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

Percentage Accurate: 86.0% → 98.2%

Time: 7.8s

Alternatives: 12

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: 86.0% 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: 98.2% 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]

Derivation

1. Initial program 85.3%

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

   1. associate-/l* 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 2: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+95}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-115}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+24}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.4e+95)
   (+ x y)
   (if (<= t -2.8e-115)
     (- x (* y (/ z t)))
     (if (<= t 4e+24) (+ x (* z (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e+95) {
		tmp = x + y;
	} else if (t <= -2.8e-115) {
		tmp = x - (y * (z / t));
	} else if (t <= 4e+24) {
		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 <= (-2.4d+95)) then
        tmp = x + y
    else if (t <= (-2.8d-115)) then
        tmp = x - (y * (z / t))
    else if (t <= 4d+24) 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 <= -2.4e+95) {
		tmp = x + y;
	} else if (t <= -2.8e-115) {
		tmp = x - (y * (z / t));
	} else if (t <= 4e+24) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.4e+95:
		tmp = x + y
	elif t <= -2.8e-115:
		tmp = x - (y * (z / t))
	elif t <= 4e+24:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.4e+95)
		tmp = Float64(x + y);
	elseif (t <= -2.8e-115)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= 4e+24)
		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 <= -2.4e+95)
		tmp = x + y;
	elseif (t <= -2.8e-115)
		tmp = x - (y * (z / t));
	elseif (t <= 4e+24)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.4e+95], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.8e-115], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+24], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4e95 or 3.9999999999999999e24 < t

   1. Initial program 73.2%

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

      1. +-commutative 73.2%

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

      2. associate-*l/ 94.6%

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

      3. fma-def 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around inf 82.5%

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

      1. +-commutative 82.5%

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

   6. Simplified 82.5%

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

   if -2.4e95 < t < -2.79999999999999987e-115

   1. Initial program 93.5%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

      1. clear-num 97.9%

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

      2. associate-/r/ 97.8%

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

      3. clear-num 97.8%

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

   5. Applied egg-rr 97.8%

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

   6. Taylor expanded in z around inf 87.3%

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

      1. associate-/l* 91.4%

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

   8. Simplified 91.4%

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

   9. Taylor expanded in a around 0 72.7%

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

       1. mul-1-neg 72.7%

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

       2. *-commutative 72.7%

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

       3. associate-*r/ 70.8%

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

       4. unsub-neg 70.8%

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

       5. associate-*r/ 72.7%

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

       6. associate-*l/ 70.7%

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

       7. *-commutative 70.7%

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

   11. Simplified 70.7%

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

   if -2.79999999999999987e-115 < t < 3.9999999999999999e24

   1. Initial program 95.5%

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

      1. +-commutative 95.5%

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

      2. associate-*l/ 98.1%

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

      3. fma-def 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in t around 0 79.0%

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

      1. +-commutative 79.0%

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

      2. associate-/l* 78.6%

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

   6. Simplified 78.6%

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

      1. associate-/r/ 79.3%

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

   8. Applied egg-rr 79.3%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+95}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-115}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+24}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+96} \lor \neg \left(t \leq 6 \cdot 10^{+101}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.4e+96) (not (<= t 6e+101)))
   (+ x y)
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+96) || !(t <= 6e+101)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.4d+96)) .or. (.not. (t <= 6d+101))) then
        tmp = x + y
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+96) || !(t <= 6e+101)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.4e+96) or not (t <= 6e+101):
		tmp = x + y
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.4e+96) || !(t <= 6e+101))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.4e+96) || ~((t <= 6e+101)))
		tmp = x + y;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.4e+96], N[Not[LessEqual[t, 6e+101]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.39999999999999993e96 or 5.99999999999999986e101 < 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. associate-*l/ 93.7%

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

      3. fma-def 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in t around inf 85.2%

