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

Percentage Accurate: 85.4% → 98.0%

Time: 9.4s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (t * ((y - z) / (a - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.0%

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

   1. associate-/l* 97.3%

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

3. Simplified 97.3%

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

5. Taylor expanded in y around 0 86.5%

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

   1. associate-*r/ 86.5%

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

   2. mul-1-neg 86.5%

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

   3. distribute-rgt-neg-out 86.5%

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

   4. associate-*l/ 88.7%

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

   5. associate-*l/ 95.3%

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

   6. distribute-lft-in 97.3%

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

   7. +-commutative 97.3%

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

   8. sub-neg 97.3%

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

   9. associate-*l/ 87.0%

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

   10. associate-*r/ 98.8%

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

7. Simplified 98.8%

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

Alternative 2: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6800000000000:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-89}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+50}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6800000000000.0)
   (+ x t)
   (if (<= z -1.05e-89)
     (- x (* t (/ y z)))
     (if (<= z 2.2e+50) (+ x (* t (/ y a))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6800000000000.0) {
		tmp = x + t;
	} else if (z <= -1.05e-89) {
		tmp = x - (t * (y / z));
	} else if (z <= 2.2e+50) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + 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 <= (-6800000000000.0d0)) then
        tmp = x + t
    else if (z <= (-1.05d-89)) then
        tmp = x - (t * (y / z))
    else if (z <= 2.2d+50) then
        tmp = x + (t * (y / a))
    else
        tmp = x + 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 <= -6800000000000.0) {
		tmp = x + t;
	} else if (z <= -1.05e-89) {
		tmp = x - (t * (y / z));
	} else if (z <= 2.2e+50) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6800000000000.0:
		tmp = x + t
	elif z <= -1.05e-89:
		tmp = x - (t * (y / z))
	elif z <= 2.2e+50:
		tmp = x + (t * (y / a))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6800000000000.0)
		tmp = Float64(x + t);
	elseif (z <= -1.05e-89)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 2.2e+50)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6800000000000.0)
		tmp = x + t;
	elseif (z <= -1.05e-89)
		tmp = x - (t * (y / z));
	elseif (z <= 2.2e+50)
		tmp = x + (t * (y / a));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6800000000000.0], N[(x + t), $MachinePrecision], If[LessEqual[z, -1.05e-89], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+50], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8e12 or 2.20000000000000017e50 < z

   1. Initial program 77.0%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in z around inf 77.8%

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

   if -6.8e12 < z < -1.05e-89

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 90.7%

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

      1. mul-1-neg 90.7%

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

      2. unsub-neg 90.7%

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

      3. associate-/l* 90.6%

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

   7. Simplified 90.6%

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

   8. Taylor expanded in y around inf 95.1%

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

      1. associate-/l* 95.1%

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

   10. Simplified 95.1%

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

   if -1.05e-89 < z < 2.20000000000000017e50

   1. Initial program 93.9%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in z around 0 81.2%

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

      1. associate-/l* 86.0%

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

   7. Simplified 86.0%

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

Alternative 3: 86.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -15600000000000 \lor \neg \left(z \leq 1.9 \cdot 10^{+131}\right):\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -15600000000000.0) (not (<= z 1.9e+131)))
   (+ x (* t (/ z (- z a))))
   (+ x (* y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -15600000000000.0) || !(z <= 1.9e+131)) {
		tmp = x + (t * (z / (z - a)));
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-15600000000000.0d0)) .or. (.not. (z <= 1.9d+131))) then
        tmp = x + (t * (z / (z - a)))
    else
        tmp = x + (y * (t / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -15600000000000.0) || !(z <= 1.9e+131)) {
		tmp = x + (t * (z / (z - a)));
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -15600000000000.0) or not (z <= 1.9e+131):
		tmp = x + (t * (z / (z - a)))
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -15600000000000.0) || !(z <= 1.9e+131))
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -15600000000000.0) || ~((z <= 1.9e+131)))
		tmp = x + (t * (z / (z - a)));
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -15600000000000.0], N[Not[LessEqual[z, 1.9e+131]], $MachinePrecision]], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.56e13 or 1.9000000000000002e131 < z

