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

Percentage Accurate: 98.2% → 98.2%

Time: 7.4s

Alternatives: 11

Speedup: 1.0×

Specification

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]

Initial Program: 98.2% 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]

Alternative 1: 98.2% 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 98.8%

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

2. Final simplification 98.8%

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

Alternative 2: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+119} \lor \neg \left(t \leq 8.2 \cdot 10^{+78}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.5e+119) (not (<= t 8.2e+78)))
   (+ x y)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.5e+119) || !(t <= 8.2e+78)) {
		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 <= (-6.5d+119)) .or. (.not. (t <= 8.2d+78))) 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 <= -6.5e+119) || !(t <= 8.2e+78)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.5e+119) or not (t <= 8.2e+78):
		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 <= -6.5e+119) || !(t <= 8.2e+78))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + 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 <= -6.5e+119) || ~((t <= 8.2e+78)))
		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, -6.5e+119], N[Not[LessEqual[t, 8.2e+78]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.4999999999999997e119 or 8.1999999999999994e78 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 87.7%

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

   if -6.4999999999999997e119 < t < 8.1999999999999994e78

   1. Initial program 98.0%

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

   2. Taylor expanded in z around inf 88.5%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+119} \lor \neg \left(t \leq 8.2 \cdot 10^{+78}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 3: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+122}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+115}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.2e+122)
   (+ x y)
   (if (<= t 3.1e+115) (+ x (* z (/ y (- a t)))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e+122) {
		tmp = x + y;
	} else if (t <= 3.1e+115) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.2d+122)) then
        tmp = x + y
    else if (t <= 3.1d+115) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e+122) {
		tmp = x + y;
	} else if (t <= 3.1e+115) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.2e+122:
		tmp = x + y
	elif t <= 3.1e+115:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.2e+122)
		tmp = Float64(x + y);
	elseif (t <= 3.1e+115)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.2e+122)
		tmp = x + y;
	elseif (t <= 3.1e+115)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.2e+122], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.1e+115], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2000000000000001e122 or 3.10000000000000005e115 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 88.4%

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

   if -1.2000000000000001e122 < t < 3.10000000000000005e115

   1. Initial program 98.1%

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

   2. Taylor expanded in x around 0 92.9%

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

      1. *-commutative 92.9%

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

      2. associate-/l* 96.9%

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

   4. Simplified 96.9%

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

   5. Taylor expanded in z around inf 83.4%

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

      1. *-commutative 83.4%

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

      2. associate-*r/ 88.2%

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

   7. Simplified 88.2%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+122}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+115}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+123}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+14}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{t - a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.2e+123)
   (+ x y)
   (if (<= t 1.65e+14) (+ x (* z (/ y (- a t)))) (+ x (/ t (/ (- t a) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.2e+123) {
		tmp = x + y;
	} else if (t <= 1.65e+14) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (t / ((t - a) / 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 <= (-3.2d+123)) then
        tmp = x + y
    else if (t <= 1.65d+14) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + (t / ((t - a) / 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 <= -3.2e+123) {
		tmp = x + y;
	} else if (t <= 1.65e+14) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (t / ((t - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.2e+123:
		tmp = x + y
	elif t <= 1.65e+14:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + (t / ((t - a) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.2e+123)
		tmp = Float64(x + y);
	elseif (t <= 1.65e+14)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(t - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.2e+123)
		tmp = x + y;
	elseif (t <= 1.65e+14)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + (t / ((t - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.2e+123], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.65e+14], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.20000000000000005e123

