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

Percentage Accurate: 85.2% → 98.2%

Time: 8.0s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% 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

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

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 87.0%

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

   1. associate-/l* 98.3%

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

3. Simplified 98.3%

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

Alternative 2: 85.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - y \cdot \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-89}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+40}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- y (* y (/ z t))))))
   (if (<= t -2e+125)
     t_1
     (if (<= t -2.9e-89)
       (+ x (* t (/ y (- t a))))
       (if (<= t 6.8e+40) (+ x (/ (* y z) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - (y * (z / t)));
	double tmp;
	if (t <= -2e+125) {
		tmp = t_1;
	} else if (t <= -2.9e-89) {
		tmp = x + (t * (y / (t - a)));
	} else if (t <= 6.8e+40) {
		tmp = x + ((y * z) / (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 - (y * (z / t)))
    if (t <= (-2d+125)) then
        tmp = t_1
    else if (t <= (-2.9d-89)) then
        tmp = x + (t * (y / (t - a)))
    else if (t <= 6.8d+40) then
        tmp = x + ((y * z) / (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 - (y * (z / t)));
	double tmp;
	if (t <= -2e+125) {
		tmp = t_1;
	} else if (t <= -2.9e-89) {
		tmp = x + (t * (y / (t - a)));
	} else if (t <= 6.8e+40) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y - (y * (z / t)))
	tmp = 0
	if t <= -2e+125:
		tmp = t_1
	elif t <= -2.9e-89:
		tmp = x + (t * (y / (t - a)))
	elif t <= 6.8e+40:
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y - Float64(y * Float64(z / t))))
	tmp = 0.0
	if (t <= -2e+125)
		tmp = t_1;
	elseif (t <= -2.9e-89)
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	elseif (t <= 6.8e+40)
		tmp = Float64(x + Float64(Float64(y * z) / 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 - (y * (z / t)));
	tmp = 0.0;
	if (t <= -2e+125)
		tmp = t_1;
	elseif (t <= -2.9e-89)
		tmp = x + (t * (y / (t - a)));
	elseif (t <= 6.8e+40)
		tmp = x + ((y * z) / (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[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+125], t$95$1, If[LessEqual[t, -2.9e-89], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e+40], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9999999999999998e125 or 6.79999999999999977e40 < t

   1. Initial program 66.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. associate-/l* 92.1%

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

      3. distribute-lft-neg-in 92.1%

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

      4. div-sub 92.1%

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

      5. sub-neg 92.1%

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

      6. *-inverses 92.1%

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

      7. metadata-eval 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in z around 0 80.9%

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

      1. mul-1-neg 80.9%

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

      2. associate-*r/ 92.1%

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

      3. unsub-neg 92.1%

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

   10. Simplified 92.1%

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

   if -1.9999999999999998e125 < t < -2.89999999999999992e-89

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      2. associate-/l* 96.6%

