-inv 94.2%

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

   6. Applied egg-rr 94.2%

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

   7. Taylor expanded in z around inf 81.3%

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

   if -3.34999999999999981e-9 < z < 7.50000000000000072e-21

   1. Initial program 86.3%

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

      1. *-commutative 86.3%

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

      2. associate-*r/ 94.6%

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

      3. *-commutative 94.6%

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

   4. Applied egg-rr 94.6%

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

   5. Taylor expanded in z around 0 79.2%

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

      1. associate-*r/ 89.8%

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

      2. neg-mul-1 89.8%

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

      3. unsub-neg 89.8%

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

   7. Simplified 89.8%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.35 \cdot 10^{-9} \lor \neg \left(z \leq 7.5 \cdot 10^{-21}\right):\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+156} \lor \neg \left(t \leq 1.15 \cdot 10^{-13}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.7e+156) (not (<= t 1.15e-13)))
   (+ x y)
   (+ x (/ z (/ (- a t) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.7e+156) || !(t <= 1.15e-13)) {
		tmp = x + y;
	} else {
		tmp = x + (z / ((a - t) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.7d+156)) .or. (.not. (t <= 1.15d-13))) then
        tmp = x + y
    else
        tmp = x + (z / ((a - t) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.7e+156) || !(t <= 1.15e-13)) {
		tmp = x + y;
	} else {
		tmp = x + (z / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.7e+156) or not (t <= 1.15e-13):
		tmp = x + y
	else:
		tmp = x + (z / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.7e+156) || !(t <= 1.15e-13))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.7e+156) || ~((t <= 1.15e-13)))
		tmp = x + y;
	else
		tmp = x + (z / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.7e+156], N[Not[LessEqual[t, 1.15e-13]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7e156 or 1.1499999999999999e-13 < t

   1. Initial program 69.9%

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

      1. +-commutative 69.9%

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

      2. *-commutative 69.9%

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

      3. associate-/l* 94.3%

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

      4. fma-define 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in t around inf 79.4%

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

      1. +-commutative 79.4%

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

   7. Simplified 79.4%

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

   if -2.7e156 < t < 1.1499999999999999e-13

   1. Initial program 92.0%

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

      1. +-commutative 92.0%

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

      2. *-commutative 92.0%

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

      3. associate-/l* 94.6%

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

      4. fma-define 94.7%

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

   3. Simplified 94.7%

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

      1. fma-undefine 94.6%

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

      2. clear-num 94.6%

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

      3. un-div-inv 94.7%

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

   6. Applied egg-rr 94.7%

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

   7. Taylor expanded in z around inf 83.4%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+156} \lor \neg \left(t \leq 1.15 \cdot 10^{-13}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+67} \lor \neg \left(t \leq 1.3 \cdot 10^{-44}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.2e+67) (not (<= t 1.3e-44)))
   (+ x y)
   (+ x (/ (* y z) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.2e+67) || !(t <= 1.3e-44)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7.2d+67)) .or. (.not. (t <= 1.3d-44))) then
        tmp = x + y
    else
        tmp = x + ((y * z) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.2e+67) || !(t <= 1.3e-44)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.2e+67) or not (t <= 1.3e-44):
		tmp = x + y
	else:
		tmp = x + ((y * z) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.2e+67) || !(t <= 1.3e-44))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.2e+67) || ~((t <= 1.3e-44)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.2e+67], N[Not[LessEqual[t, 1.3e-44]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.1999999999999998e67 or 1.2999999999999999e-44 < t

   1. Initial program 71.0%

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

      1. +-commutative 71.0%

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

      2. *-commutative 71.0%

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

      3. associate-/l* 94.2%

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

      4. fma-define 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in t around inf 76.7%