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

      1. +-commutative 85.2%

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

   6. Simplified 85.2%

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

   if -2.39999999999999993e96 < t < 5.99999999999999986e101

   1. Initial program 94.1%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around inf 88.6%

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

      1. associate-*l/ 89.8%

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

      2. *-commutative 89.8%

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

   6. Simplified 89.8%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+96} \lor \neg \left(t \leq 6 \cdot 10^{+101}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 4: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+96} \lor \neg \left(t \leq 3.3 \cdot 10^{+100}\right):\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.2e+96) (not (<= t 3.3e+100)))
   (+ x (- y (* z (/ y t))))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.2e+96) || !(t <= 3.3e+100)) {
		tmp = x + (y - (z * (y / t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7.2d+96)) .or. (.not. (t <= 3.3d+100))) then
        tmp = x + (y - (z * (y / t)))
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.2e+96) || !(t <= 3.3e+100)) {
		tmp = x + (y - (z * (y / t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.2e+96) or not (t <= 3.3e+100):
		tmp = x + (y - (z * (y / t)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.2e+96) || !(t <= 3.3e+100))
		tmp = Float64(x + Float64(y - Float64(z * Float64(y / t))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.2e+96) || ~((t <= 3.3e+100)))
		tmp = x + (y - (z * (y / t)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.2e+96], N[Not[LessEqual[t, 3.3e+100]], $MachinePrecision]], N[(x + N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.20000000000000026e96 or 3.3000000000000001e100 < 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. associate-*l/ 93.7%

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

      3. fma-def 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in a around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. unsub-neg 68.2%

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

      3. associate-/l* 95.1%

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

   6. Simplified 95.1%

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

   7. Taylor expanded in t around 0 80.5%

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

      1. cancel-sign-sub-inv 80.5%

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

      2. metadata-eval 80.5%

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

      3. *-lft-identity 80.5%

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

      4. associate-+l+ 80.5%

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

      5. +-commutative 80.5%

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

      6. mul-1-neg 80.5%

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

      7. unsub-neg 80.5%

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

      8. associate-*l/ 94.2%

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

      9. *-commutative 94.2%

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

   9. Simplified 94.2%

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

   if -7.20000000000000026e96 < t < 3.3000000000000001e100

   1. Initial program 94.1%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around inf 88.6%

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

      1. associate-*l/ 89.8%

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

      2. *-commutative 89.8%

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

   6. Simplified 89.8%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+96} \lor \neg \left(t \leq 3.3 \cdot 10^{+100}\right):\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 5: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+95} \lor \neg \left(t \leq 2.6 \cdot 10^{+56}\right):\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.16e+95) (not (<= t 2.6e+56)))
   (+ x (- y (* z (/ y t))))
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.16e+95) || !(t <= 2.6e+56)) {
		tmp = x + (y - (z * (y / 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 ((t <= (-1.16d+95)) .or. (.not. (t <= 2.6d+56))) then
        tmp = x + (y - (z * (y / 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 ((t <= -1.16e+95) || !(t <= 2.6e+56)) {
		tmp = x + (y - (z * (y / t)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.16e+95) or not (t <= 2.6e+56):
		tmp = x + (y - (z * (y / t)))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.16e+95) || !(t <= 2.6e+56))
		tmp = Float64(x + Float64(y - Float64(z * Float64(y / t))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.16e+95) || ~((t <= 2.6e+56)))
		tmp = x + (y - (z * (y / t)));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.16e+95], N[Not[LessEqual[t, 2.6e+56]], $MachinePrecision]], N[(x + N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1599999999999999e95 or 2.60000000000000011e56 < t

   1. Initial program 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-*l/ 94.3%

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

      3. fma-def 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in a around 0 69.3%