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

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in z around 0 87.2%

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

      1. mul-1-neg 87.2%

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

      2. associate-/l* 87.2%

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

      3. distribute-lft-neg-out 87.2%

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

      4. *-commutative 87.2%

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

   7. Simplified 87.2%

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

      1. associate-*l/ 87.2%

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

      2. frac-2neg 87.2%

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

      3. add-sqr-sqrt 87.0%

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

      4. sqrt-unprod 87.2%

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

      5. sqr-neg 87.2%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 63.7%

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

      8. distribute-rgt-neg-out 63.7%

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

      9. add-sqr-sqrt 63.7%

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

      10. sqrt-unprod 63.7%

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

      11. sqr-neg 63.7%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 87.2%

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

      14. sub-neg 87.2%

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

      15. distribute-neg-in 87.2%

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

      16. add-sqr-sqrt 87.0%

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

      17. sqrt-unprod 87.2%

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

      18. sqr-neg 87.2%

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

      19. sqrt-unprod 0.0%

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

      20. add-sqr-sqrt 74.8%

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

      21. add-sqr-sqrt 74.8%

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

      22. sqrt-unprod 74.8%

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

      23. sqr-neg 74.8%

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

      24. sqrt-unprod 0.0%

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

      25. add-sqr-sqrt 87.2%

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

   9. Applied egg-rr 87.2%

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

       1. *-commutative 87.2%

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

       2. associate-/l* 87.2%

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

       3. +-commutative 87.2%

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

       4. unsub-neg 87.2%

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

   11. Simplified 87.2%

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

   if -2.89999999999999992e-89 < t < 6.79999999999999977e40

   1. Initial program 98.7%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around inf 89.0%

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

Alternative 3: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - y \cdot \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-89}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+40}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- y (* y (/ z t))))))
   (if (<= t -1.02e+124)
     t_1
     (if (<= t -2.8e-89)
       (+ x (* t (/ y (- t a))))
       (if (<= t 4.8e+40) (+ x (/ y (/ (- a t) z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - (y * (z / t)));
	double tmp;
	if (t <= -1.02e+124) {
		tmp = t_1;
	} else if (t <= -2.8e-89) {
		tmp = x + (t * (y / (t - a)));
	} else if (t <= 4.8e+40) {
		tmp = x + (y / ((a - t) / z));
	} 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 - (y * (z / t)))
    if (t <= (-1.02d+124)) then
        tmp = t_1
    else if (t <= (-2.8d-89)) then
        tmp = x + (t * (y / (t - a)))
    else if (t <= 4.8d+40) then
        tmp = x + (y / ((a - t) / z))
    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 - (y * (z / t)));
	double tmp;
	if (t <= -1.02e+124) {
		tmp = t_1;
	} else if (t <= -2.8e-89) {
		tmp = x + (t * (y / (t - a)));
	} else if (t <= 4.8e+40) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y - (y * (z / t)))
	tmp = 0
	if t <= -1.02e+124:
		tmp = t_1
	elif t <= -2.8e-89:
		tmp = x + (t * (y / (t - a)))
	elif t <= 4.8e+40:
		tmp = x + (y / ((a - t) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y - Float64(y * Float64(z / t))))
	tmp = 0.0
	if (t <= -1.02e+124)
		tmp = t_1;
	elseif (t <= -2.8e-89)
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	elseif (t <= 4.8e+40)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y - (y * (z / t)));
	tmp = 0.0;
	if (t <= -1.02e+124)
		tmp = t_1;
	elseif (t <= -2.8e-89)
		tmp = x + (t * (y / (t - a)));
	elseif (t <= 4.8e+40)
		tmp = x + (y / ((a - t) / z));
	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[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.02e+124], t$95$1, If[LessEqual[t, -2.8e-89], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+40], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.01999999999999994e124 or 4.8e40 < t

   1. Initial program 66.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. associate-/l* 92.1%

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

      3. distribute-lft-neg-in 92.1%

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

      4. div-sub 92.1%

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

      5. sub-neg 92.1%

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

      6. *-inverses 92.1%

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

      7. metadata-eval 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in z around 0 80.9%

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

      1. mul-1-neg 80.9%

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

      2. associate-*r/ 92.1%

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

      3. unsub-neg 92.1%

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

   10. Simplified 92.1%

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

   if -1.01999999999999994e124 < t < -2.7999999999999999e-89

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      2. associate-/l* 96.6%