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 87.0%

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

   if -3.20000000000000005e123 < t < 1.65e14

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0 93.2%

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

      1. *-commutative 93.2%

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

      2. associate-/l* 96.4%

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

   4. Simplified 96.4%

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

   5. Taylor expanded in z around inf 84.7%

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

      1. *-commutative 84.7%

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

      2. associate-*r/ 89.6%

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

   7. Simplified 89.6%

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

   if 1.65e14 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 57.8%

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

      1. *-commutative 57.8%

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

      2. associate-/l* 97.2%

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

   4. Simplified 97.2%

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

   5. Taylor expanded in z around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. *-commutative 54.8%

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

      3. associate-*r/ 91.1%

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

      4. distribute-lft-neg-in 91.1%

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

   7. Simplified 91.1%

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

      1. associate-*r/ 54.8%

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

      2. frac-2neg 54.8%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 23.8%

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

      5. sqr-neg 23.8%

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

      6. sqrt-unprod 36.3%

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

      7. add-sqr-sqrt 36.3%

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

      8. distribute-lft-neg-out 36.3%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 35.6%

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

      11. sqr-neg 35.6%

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

      12. sqrt-unprod 54.7%

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

      13. add-sqr-sqrt 54.8%

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

      14. sub-neg 54.8%

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

      15. distribute-neg-in 54.8%

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

      16. add-sqr-sqrt 0.0%

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

      17. sqrt-unprod 38.4%

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

      18. sqr-neg 38.4%

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

      19. sqrt-unprod 38.7%

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

      20. add-sqr-sqrt 38.7%

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

      21. add-sqr-sqrt 0.0%

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

      22. sqrt-unprod 45.4%

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

      23. sqr-neg 45.4%

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

      24. sqrt-unprod 54.7%

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

      25. add-sqr-sqrt 54.8%

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

   9. Applied egg-rr 54.8%

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

       1. associate-/l* 90.1%

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

       2. +-commutative 90.1%

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

       3. unsub-neg 90.1%

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

   11. Simplified 90.1%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+123}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+14}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{t - a}{y}}\\ \end{array} \]

Alternative 5: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 95000000000000:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{t - a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.6e+59)
   (+ x (* (/ y t) (- t z)))
   (if (<= t 95000000000000.0)
     (+ x (* z (/ y (- a t))))
     (+ x (/ t (/ (- t a) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e+59) {
		tmp = x + ((y / t) * (t - z));
	} else if (t <= 95000000000000.0) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (t / ((t - a) / 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 <= (-3.6d+59)) then
        tmp = x + ((y / t) * (t - z))
    else if (t <= 95000000000000.0d0) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + (t / ((t - a) / 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 <= -3.6e+59) {
		tmp = x + ((y / t) * (t - z));
	} else if (t <= 95000000000000.0) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (t / ((t - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.6e+59:
		tmp = x + ((y / t) * (t - z))
	elif t <= 95000000000000.0:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + (t / ((t - a) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.6e+59)
		tmp = Float64(x + Float64(Float64(y / t) * Float64(t - z)));
	elseif (t <= 95000000000000.0)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(t - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.6e+59)
		tmp = x + ((y / t) * (t - z));
	elseif (t <= 95000000000000.0)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + (t / ((t - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.6e+59], N[(x + N[(N[(y / t), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 95000000000000.0], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.5999999999999999e59

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 68.9%

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

      1. +-commutative 68.9%

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

      2. mul-1-neg 68.9%

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

      3. unsub-neg 68.9%

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

      4. *-commutative 68.9%

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

      5. associate-/l* 93.2%

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

      6. associate-/r/ 86.5%

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

   4. Simplified 86.5%

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

   if -3.5999999999999999e59 < t < 9.5e13

   1. Initial program 97.6%

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

   2. Taylor expanded in x around 0 93.4%

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

      1. *-commutative 93.4%

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

      2. associate-/l* 96.1%

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

   4. Simplified 96.1%

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

   5. Taylor expanded in z around inf 86.3%

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

      1. *-commutative 86.3%

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

      2. associate-*r/ 90.8%

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

   7. Simplified 90.8%

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

   if 9.5e13 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 57.8%

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

      1. *-commutative 57.8%

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

      2. associate-/l* 97.2%

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

   4. Simplified 97.2%

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

   5. Taylor expanded in z around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. *-commutative 54.8%

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

      3. associate-*r/ 91.1%

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

      4. distribute-lft-neg-in 91.1%

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

   7. Simplified 91.1%

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

      1. associate-*r/ 54.8%

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

      2. frac-2neg 54.8%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 23.8%

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

      5. sqr-neg 23.8%

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

      6. sqrt-unprod 36.3%

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

      7. add-sqr-sqrt 36.3%

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

      8. distribute-lft-neg-out 36.3%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 35.6%