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

      1. mul-1-neg 69.3%

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

      2. unsub-neg 69.3%

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

      3. associate-/l* 93.8%

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

   6. Simplified 93.8%

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

   7. Taylor expanded in t around 0 80.5%

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

      1. cancel-sign-sub-inv 80.5%

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

      2. metadata-eval 80.5%

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

      3. *-lft-identity 80.5%

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

      4. associate-+l+ 80.5%

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

      5. +-commutative 80.5%

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

      6. mul-1-neg 80.5%

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

      7. unsub-neg 80.5%

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

      8. associate-*l/ 92.9%

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

      9. *-commutative 92.9%

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

   9. Simplified 92.9%

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

   if -1.1599999999999999e95 < t < 2.60000000000000011e56

   1. Initial program 95.0%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

      1. clear-num 97.3%

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

      2. associate-/r/ 96.7%

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

      3. clear-num 96.7%

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

   5. Applied egg-rr 96.7%

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

   6. Taylor expanded in z around inf 89.1%

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

      1. associate-/l* 90.7%

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

   8. Simplified 90.7%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+95} \lor \neg \left(t \leq 2.6 \cdot 10^{+56}\right):\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 6: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+94}:\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+100}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.6e+94)
   (+ x (- y (* z (/ y t))))
   (if (<= t 3.3e+100) (+ x (/ y (/ (- a t) z))) (+ x (* y (/ (- t z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.6e+94) {
		tmp = x + (y - (z * (y / t)));
	} else if (t <= 3.3e+100) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x + (y * ((t - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-8.6d+94)) then
        tmp = x + (y - (z * (y / t)))
    else if (t <= 3.3d+100) then
        tmp = x + (y / ((a - t) / z))
    else
        tmp = x + (y * ((t - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.6e+94) {
		tmp = x + (y - (z * (y / t)));
	} else if (t <= 3.3e+100) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x + (y * ((t - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.6e+94:
		tmp = x + (y - (z * (y / t)))
	elif t <= 3.3e+100:
		tmp = x + (y / ((a - t) / z))
	else:
		tmp = x + (y * ((t - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.6e+94)
		tmp = Float64(x + Float64(y - Float64(z * Float64(y / t))));
	elseif (t <= 3.3e+100)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8.6e+94)
		tmp = x + (y - (z * (y / t)));
	elseif (t <= 3.3e+100)
		tmp = x + (y / ((a - t) / z));
	else
		tmp = x + (y * ((t - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.6e+94], N[(x + N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+100], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.6e94

   1. Initial program 63.9%

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

      1. +-commutative 63.9%

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

      2. associate-*l/ 94.8%

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

      3. fma-def 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in a around 0 60.5%

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

      1. mul-1-neg 60.5%

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

      2. unsub-neg 60.5%

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

      3. associate-/l* 94.8%

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

   6. Simplified 94.8%

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

   7. Taylor expanded in t around 0 77.3%

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

      1. cancel-sign-sub-inv 77.3%

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

      2. metadata-eval 77.3%

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

      3. *-lft-identity 77.3%

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

      4. associate-+l+ 77.3%

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

      5. +-commutative 77.3%

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

      6. mul-1-neg 77.3%

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

      7. unsub-neg 77.3%

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

      8. associate-*l/ 94.9%

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

      9. *-commutative 94.9%

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

   9. Simplified 94.9%

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

   if -8.6e94 < t < 3.3000000000000001e100

   1. Initial program 94.1%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

      1. clear-num 97.5%

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

      2. associate-/r/ 96.9%

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

      3. clear-num 96.9%

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

   5. Applied egg-rr 96.9%

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

   6. Taylor expanded in z around inf 88.6%

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

      1. associate-/l* 90.1%

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

   8. Simplified 90.1%

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

   if 3.3000000000000001e100 < t

   1. Initial program 80.1%

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

      1. +-commutative 80.1%

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

      2. associate-*l/ 92.4%

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

      3. fma-def 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in a around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. unsub-neg 78.1%

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

      3. associate-/l* 95.5%

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

   6. Simplified 95.5%

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

      1. clear-num 95.5%

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

      2. associate-/r/ 95.5%

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

      3. clear-num 95.5%

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

   8. Applied egg-rr 95.5%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+94}:\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+100}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \end{array} \]