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

      1. +-commutative 76.7%

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

   7. Simplified 76.7%

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

   if -7.1999999999999998e67 < t < 1.2999999999999999e-44

   1. Initial program 96.5%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around inf 86.6%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+67} \lor \neg \left(t \leq 1.3 \cdot 10^{-44}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-90}:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-83}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.2e-90)
   (+ x (* y (/ (- t z) t)))
   (if (<= t 1.85e-83) (+ x (/ (* y z) (- a t))) (- x (* y (/ t (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.2e-90) {
		tmp = x + (y * ((t - z) / t));
	} else if (t <= 1.85e-83) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x - (y * (t / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.2d-90)) then
        tmp = x + (y * ((t - z) / t))
    else if (t <= 1.85d-83) then
        tmp = x + ((y * z) / (a - t))
    else
        tmp = x - (y * (t / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.2e-90) {
		tmp = x + (y * ((t - z) / t));
	} else if (t <= 1.85e-83) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x - (y * (t / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.2e-90:
		tmp = x + (y * ((t - z) / t))
	elif t <= 1.85e-83:
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = x - (y * (t / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.2e-90)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / t)));
	elseif (t <= 1.85e-83)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.2e-90)
		tmp = x + (y * ((t - z) / t));
	elseif (t <= 1.85e-83)
		tmp = x + ((y * z) / (a - t));
	else
		tmp = x - (y * (t / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.2e-90], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e-83], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.20000000000000007e-90

   1. Initial program 79.9%

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

      1. +-commutative 79.9%

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

      2. *-commutative 79.9%

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

      3. associate-/l* 93.5%

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

      4. fma-define 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in a around 0 70.0%

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

      1. mul-1-neg 70.0%

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

      2. unsub-neg 70.0%

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

      3. associate-/l* 81.4%

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

      4. div-sub 81.3%

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

      5. sub-neg 81.3%

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

      6. *-inverses 81.3%

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

      7. metadata-eval 81.3%

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

   7. Simplified 81.3%

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

   8. Taylor expanded in t around 0 69.8%

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

      1. +-commutative 69.8%

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

      2. mul-1-neg 69.8%

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

      3. *-commutative 69.8%

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

      4. distribute-rgt-neg-in 69.8%

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

      5. distribute-lft-in 70.0%

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

      6. sub-neg 70.0%

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

      7. associate-/l* 81.4%

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

   10. Simplified 81.4%

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

   if -3.20000000000000007e-90 < t < 1.84999999999999997e-83

   1. Initial program 97.2%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around inf 95.9%

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

   if 1.84999999999999997e-83 < t

   1. Initial program 72.4%

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

      1. +-commutative 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-/l* 96.6%

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

      4. fma-define 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in z around 0 65.1%

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

      1. mul-1-neg 65.1%

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

      2. unsub-neg 65.1%

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

      3. *-commutative 65.1%

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

      4. *-lft-identity 65.1%

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

      5. times-frac 90.3%

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

      6. /-rgt-identity 90.3%

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

   7. Simplified 90.3%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-90}:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-83}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-90}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.2e-90)
   (- x (* y (+ (/ z t) -1.0)))
   (if (<= t 1.15e-84) (+ x (/ (* y z) (- a t))) (+ x (* y (/ t (- t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.2e-90) {
		tmp = x - (y * ((z / t) + -1.0));
	} else if (t <= 1.15e-84) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (y * (t / (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 <= (-3.2d-90)) then
        tmp = x - (y * ((z / t) + (-1.0d0)))
    else if (t <= 1.15d-84) then
        tmp = x + ((y * z) / (a - t))
    else
        tmp = x + (y * (t / (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 <= -3.2e-90) {
		tmp = x - (y * ((z / t) + -1.0));
	} else if (t <= 1.15e-84) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (y * (t / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.2e-90:
		tmp = x - (y * ((z / t) + -1.0))
	elif t <= 1.15e-84:
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = x + (y * (t / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.2e-90)
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	elseif (t <= 1.15e-84)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.2e-90)
		tmp = x - (y * ((z / t) + -1.0));
	elseif (t <= 1.15e-84)
		tmp = x + ((y * z) / (a - t));
	else
		tmp = x + (y * (t / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.2e-90], N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-84], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.20000000000000007e-90

   1. Initial program 79.9%

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

      1. +-commutative 79.9%

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

      2. *-commutative 79.9%

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

      3. associate-/l* 93.5%

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

      4. fma-define 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in a around 0 70.0%