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

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in z around 0 87.2%

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

      1. mul-1-neg 87.2%

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

      2. associate-/l* 87.2%

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

      3. distribute-lft-neg-out 87.2%

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

      4. *-commutative 87.2%

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

   7. Simplified 87.2%

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

      1. associate-*l/ 87.2%

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

      2. frac-2neg 87.2%

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

      3. add-sqr-sqrt 87.0%

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

      4. sqrt-unprod 87.2%

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

      5. sqr-neg 87.2%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 63.7%

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

      8. distribute-rgt-neg-out 63.7%

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

      9. add-sqr-sqrt 63.7%

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

      10. sqrt-unprod 63.7%

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

      11. sqr-neg 63.7%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 87.2%

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

      14. sub-neg 87.2%

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

      15. distribute-neg-in 87.2%

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

      16. add-sqr-sqrt 87.0%

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

      17. sqrt-unprod 87.2%

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

      18. sqr-neg 87.2%

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

      19. sqrt-unprod 0.0%

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

      20. add-sqr-sqrt 74.8%

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

      21. add-sqr-sqrt 74.8%

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

      22. sqrt-unprod 74.8%

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

      23. sqr-neg 74.8%

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

      24. sqrt-unprod 0.0%

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

      25. add-sqr-sqrt 87.2%

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

   9. Applied egg-rr 87.2%

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

       1. *-commutative 87.2%

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

       2. associate-/l* 87.2%

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

       3. +-commutative 87.2%

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

       4. unsub-neg 87.2%

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

   11. Simplified 87.2%

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

   if -2.7999999999999999e-89 < t < 4.8e40

   1. Initial program 98.7%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around inf 89.0%

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

      1. associate-/l* 87.4%

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

   7. Simplified 87.4%

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

      1. clear-num 87.3%

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

      2. un-div-inv 88.8%

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

   9. Applied egg-rr 88.8%

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

Alternative 4: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - y \cdot \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-89}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+40}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- y (* y (/ z t))))))
   (if (<= t -5.2e+122)
     t_1
     (if (<= t -2.95e-89)
       (+ x (* t (/ y (- t a))))
       (if (<= t 3.3e+40) (+ x (* y (/ z (- a t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - (y * (z / t)));
	double tmp;
	if (t <= -5.2e+122) {
		tmp = t_1;
	} else if (t <= -2.95e-89) {
		tmp = x + (t * (y / (t - a)));
	} else if (t <= 3.3e+40) {
		tmp = x + (y * (z / (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 - (y * (z / t)))
    if (t <= (-5.2d+122)) then
        tmp = t_1
    else if (t <= (-2.95d-89)) then
        tmp = x + (t * (y / (t - a)))
    else if (t <= 3.3d+40) then
        tmp = x + (y * (z / (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 - (y * (z / t)));
	double tmp;
	if (t <= -5.2e+122) {
		tmp = t_1;
	} else if (t <= -2.95e-89) {
		tmp = x + (t * (y / (t - a)));
	} else if (t <= 3.3e+40) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y - (y * (z / t)))
	tmp = 0
	if t <= -5.2e+122:
		tmp = t_1
	elif t <= -2.95e-89:
		tmp = x + (t * (y / (t - a)))
	elif t <= 3.3e+40:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y - Float64(y * Float64(z / t))))
	tmp = 0.0
	if (t <= -5.2e+122)
		tmp = t_1;
	elseif (t <= -2.95e-89)
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	elseif (t <= 3.3e+40)
		tmp = Float64(x + Float64(y * Float64(z / 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 - (y * (z / t)));
	tmp = 0.0;
	if (t <= -5.2e+122)
		tmp = t_1;
	elseif (t <= -2.95e-89)
		tmp = x + (t * (y / (t - a)));
	elseif (t <= 3.3e+40)
		tmp = x + (y * (z / (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[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+122], t$95$1, If[LessEqual[t, -2.95e-89], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+40], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.20000000000000015e122 or 3.2999999999999998e40 < t

   1. Initial program 66.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. associate-/l* 92.1%

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

      3. distribute-lft-neg-in 92.1%

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

      4. div-sub 92.1%

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

      5. sub-neg 92.1%

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

      6. *-inverses 92.1%

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

      7. metadata-eval 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in z around 0 80.9%

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

      1. mul-1-neg 80.9%

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

      2. associate-*r/ 92.1%

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

      3. unsub-neg 92.1%

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

   10. Simplified 92.1%

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

   if -5.20000000000000015e122 < t < -2.9500000000000001e-89

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      2. associate-/l* 96.6%