   1. Initial program 73.0%

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

      1. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in y around 0 68.3%

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

      1. associate-*r/ 68.3%

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

      2. mul-1-neg 68.3%

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

      3. distribute-rgt-neg-out 68.3%

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

      4. associate-*l/ 86.9%

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

      5. *-commutative 86.9%

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

      6. distribute-lft-neg-out 86.9%

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

      7. distribute-rgt-neg-in 86.9%

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

      8. distribute-frac-neg2 86.9%

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

      9. neg-sub0 86.9%

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

      10. sub-neg 86.9%

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

      11. +-commutative 86.9%

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

      12. associate--r+ 86.9%

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

      13. neg-sub0 86.9%

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

      14. remove-double-neg 86.9%

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

   7. Simplified 86.9%

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

      1. clear-num 86.8%

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

      2. un-div-inv 86.9%

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

   9. Applied egg-rr 86.9%

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

       1. associate-/r/ 91.2%

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

   11. Simplified 91.2%

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

   if -1.56e13 < z < 1.9000000000000002e131

   1. Initial program 94.8%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around inf 92.6%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15600000000000 \lor \neg \left(z \leq 1.9 \cdot 10^{+131}\right):\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+139} \lor \neg \left(z \leq 4.8 \cdot 10^{+138}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.2e+139) (not (<= z 4.8e+138)))
   (+ x t)
   (+ x (* y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+139) || !(z <= 4.8e+138)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.2d+139)) .or. (.not. (z <= 4.8d+138))) then
        tmp = x + t
    else
        tmp = x + (y * (t / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+139) || !(z <= 4.8e+138)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.2e+139) or not (z <= 4.8e+138):
		tmp = x + t
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.2e+139) || !(z <= 4.8e+138))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.2e+139) || ~((z <= 4.8e+138)))
		tmp = x + t;
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.2e+139], N[Not[LessEqual[z, 4.8e+138]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1999999999999997e139 or 4.8000000000000002e138 < z

   1. Initial program 65.0%

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

      1. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in z around inf 89.7%

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

   if -4.1999999999999997e139 < z < 4.8000000000000002e138

   1. Initial program 94.1%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in y around inf 89.6%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+139} \lor \neg \left(z \leq 4.8 \cdot 10^{+138}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+137} \lor \neg \left(z \leq 4.45 \cdot 10^{+142}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.5e+137) (not (<= z 4.45e+142)))
   (+ x t)
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e+137) || !(z <= 4.45e+142)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.5d+137)) .or. (.not. (z <= 4.45d+142))) then
        tmp = x + t
    else
        tmp = x + (t * (y / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e+137) || !(z <= 4.45e+142)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.5e+137) or not (z <= 4.45e+142):
		tmp = x + t
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.5e+137) || !(z <= 4.45e+142))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.5e+137) || ~((z <= 4.45e+142)))
		tmp = x + t;
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.5e+137], N[Not[LessEqual[z, 4.45e+142]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5000000000000002e137 or 4.45000000000000008e142 < z

   1. Initial program 65.0%

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

      1. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in z around inf 89.7%

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

   if -6.5000000000000002e137 < z < 4.45000000000000008e142

   1. Initial program 94.1%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in y around inf 85.8%

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

      1. associate-/l* 89.1%

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

   7. Simplified 89.1%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+137} \lor \neg \left(z \leq 4.45 \cdot 10^{+142}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7800000000000:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+50}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7800000000000.0)
   (+ x (* t (/ z (- z a))))
   (if (<= z 1.5e+50) (+ x (* y (/ t (- a z)))) (+ x (* t (/ (- z y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7800000000000.0) {
		tmp = x + (t * (z / (z - a)));
	} else if (z <= 1.5e+50) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (t * ((z - y) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7800000000000.0d0)) then
        tmp = x + (t * (z / (z - a)))
    else if (z <= 1.5d+50) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + (t * ((z - y) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7800000000000.0) {
		tmp = x + (t * (z / (z - a)));
	} else if (z <= 1.5e+50) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (t * ((z - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7800000000000.0:
		tmp = x + (t * (z / (z - a)))
	elif z <= 1.5e+50:
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + (t * ((z - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7800000000000.0)
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	elseif (z <= 1.5e+50)
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(t * Float64(Float64(z - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7800000000000.0)
		tmp = x + (t * (z / (z - a)));
	elseif (z <= 1.5e+50)
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + (t * ((z - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7800000000000.0], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+50], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.8e12