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

      1. mul-1-neg 70.0%

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

      2. unsub-neg 70.0%

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

      3. associate-/l* 81.4%

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

      4. div-sub 81.3%

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

      5. sub-neg 81.3%

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

      6. *-inverses 81.3%

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

      7. metadata-eval 81.3%

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

   7. Simplified 81.3%

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

   if -3.20000000000000007e-90 < t < 1.1499999999999999e-84

   1. Initial program 97.2%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around inf 95.9%

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

   if 1.1499999999999999e-84 < t

   1. Initial program 72.4%

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

      1. +-commutative 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-/l* 96.6%

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

      4. fma-define 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in z around 0 65.1%

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

      1. mul-1-neg 65.1%

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

      2. unsub-neg 65.1%

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

      3. *-commutative 65.1%

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

      4. *-lft-identity 65.1%

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

      5. times-frac 90.3%

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

      6. /-rgt-identity 90.3%

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

   7. Simplified 90.3%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-90}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-90}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.2e-90)
   (- x (* y (+ (/ z t) -1.0)))
   (if (<= t 2.3e-84) (+ x (/ (* y z) (- a t))) (+ x (* t (/ y (- t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.2e-90) {
		tmp = x - (y * ((z / t) + -1.0));
	} else if (t <= 2.3e-84) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (t * (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 <= (-3.2d-90)) then
        tmp = x - (y * ((z / t) + (-1.0d0)))
    else if (t <= 2.3d-84) then
        tmp = x + ((y * z) / (a - t))
    else
        tmp = x + (t * (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 <= -3.2e-90) {
		tmp = x - (y * ((z / t) + -1.0));
	} else if (t <= 2.3e-84) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (t * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.2e-90:
		tmp = x - (y * ((z / t) + -1.0))
	elif t <= 2.3e-84:
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = x + (t * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.2e-90)
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	elseif (t <= 2.3e-84)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.2e-90)
		tmp = x - (y * ((z / t) + -1.0));
	elseif (t <= 2.3e-84)
		tmp = x + ((y * z) / (a - t));
	else
		tmp = x + (t * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.2e-90], N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e-84], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.20000000000000007e-90

   1. Initial program 79.9%

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

      1. +-commutative 79.9%

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

      2. *-commutative 79.9%

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

      3. associate-/l* 93.5%

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

      4. fma-define 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in a around 0 70.0%

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

      1. mul-1-neg 70.0%

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

      2. unsub-neg 70.0%

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

      3. associate-/l* 81.4%

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

      4. div-sub 81.3%

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

      5. sub-neg 81.3%

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

      6. *-inverses 81.3%

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

      7. metadata-eval 81.3%

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

   7. Simplified 81.3%

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

   if -3.20000000000000007e-90 < t < 2.29999999999999981e-84

   1. Initial program 97.2%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around inf 95.9%

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

   if 2.29999999999999981e-84 < t

   1. Initial program 72.4%

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

      1. *-commutative 72.4%

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

      2. associate-*r/ 96.6%

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

      3. *-commutative 96.6%

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

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in z around 0 65.1%

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

      1. associate-*r/ 87.1%

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

      2. neg-mul-1 87.1%

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

      3. unsub-neg 87.1%

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

   7. Simplified 87.1%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-90}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 77.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+58} \lor \neg \left(t \leq 2.1 \cdot 10^{-46}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.5e+58) (not (<= t 2.1e-46))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.5e+58) || !(t <= 2.1e-46)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.5d+58)) .or. (.not. (t <= 2.1d-46))) then
        tmp = x + y
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.5e+58) || !(t <= 2.1e-46)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.5e+58) or not (t <= 2.1e-46):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.5e+58) || !(t <= 2.1e-46))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.5e+58) || ~((t <= 2.1e-46)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.5e+58], N[Not[LessEqual[t, 2.1e-46]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4999999999999997e58 or 2.09999999999999987e-46 < t

   1. Initial program 71.8%

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

      1. +-commutative 71.8%

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

      2. *-commutative 71.8%

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

      3. associate-/l* 94.4%

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

      4. fma-define 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in t around inf 76.1%