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

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in z around 0 87.2%

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

      1. mul-1-neg 87.2%

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

      2. associate-/l* 87.2%

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

      3. distribute-lft-neg-out 87.2%

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

      4. *-commutative 87.2%

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

   7. Simplified 87.2%

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

      1. associate-*l/ 87.2%

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

      2. frac-2neg 87.2%

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

      3. add-sqr-sqrt 87.0%

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

      4. sqrt-unprod 87.2%

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

      5. sqr-neg 87.2%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 63.7%

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

      8. distribute-rgt-neg-out 63.7%

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

      9. add-sqr-sqrt 63.7%

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

      10. sqrt-unprod 63.7%

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

      11. sqr-neg 63.7%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 87.2%

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

      14. sub-neg 87.2%

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

      15. distribute-neg-in 87.2%

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

      16. add-sqr-sqrt 87.0%

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

      17. sqrt-unprod 87.2%

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

      18. sqr-neg 87.2%

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

      19. sqrt-unprod 0.0%

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

      20. add-sqr-sqrt 74.8%

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

      21. add-sqr-sqrt 74.8%

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

      22. sqrt-unprod 74.8%

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

      23. sqr-neg 74.8%

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

      24. sqrt-unprod 0.0%

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

      25. add-sqr-sqrt 87.2%

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

   9. Applied egg-rr 87.2%

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

       1. *-commutative 87.2%

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

       2. associate-/l* 87.2%

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

       3. +-commutative 87.2%

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

       4. unsub-neg 87.2%

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

   11. Simplified 87.2%

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

   if -2.9500000000000001e-89 < t < 3.2999999999999998e40

   1. Initial program 98.7%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around inf 89.0%

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

      1. associate-/l* 87.4%

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

   7. Simplified 87.4%

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

Alternative 5: 85.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+96} \lor \neg \left(z \leq 7.8 \cdot 10^{+26}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e+96) (not (<= z 7.8e+26)))
   (+ x (* y (/ z (- a t))))
   (+ x (* t (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e+96) || !(z <= 7.8e+26)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (t * (y / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.5d+96)) .or. (.not. (z <= 7.8d+26))) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = x + (t * (y / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e+96) || !(z <= 7.8e+26)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (t * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.5e+96) or not (z <= 7.8e+26):
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + (t * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.5e+96) || !(z <= 7.8e+26))
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.5e+96) || ~((z <= 7.8e+26)))
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x + (t * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.5e+96], N[Not[LessEqual[z, 7.8e+26]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4999999999999999e96 or 7.8e26 < z