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

      11. sqr-neg 35.6%

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

      12. sqrt-unprod 54.7%

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

      13. add-sqr-sqrt 54.8%

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

      14. sub-neg 54.8%

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

      15. distribute-neg-in 54.8%

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

      16. add-sqr-sqrt 0.0%

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

      17. sqrt-unprod 38.4%

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

      18. sqr-neg 38.4%

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

      19. sqrt-unprod 38.7%

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

      20. add-sqr-sqrt 38.7%

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

      21. add-sqr-sqrt 0.0%

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

      22. sqrt-unprod 45.4%

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

      23. sqr-neg 45.4%

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

      24. sqrt-unprod 54.7%

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

      25. add-sqr-sqrt 54.8%

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

   9. Applied egg-rr 54.8%

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

       1. associate-/l* 90.1%

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

       2. +-commutative 90.1%

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

       3. unsub-neg 90.1%

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

   11. Simplified 90.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 95000000000000:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{t - a}{y}}\\ \end{array} \]

Alternative 6: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+59}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{t}{z}}\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+14}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{t - a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.5e+59)
   (+ x (- y (/ y (/ t z))))
   (if (<= t 7e+14) (+ x (* z (/ y (- a t)))) (+ x (/ t (/ (- t a) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e+59) {
		tmp = x + (y - (y / (t / z)));
	} else if (t <= 7e+14) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (t / ((t - a) / 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 <= (-5.5d+59)) then
        tmp = x + (y - (y / (t / z)))
    else if (t <= 7d+14) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + (t / ((t - a) / 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 <= -5.5e+59) {
		tmp = x + (y - (y / (t / z)));
	} else if (t <= 7e+14) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (t / ((t - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.5e+59:
		tmp = x + (y - (y / (t / z)))
	elif t <= 7e+14:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + (t / ((t - a) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.5e+59)
		tmp = Float64(x + Float64(y - Float64(y / Float64(t / z))));
	elseif (t <= 7e+14)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(t - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.5e+59)
		tmp = x + (y - (y / (t / z)));
	elseif (t <= 7e+14)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + (t / ((t - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.5e+59], N[(x + N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+14], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.4999999999999999e59

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 71.2%

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

      1. *-commutative 71.2%

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

      2. associate-/l* 93.2%

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

   4. Simplified 93.2%

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

   5. Taylor expanded in a around 0 68.9%

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

      1. +-commutative 68.9%

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

      2. mul-1-neg 68.9%

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

      3. *-commutative 68.9%

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

      4. unsub-neg 68.9%

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

      5. *-commutative 68.9%

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

      6. associate-/l* 93.2%

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

   7. Simplified 93.2%

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

   8. Taylor expanded in t around 0 80.7%

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

      1. neg-mul-1 80.7%

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

      2. unsub-neg 80.7%

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

      3. associate-/l* 93.2%

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

   10. Simplified 93.2%

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

   if -5.4999999999999999e59 < t < 7e14

   1. Initial program 97.6%

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

   2. Taylor expanded in x around 0 93.4%

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

      1. *-commutative 93.4%

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

      2. associate-/l* 96.1%

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

   4. Simplified 96.1%

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

   5. Taylor expanded in z around inf 86.3%

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

      1. *-commutative 86.3%

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

      2. associate-*r/ 90.8%

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

   7. Simplified 90.8%

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

   if 7e14 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 57.8%

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

      1. *-commutative 57.8%

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

      2. associate-/l* 97.2%

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

   4. Simplified 97.2%

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

   5. Taylor expanded in z around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. *-commutative 54.8%

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

      3. associate-*r/ 91.1%

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

      4. distribute-lft-neg-in 91.1%

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

   7. Simplified 91.1%

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

      1. associate-*r/ 54.8%

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

      2. frac-2neg 54.8%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 23.8%

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

      5. sqr-neg 23.8%

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

      6. sqrt-unprod 36.3%

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

      7. add-sqr-sqrt 36.3%

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

      8. distribute-lft-neg-out 36.3%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 35.6%