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

      1. +-commutative 76.1%

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

   7. Simplified 76.1%

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

   if -3.4999999999999997e58 < t < 2.09999999999999987e-46

   1. Initial program 96.4%

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

      1. +-commutative 96.4%

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

      2. *-commutative 96.4%

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

      3. associate-/l* 94.7%

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

      4. fma-define 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in t around 0 73.2%

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

      1. +-commutative 73.2%

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

      2. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+58} \lor \neg \left(t \leq 2.1 \cdot 10^{-46}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-219} \lor \neg \left(t \leq 2.7 \cdot 10^{-85}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.25e-219) (not (<= t 2.7e-85))) (+ x y) (* y (/ z (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.25e-219) || !(t <= 2.7e-85)) {
		tmp = x + y;
	} else {
		tmp = y * (z / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.25d-219)) .or. (.not. (t <= 2.7d-85))) then
        tmp = x + y
    else
        tmp = y * (z / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.25e-219) || !(t <= 2.7e-85)) {
		tmp = x + y;
	} else {
		tmp = y * (z / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.25e-219) or not (t <= 2.7e-85):
		tmp = x + y
	else:
		tmp = y * (z / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.25e-219) || !(t <= 2.7e-85))
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.25e-219) || ~((t <= 2.7e-85)))
		tmp = x + y;
	else
		tmp = y * (z / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.25e-219], N[Not[LessEqual[t, 2.7e-85]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.25e-219 or 2.7000000000000001e-85 < t

   1. Initial program 79.1%

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

      1. +-commutative 79.1%

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

      2. *-commutative 79.1%

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

      3. associate-/l* 94.6%

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

      4. fma-define 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in t around inf 69.2%

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

      1. +-commutative 69.2%

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

   7. Simplified 69.2%

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

   if -1.25e-219 < t < 2.7000000000000001e-85

   1. Initial program 95.9%

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

      1. +-commutative 95.9%

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

      2. *-commutative 95.9%

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

      3. associate-/l* 93.9%

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

      4. fma-define 93.9%

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

   3. Simplified 93.9%

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

      1. fma-undefine 93.9%

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

      2. clear-num 93.9%

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

      3. un-div-inv 93.9%

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

   6. Applied egg-rr 93.9%

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

      1. div-sub 94.0%

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

   8. Applied egg-rr 94.0%

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

   9. Taylor expanded in z around inf 54.5%

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

       1. div-sub 54.4%

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

       2. associate-/r/ 60.1%

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

   11. Simplified 60.1%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-219} \lor \neg \left(t \leq 2.7 \cdot 10^{-85}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+232}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+117}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.8e+232) x (if (<= a 3.6e+117) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.8e+232) {
		tmp = x;
	} else if (a <= 3.6e+117) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.8d+232)) then
        tmp = x
    else if (a <= 3.6d+117) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.8e+232) {
		tmp = x;
	} else if (a <= 3.6e+117) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.8e+232:
		tmp = x
	elif a <= 3.6e+117:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.8e+232)
		tmp = x;
	elseif (a <= 3.6e+117)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.8e+232)
		tmp = x;
	elseif (a <= 3.6e+117)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.8e+232], x, If[LessEqual[a, 3.6e+117], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.8000000000000001e232 or 3.60000000000000013e117 < a

   1. Initial program 75.8%

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

      1. +-commutative 75.8%

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

      2. *-commutative 75.8%

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

      3. associate-/l* 96.8%

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

      4. fma-define 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in y around 0 70.0%

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

   if -3.8000000000000001e232 < a < 3.60000000000000013e117

   1. Initial program 84.2%

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

      1. +-commutative 84.2%

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

      2. *-commutative 84.2%

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

      3. associate-/l* 93.8%

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

      4. fma-define 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in t around inf 64.0%

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

      1. +-commutative 64.0%

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

   7. Simplified 64.0%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+232}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+117}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.1% 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 82.3%

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

   1. +-commutative 82.3%

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

   2. *-commutative 82.3%

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

   3. associate-/l* 94.5%

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

   4. fma-define 94.5%

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

3. Simplified 94.5%

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

5. Taylor expanded in y around 0 48.2%

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

Developer Target 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024172 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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