   1. Initial program 86.1%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around inf 82.2%

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

      1. associate-/l* 84.4%

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

   7. Simplified 84.4%

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

   if -3.4999999999999999e96 < z < 7.8e26

   1. Initial program 87.3%

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

      1. *-commutative 87.3%

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

      2. associate-/l* 97.5%

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

   4. Applied egg-rr 97.5%

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

   5. Taylor expanded in z around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. associate-/l* 88.1%

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

      3. distribute-lft-neg-out 88.1%

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

      4. *-commutative 88.1%

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

   7. Simplified 88.1%

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

      1. associate-*l/ 78.1%

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

      2. frac-2neg 78.1%

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

      3. add-sqr-sqrt 43.6%

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

      4. sqrt-unprod 56.7%

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

      5. sqr-neg 56.7%

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

      6. sqrt-unprod 22.8%

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

      7. add-sqr-sqrt 54.2%

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

      8. distribute-rgt-neg-out 54.2%

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

      9. add-sqr-sqrt 31.4%

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

      10. sqrt-unprod 54.8%

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

      11. sqr-neg 54.8%

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

      12. sqrt-unprod 34.3%

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

      13. add-sqr-sqrt 78.1%

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

      14. sub-neg 78.1%

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

      15. distribute-neg-in 78.1%

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

      16. add-sqr-sqrt 43.6%

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

      17. sqrt-unprod 64.9%

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

      18. sqr-neg 64.9%

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

      19. sqrt-unprod 24.4%

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

      20. add-sqr-sqrt 59.6%

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

      21. add-sqr-sqrt 35.2%

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

      22. sqrt-unprod 66.2%

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

      23. sqr-neg 66.2%

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

      24. sqrt-unprod 34.3%

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

      25. add-sqr-sqrt 78.1%

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

   9. Applied egg-rr 78.1%

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

       1. *-commutative 78.1%

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

       2. associate-/l* 88.1%

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

       3. +-commutative 88.1%

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

       4. unsub-neg 88.1%

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

   11. Simplified 88.1%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+96} \lor \neg \left(z \leq 7.8 \cdot 10^{+26}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{-89} \lor \neg \left(t \leq 4.8 \cdot 10^{-11}\right):\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.95e-89) (not (<= t 4.8e-11)))
   (+ x (* t (/ y (- t a))))
   (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.95e-89) || !(t <= 4.8e-11)) {
		tmp = x + (t * (y / (t - a)));
	} 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 <= (-2.95d-89)) .or. (.not. (t <= 4.8d-11))) then
        tmp = x + (t * (y / (t - a)))
    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 <= -2.95e-89) || !(t <= 4.8e-11)) {
		tmp = x + (t * (y / (t - a)));
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.95e-89) or not (t <= 4.8e-11):
		tmp = x + (t * (y / (t - a)))
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.95e-89) || !(t <= 4.8e-11))
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	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 <= -2.95e-89) || ~((t <= 4.8e-11)))
		tmp = x + (t * (y / (t - a)));
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.95e-89], N[Not[LessEqual[t, 4.8e-11]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9500000000000001e-89 or 4.8000000000000002e-11 < t

   1. Initial program 79.5%

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

      1. *-commutative 79.5%

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

      2. associate-/l* 96.3%

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

   4. Applied egg-rr 96.3%

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

   5. Taylor expanded in z around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. associate-/l* 85.3%

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

      3. distribute-lft-neg-out 85.3%

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

      4. *-commutative 85.3%

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

   7. Simplified 85.3%

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

      1. associate-*l/ 71.2%

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

      2. frac-2neg 71.2%

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

      3. add-sqr-sqrt 42.1%

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

      4. sqrt-unprod 47.5%

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

      5. sqr-neg 47.5%

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

      6. sqrt-unprod 18.6%

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

      7. add-sqr-sqrt 47.5%

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

      8. distribute-rgt-neg-out 47.5%

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

      9. add-sqr-sqrt 28.8%

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

      10. sqrt-unprod 42.1%

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

      11. sqr-neg 42.1%

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

      12. sqrt-unprod 28.9%

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

      13. add-sqr-sqrt 71.2%

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

      14. sub-neg 71.2%

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

      15. distribute-neg-in 71.2%

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

      16. add-sqr-sqrt 42.1%

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

      17. sqrt-unprod 58.5%

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

      18. sqr-neg 58.5%

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

      19. sqrt-unprod 19.8%

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

      20. add-sqr-sqrt 52.7%

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

      21. add-sqr-sqrt 32.9%

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

      22. sqrt-unprod 56.7%

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

      23. sqr-neg 56.7%

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

      24. sqrt-unprod 28.9%

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

      25. add-sqr-sqrt 71.2%

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

   9. Applied egg-rr 71.2%

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

       1. *-commutative 71.2%

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

       2. associate-/l* 85.3%

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

       3. +-commutative 85.3%

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

       4. unsub-neg 85.3%

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

   11. Simplified 85.3%

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

   if -2.9500000000000001e-89 < t < 4.8000000000000002e-11

   1. Initial program 98.6%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around 0 84.7%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{-89} \lor \neg \left(t \leq 4.8 \cdot 10^{-11}\right):\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+96}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+48}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e+96)
   (+ x (/ y (/ (- a t) z)))
   (if (<= z 2.3e+48) (+ x (* y (/ t (- t a)))) (+ x (* y (/ z (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+96) {
		tmp = x + (y / ((a - t) / z));
	} else if (z <= 2.3e+48) {
		tmp = x + (y * (t / (t - a)));
	} 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 (z <= (-6.8d+96)) then
        tmp = x + (y / ((a - t) / z))
    else if (z <= 2.3d+48) then
        tmp = x + (y * (t / (t - a)))
    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 (z <= -6.8e+96) {
		tmp = x + (y / ((a - t) / z));
	} else if (z <= 2.3e+48) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e+96:
		tmp = x + (y / ((a - t) / z))
	elif z <= 2.3e+48:
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e+96)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	elseif (z <= 2.3e+48)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	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 (z <= -6.8e+96)
		tmp = x + (y / ((a - t) / z));
	elseif (z <= 2.3e+48)
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e+96], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+48], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8000000000000002e96