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

      11. sqr-neg 35.6%

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

      12. sqrt-unprod 54.7%

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

      13. add-sqr-sqrt 54.8%

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

      14. sub-neg 54.8%

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

      15. distribute-neg-in 54.8%

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

      16. add-sqr-sqrt 0.0%

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

      17. sqrt-unprod 38.4%

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

      18. sqr-neg 38.4%

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

      19. sqrt-unprod 38.7%

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

      20. add-sqr-sqrt 38.7%

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

      21. add-sqr-sqrt 0.0%

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

      22. sqrt-unprod 45.4%

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

      23. sqr-neg 45.4%

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

      24. sqrt-unprod 54.7%

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

      25. add-sqr-sqrt 54.8%

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

   9. Applied egg-rr 54.8%

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

       1. associate-/l* 90.1%

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

       2. +-commutative 90.1%

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

       3. unsub-neg 90.1%

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

   11. Simplified 90.1%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+59}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{t}{z}}\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+14}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{t - a}{y}}\\ \end{array} \]

Alternative 7: 87.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+59}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{t}{z}}\right)\\ \mathbf{elif}\;t \leq 6400000000:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.8e+59)
   (+ x (- y (/ y (/ t z))))
   (if (<= t 6400000000.0)
     (+ x (* z (/ y (- a t))))
     (- x (/ y (+ (/ a t) -1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.8e+59) {
		tmp = x + (y - (y / (t / z)));
	} else if (t <= 6400000000.0) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y / ((a / t) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.8d+59)) then
        tmp = x + (y - (y / (t / z)))
    else if (t <= 6400000000.0d0) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x - (y / ((a / t) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.8e+59) {
		tmp = x + (y - (y / (t / z)));
	} else if (t <= 6400000000.0) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y / ((a / t) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.8e+59:
		tmp = x + (y - (y / (t / z)))
	elif t <= 6400000000.0:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x - (y / ((a / t) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.8e+59)
		tmp = Float64(x + Float64(y - Float64(y / Float64(t / z))));
	elseif (t <= 6400000000.0)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.8e+59)
		tmp = x + (y - (y / (t / z)));
	elseif (t <= 6400000000.0)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x - (y / ((a / t) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.8e+59], N[(x + N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6400000000.0], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.8000000000000004e59

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 71.2%

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

      1. *-commutative 71.2%

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

      2. associate-/l* 93.2%

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

   4. Simplified 93.2%

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

   5. Taylor expanded in a around 0 68.9%

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

      1. +-commutative 68.9%

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

      2. mul-1-neg 68.9%

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

      3. *-commutative 68.9%

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

      4. unsub-neg 68.9%

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

      5. *-commutative 68.9%

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

      6. associate-/l* 93.2%

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

   7. Simplified 93.2%

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

   8. Taylor expanded in t around 0 80.7%

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

      1. neg-mul-1 80.7%

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

      2. unsub-neg 80.7%

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

      3. associate-/l* 93.2%

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

   10. Simplified 93.2%

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

   if -4.8000000000000004e59 < t < 6.4e9

   1. Initial program 97.6%

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

   2. Taylor expanded in x around 0 93.4%

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

      1. *-commutative 93.4%

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

      2. associate-/l* 96.1%

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

   4. Simplified 96.1%

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

   5. Taylor expanded in z around inf 86.3%

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

      1. *-commutative 86.3%

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

      2. associate-*r/ 90.8%

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

   7. Simplified 90.8%

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

   if 6.4e9 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 54.8%

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

      1. +-commutative 54.8%

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

      2. mul-1-neg 54.8%

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

      3. unsub-neg 54.8%

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

      4. associate-/l* 92.9%

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

      5. div-sub 92.9%

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

      6. *-inverses 92.9%

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

   4. Simplified 92.9%

      \[\leadsto \color{blue}{x - \frac{y}{\frac{a}{t} - 1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+59}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{t}{z}}\right)\\ \mathbf{elif}\;t \leq 6400000000:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \]