Alternative 7: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+95}:\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+101}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.55e+95)
   (+ x (- y (* z (/ y t))))
   (if (<= t 3.5e+101) (+ x (/ y (/ (- a t) z))) (- x (/ y (/ t (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.55e+95) {
		tmp = x + (y - (z * (y / t)));
	} else if (t <= 3.5e+101) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x - (y / (t / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.55d+95)) then
        tmp = x + (y - (z * (y / t)))
    else if (t <= 3.5d+101) then
        tmp = x + (y / ((a - t) / z))
    else
        tmp = x - (y / (t / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.55e+95) {
		tmp = x + (y - (z * (y / t)));
	} else if (t <= 3.5e+101) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x - (y / (t / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.55e+95:
		tmp = x + (y - (z * (y / t)))
	elif t <= 3.5e+101:
		tmp = x + (y / ((a - t) / z))
	else:
		tmp = x - (y / (t / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.55e+95)
		tmp = Float64(x + Float64(y - Float64(z * Float64(y / t))));
	elseif (t <= 3.5e+101)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	else
		tmp = Float64(x - Float64(y / Float64(t / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.55e+95)
		tmp = x + (y - (z * (y / t)));
	elseif (t <= 3.5e+101)
		tmp = x + (y / ((a - t) / z));
	else
		tmp = x - (y / (t / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.55e+95], N[(x + N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+101], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.5500000000000001e95

   1. Initial program 63.9%

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

      1. +-commutative 63.9%

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

      2. associate-*l/ 94.8%

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

      3. fma-def 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in a around 0 60.5%

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

      1. mul-1-neg 60.5%

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

      2. unsub-neg 60.5%

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

      3. associate-/l* 94.8%

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

   6. Simplified 94.8%

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

   7. Taylor expanded in t around 0 77.3%

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

      1. cancel-sign-sub-inv 77.3%

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

      2. metadata-eval 77.3%

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

      3. *-lft-identity 77.3%

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

      4. associate-+l+ 77.3%

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

      5. +-commutative 77.3%

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

      6. mul-1-neg 77.3%

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

      7. unsub-neg 77.3%

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

      8. associate-*l/ 94.9%

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

      9. *-commutative 94.9%

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

   9. Simplified 94.9%

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

   if -1.5500000000000001e95 < t < 3.50000000000000023e101

   1. Initial program 94.1%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

      1. clear-num 97.5%

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

      2. associate-/r/ 96.9%

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

      3. clear-num 96.9%

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

   5. Applied egg-rr 96.9%

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

   6. Taylor expanded in z around inf 88.6%

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

      1. associate-/l* 90.1%

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

   8. Simplified 90.1%

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

   if 3.50000000000000023e101 < t

   1. Initial program 80.1%

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

      1. +-commutative 80.1%

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

      2. associate-*l/ 92.4%

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

      3. fma-def 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in a around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. unsub-neg 78.1%

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

      3. associate-/l* 95.5%

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

   6. Simplified 95.5%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+95}:\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+101}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \end{array} \]

Alternative 8: 75.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+55} \lor \neg \left(t \leq 3.5 \cdot 10^{+66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.8e+55) (not (<= t 3.5e+66))) (+ x y) (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.8e+55) || !(t <= 3.5e+66)) {
		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 <= (-8.8d+55)) .or. (.not. (t <= 3.5d+66))) 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 <= -8.8e+55) || !(t <= 3.5e+66)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.8e+55) or not (t <= 3.5e+66):
		tmp = x + y
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.8e+55) || !(t <= 3.5e+66))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.8e+55) || ~((t <= 3.5e+66)))
		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, -8.8e+55], N[Not[LessEqual[t, 3.5e+66]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.80000000000000042e55 or 3.4999999999999997e66 < t