   1. Initial program 84.9%

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

      1. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in z around inf 82.7%

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

      1. associate-/l* 82.5%

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

   7. Simplified 82.5%

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

      1. clear-num 82.4%

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

      2. un-div-inv 84.5%

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

   9. Applied egg-rr 84.5%

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

   if -6.8000000000000002e96 < z < 2.3e48

   1. Initial program 87.6%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 78.0%

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

      1. associate-*r/ 78.0%

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

      2. mul-1-neg 78.0%

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

      3. distribute-lft-neg-out 78.0%

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

      4. *-commutative 78.0%

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

      5. associate-/l* 90.1%

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

      6. distribute-neg-frac 90.1%

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

      7. distribute-neg-frac2 90.1%

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

      8. neg-sub0 90.1%

         \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(a - t\right)}} \]

      9. associate--r- 90.1%

         \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - a\right) + t}} \]

      10. neg-sub0 90.1%

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

   7. Simplified 90.1%

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

   if 2.3e48 < z

   1. Initial program 86.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 82.8%

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

      1. associate-/l* 87.5%

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

   7. Simplified 87.5%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+96}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+48}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+29} \lor \neg \left(t \leq 5 \cdot 10^{-11}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.1e+29) (not (<= t 5e-11))) (+ x y) (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e+29) || !(t <= 5e-11)) {
		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 <= (-2.1d+29)) .or. (.not. (t <= 5d-11))) 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 <= -2.1e+29) || !(t <= 5e-11)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.1e+29) or not (t <= 5e-11):
		tmp = x + y
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.1e+29) || !(t <= 5e-11))
		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 <= -2.1e+29) || ~((t <= 5e-11)))
		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, -2.1e+29], N[Not[LessEqual[t, 5e-11]], $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 < -2.1000000000000002e29 or 5.00000000000000018e-11 < t

   1. Initial program 74.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 78.1%

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

   if -2.1000000000000002e29 < t < 5.00000000000000018e-11

   1. Initial program 98.9%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around 0 81.4%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+29} \lor \neg \left(t \leq 5 \cdot 10^{-11}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+25} \lor \neg \left(t \leq 4.8 \cdot 10^{-11}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.8e+25) (not (<= t 4.8e-11))) (+ 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+25) || !(t <= 4.8e-11)) {
		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+25)) .or. (.not. (t <= 4.8d-11))) 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+25) || !(t <= 4.8e-11)) {
		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+25) or not (t <= 4.8e-11):
		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+25) || !(t <= 4.8e-11))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.8e+25) || ~((t <= 4.8e-11)))
		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+25], N[Not[LessEqual[t, 4.8e-11]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.8000000000000003e25 or 4.8000000000000002e-11 < t

   1. Initial program 74.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 78.1%

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

   if -8.8000000000000003e25 < t < 4.8000000000000002e-11

   1. Initial program 98.9%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around 0 81.4%

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

      1. associate-/l* 79.4%

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

   7. Simplified 79.4%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+25} \lor \neg \left(t \leq 4.8 \cdot 10^{-11}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+27} \lor \neg \left(t \leq 3.2 \cdot 10^{-142}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.5e+27) (not (<= t 3.2e-142))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.5e+27) || !(t <= 3.2e-142)) {
		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 <= (-3.5d+27)) .or. (.not. (t <= 3.2d-142))) 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 <= -3.5e+27) || !(t <= 3.2e-142)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.5e+27) or not (t <= 3.2e-142):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.5e+27) || !(t <= 3.2e-142))
		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 <= -3.5e+27) || ~((t <= 3.2e-142)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.5e+27], N[Not[LessEqual[t, 3.2e-142]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -3.5000000000000002e27 or 3.1999999999999998e-142 < t

   1. Initial program 78.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 74.4%

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

   if -3.5000000000000002e27 < t < 3.1999999999999998e-142

   1. Initial program 98.7%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around inf 87.8%

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

      1. associate-/l* 85.3%

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

   7. Simplified 85.3%

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

   8. Taylor expanded in x around inf 58.7%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+27} \lor \neg \left(t \leq 3.2 \cdot 10^{-142}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.9% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.0%

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

   1. associate-/l* 98.3%

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

3. Simplified 98.3%

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

5. Taylor expanded in z around inf 71.2%

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

   1. associate-/l* 71.6%

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

7. Simplified 71.6%

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

8. Taylor expanded in x around inf 51.5%

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

Developer target: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024103 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (+ x (/ y (/ (- a t) (- z t))))

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