Alternative 8: 77.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-16}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.5e+14) (+ x y) (if (<= t 1.65e-16) (+ x (* y (/ z a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.5e+14) {
		tmp = x + y;
	} else if (t <= 1.65e-16) {
		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 <= (-1.5d+14)) then
        tmp = x + y
    else if (t <= 1.65d-16) 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 <= -1.5e+14) {
		tmp = x + y;
	} else if (t <= 1.65e-16) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.5e+14:
		tmp = x + y
	elif t <= 1.65e-16:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.5e+14)
		tmp = Float64(x + y);
	elseif (t <= 1.65e-16)
		tmp = Float64(x + Float64(y * Float64(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 <= -1.5e+14)
		tmp = x + y;
	elseif (t <= 1.65e-16)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.5e+14], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.65e-16], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5e14 or 1.64999999999999994e-16 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 80.4%

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

   if -1.5e14 < t < 1.64999999999999994e-16

   1. Initial program 97.4%

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

   2. Taylor expanded in t around 0 83.6%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-16}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -20000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-17}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -20000000000000.0)
   (+ x y)
   (if (<= t 2.4e-17) (+ x (* z (/ y a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -20000000000000.0) {
		tmp = x + y;
	} else if (t <= 2.4e-17) {
		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 <= (-20000000000000.0d0)) then
        tmp = x + y
    else if (t <= 2.4d-17) 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 <= -20000000000000.0) {
		tmp = x + y;
	} else if (t <= 2.4e-17) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -20000000000000.0:
		tmp = x + y
	elif t <= 2.4e-17:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -20000000000000.0)
		tmp = Float64(x + y);
	elseif (t <= 2.4e-17)
		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 <= -20000000000000.0)
		tmp = x + y;
	elseif (t <= 2.4e-17)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -20000000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[t, 2.4e-17], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2e13 or 2.39999999999999986e-17 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 80.4%

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

   if -2e13 < t < 2.39999999999999986e-17

   1. Initial program 97.4%

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

   2. Taylor expanded in t around 0 79.4%

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

      1. associate-/l* 83.6%

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

      2. associate-/r/ 83.7%

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

   4. Simplified 83.7%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -20000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-17}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10: 63.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-163}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.9e-163) (+ x y) (if (<= t 2.4e-18) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e-163) {
		tmp = x + y;
	} else if (t <= 2.4e-18) {
		tmp = x;
	} 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 <= (-2.9d-163)) then
        tmp = x + y
    else if (t <= 2.4d-18) then
        tmp = x
    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 <= -2.9e-163) {
		tmp = x + y;
	} else if (t <= 2.4e-18) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.9e-163:
		tmp = x + y
	elif t <= 2.4e-18:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.9e-163)
		tmp = Float64(x + y);
	elseif (t <= 2.4e-18)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.9e-163)
		tmp = x + y;
	elseif (t <= 2.4e-18)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.9e-163], N[(x + y), $MachinePrecision], If[LessEqual[t, 2.4e-18], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9000000000000001e-163 or 2.39999999999999994e-18 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 76.1%

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

   if -2.9000000000000001e-163 < t < 2.39999999999999994e-18

   1. Initial program 96.6%

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

   2. Taylor expanded in x around inf 56.6%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-163}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 51.5% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

2. Taylor expanded in x around inf 49.5%

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

3. Final simplification 49.5%

   \[\leadsto x \]

Developer target: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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