   1. Initial program 75.3%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in y around 0 69.9%

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

      1. associate-*r/ 69.9%

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

      2. mul-1-neg 69.9%

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

      3. distribute-rgt-neg-out 69.9%

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

      4. associate-*l/ 86.4%

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

      5. *-commutative 86.4%

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

      6. distribute-lft-neg-out 86.4%

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

      7. distribute-rgt-neg-in 86.4%

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

      8. distribute-frac-neg2 86.4%

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

      9. neg-sub0 86.4%

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

      10. sub-neg 86.4%

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

      11. +-commutative 86.4%

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

      12. associate--r+ 86.4%

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

      13. neg-sub0 86.4%

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

      14. remove-double-neg 86.4%

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

   7. Simplified 86.4%

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

      1. clear-num 86.3%

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

      2. un-div-inv 86.4%

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

   9. Applied egg-rr 86.4%

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

       1. associate-/r/ 89.9%

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

   11. Simplified 89.9%

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

   if -7.8e12 < z < 1.4999999999999999e50

   1. Initial program 94.7%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in y around inf 95.0%

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

   if 1.4999999999999999e50 < z

   1. Initial program 79.0%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in a around 0 73.6%

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

      1. mul-1-neg 73.6%

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

      2. unsub-neg 73.6%

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

      3. associate-/l* 92.9%

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

   7. Simplified 92.9%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7800000000000:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+50}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1800000000000:\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+141}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1800000000000.0)
   (+ x (* z (/ t (- z a))))
   (if (<= z 2.1e+141) (+ x (* y (/ t (- a z)))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1800000000000.0) {
		tmp = x + (z * (t / (z - a)));
	} else if (z <= 2.1e+141) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + 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 <= (-1800000000000.0d0)) then
        tmp = x + (z * (t / (z - a)))
    else if (z <= 2.1d+141) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + 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 <= -1800000000000.0) {
		tmp = x + (z * (t / (z - a)));
	} else if (z <= 2.1e+141) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1800000000000.0:
		tmp = x + (z * (t / (z - a)))
	elif z <= 2.1e+141:
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1800000000000.0)
		tmp = Float64(x + Float64(z * Float64(t / Float64(z - a))));
	elseif (z <= 2.1e+141)
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1800000000000.0)
		tmp = x + (z * (t / (z - a)));
	elseif (z <= 2.1e+141)
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1800000000000.0], N[(x + N[(z * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+141], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8e12

   1. Initial program 75.3%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in y around 0 69.9%

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

      1. associate-*r/ 69.9%

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

      2. mul-1-neg 69.9%

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

      3. distribute-rgt-neg-out 69.9%

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

      4. associate-*l/ 86.4%

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

      5. *-commutative 86.4%

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

      6. distribute-lft-neg-out 86.4%

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

      7. distribute-rgt-neg-in 86.4%

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

      8. distribute-frac-neg2 86.4%

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

      9. neg-sub0 86.4%

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

      10. sub-neg 86.4%

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

      11. +-commutative 86.4%

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

      12. associate--r+ 86.4%

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

      13. neg-sub0 86.4%

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

      14. remove-double-neg 86.4%

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

   7. Simplified 86.4%

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

   if -1.8e12 < z < 2.0999999999999998e141

   1. Initial program 94.8%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around inf 92.6%

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

   if 2.0999999999999998e141 < z

   1. Initial program 68.2%

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

      1. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around inf 91.4%

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

Alternative 8: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-50} \lor \neg \left(z \leq 1.55 \cdot 10^{+50}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e-50) (not (<= z 1.55e+50))) (+ x t) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e-50) || !(z <= 1.55e+50)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.2d-50)) .or. (.not. (z <= 1.55d+50))) then
        tmp = x + t
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e-50) || !(z <= 1.55e+50)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e-50) or not (z <= 1.55e+50):
		tmp = x + t
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e-50) || !(z <= 1.55e+50))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.2e-50) || ~((z <= 1.55e+50)))
		tmp = x + t;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e-50], N[Not[LessEqual[z, 1.55e+50]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000001e-50 or 1.55000000000000001e50 < z

   1. Initial program 79.6%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around inf 75.6%

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

   if -1.20000000000000001e-50 < z < 1.55000000000000001e50

   1. Initial program 94.2%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around 0 80.6%

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

      1. associate-/l* 85.2%

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

   7. Simplified 85.2%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-50} \lor \neg \left(z \leq 1.55 \cdot 10^{+50}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+39} \lor \neg \left(z \leq 1.1 \cdot 10^{+50}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.8e+39) (not (<= z 1.1e+50))) (+ x t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e+39) || !(z <= 1.1e+50)) {
		tmp = x + t;
	} 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 ((z <= (-4.8d+39)) .or. (.not. (z <= 1.1d+50))) then
        tmp = x + t
    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 ((z <= -4.8e+39) || !(z <= 1.1e+50)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.8e+39) or not (z <= 1.1e+50):
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.8e+39) || !(z <= 1.1e+50))
		tmp = Float64(x + t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.8e+39) || ~((z <= 1.1e+50)))
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.8e+39], N[Not[LessEqual[z, 1.1e+50]], $MachinePrecision]], N[(x + t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.8000000000000002e39 or 1.10000000000000008e50 < z

   1. Initial program 74.7%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around inf 80.0%

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

   if -4.8000000000000002e39 < z < 1.10000000000000008e50

   1. Initial program 95.1%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in x around inf 57.4%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+39} \lor \neg \left(z \leq 1.1 \cdot 10^{+50}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.3% 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%

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

   1. associate-/l* 97.3%

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

3. Simplified 97.3%

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

5. Taylor expanded in x around inf 54.3%

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

Developer Target 1: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - 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 - z) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - 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 - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024181 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -10682974490174067/10000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 312887599100691/80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t)))))

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