   1. Initial program 73.2%

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

      1. +-commutative 73.2%

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

      2. associate-*l/ 94.6%

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

      3. fma-def 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around inf 81.6%

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

      1. +-commutative 81.6%

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

   6. Simplified 81.6%

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

   if -8.80000000000000042e55 < t < 3.4999999999999997e66

   1. Initial program 94.9%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in t around 0 73.6%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+55} \lor \neg \left(t \leq 3.5 \cdot 10^{+66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]

Alternative 9: 77.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+56} \lor \neg \left(t \leq 9.8 \cdot 10^{+26}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.8e+56) (not (<= t 9.8e+26))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.8e+56) || !(t <= 9.8e+26)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / 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 <= (-5.8d+56)) .or. (.not. (t <= 9.8d+26))) then
        tmp = x + y
    else
        tmp = x + (z * (y / 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 <= -5.8e+56) || !(t <= 9.8e+26)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.8e+56) or not (t <= 9.8e+26):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.8e+56) || !(t <= 9.8e+26))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.8e+56) || ~((t <= 9.8e+26)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.8e+56], N[Not[LessEqual[t, 9.8e+26]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.80000000000000014e56 or 9.79999999999999947e26 < t

   1. Initial program 75.1%

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

      1. +-commutative 75.1%

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

      2. associate-*l/ 95.0%

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

      3. fma-def 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in t around inf 81.4%

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

      1. +-commutative 81.4%

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

   6. Simplified 81.4%

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

   if -5.80000000000000014e56 < t < 9.79999999999999947e26

   1. Initial program 94.5%

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

      1. +-commutative 94.5%

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

      2. associate-*l/ 96.8%

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

      3. fma-def 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in t around 0 73.3%

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

      1. +-commutative 73.3%

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

      2. associate-/l* 73.0%

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

   6. Simplified 73.0%

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

      1. associate-/r/ 73.7%

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

   8. Applied egg-rr 73.7%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+56} \lor \neg \left(t \leq 9.8 \cdot 10^{+26}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10: 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 85.3%

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

   1. associate-/l* 98.4%

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

3. Simplified 98.4%

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

   1. clear-num 98.4%

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

   2. associate-/r/ 98.0%

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

   3. clear-num 98.1%

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

5. Applied egg-rr 98.1%

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

6. Final simplification 98.1%

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

Alternative 11: 62.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+94} \lor \neg \left(t \leq 3.6 \cdot 10^{-41}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8e+94) (not (<= t 3.6e-41))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8e+94) || !(t <= 3.6e-41)) {
		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 ((t <= (-8d+94)) .or. (.not. (t <= 3.6d-41))) 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 ((t <= -8e+94) || !(t <= 3.6e-41)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8e+94) or not (t <= 3.6e-41):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8e+94) || !(t <= 3.6e-41))
		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 ((t <= -8e+94) || ~((t <= 3.6e-41)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8e+94], N[Not[LessEqual[t, 3.6e-41]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -8.0000000000000002e94 or 3.6e-41 < t

   1. Initial program 74.9%

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

      1. +-commutative 74.9%

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

      2. associate-*l/ 94.9%

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

      3. fma-def 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in t around inf 81.4%

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

      1. +-commutative 81.4%

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

   6. Simplified 81.4%

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

   if -8.0000000000000002e94 < t < 3.6e-41

   1. Initial program 94.6%

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

      1. +-commutative 94.6%

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

      2. associate-*l/ 96.8%

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

      3. fma-def 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in y around 0 49.4%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+94} \lor \neg \left(t \leq 3.6 \cdot 10^{-41}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 50.7% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.3%

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

   1. +-commutative 85.3%

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

   2. associate-*l/ 95.9%

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

   3. fma-def 95.9%

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

3. Simplified 95.9%

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

4. Taylor expanded in y around 0 53.1%

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

5. Final simplification 53.1%

   \[\leadsto x \]

Developer target: 98.2% 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 2023318 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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