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

Percentage Accurate: 85.0% → 95.8%

Time: 8.4s

Alternatives: 13

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: 85.0% 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: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.3%

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

   1. associate-/l* 97.2%

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

3. Simplified 97.2%

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

   1. clear-num 97.1%

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

   2. un-div-inv 97.7%

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

6. Applied egg-rr 97.7%

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

Alternative 2: 62.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-230} \lor \neg \left(a \leq 2.05 \cdot 10^{-246}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+117)
   x
   (if (or (<= a -1.1e-230) (not (<= a 2.05e-246)))
     (+ x t)
     (* t (- 1.0 (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+117) {
		tmp = x;
	} else if ((a <= -1.1e-230) || !(a <= 2.05e-246)) {
		tmp = x + t;
	} else {
		tmp = t * (1.0 - (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 (a <= (-9.5d+117)) then
        tmp = x
    else if ((a <= (-1.1d-230)) .or. (.not. (a <= 2.05d-246))) then
        tmp = x + t
    else
        tmp = t * (1.0d0 - (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 (a <= -9.5e+117) {
		tmp = x;
	} else if ((a <= -1.1e-230) || !(a <= 2.05e-246)) {
		tmp = x + t;
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+117:
		tmp = x
	elif (a <= -1.1e-230) or not (a <= 2.05e-246):
		tmp = x + t
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+117)
		tmp = x;
	elseif ((a <= -1.1e-230) || !(a <= 2.05e-246))
		tmp = Float64(x + t);
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e+117)
		tmp = x;
	elseif ((a <= -1.1e-230) || ~((a <= 2.05e-246)))
		tmp = x + t;
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+117], x, If[Or[LessEqual[a, -1.1e-230], N[Not[LessEqual[a, 2.05e-246]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.50000000000000041e117

   1. Initial program 71.4%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf 73.2%

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

   if -9.50000000000000041e117 < a < -1.0999999999999999e-230 or 2.04999999999999993e-246 < a

   1. Initial program 86.3%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around inf 69.9%

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

   if -1.0999999999999999e-230 < a < 2.04999999999999993e-246

   1. Initial program 84.5%

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

      1. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in a around 0 89.8%

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

      1. associate-*r/ 89.8%

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

      2. neg-mul-1 89.8%

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

   7. Simplified 89.8%

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

   8. Taylor expanded in y around 0 94.6%

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

      1. associate-+r+ 94.6%

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

      2. mul-1-neg 94.6%

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

      3. unsub-neg 94.6%

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

      4. associate-/l* 92.5%

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

   10. Simplified 92.5%

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

   11. Taylor expanded in t around inf 69.0%

       \[\leadsto \color{blue}{t \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-230} \lor \neg \left(a \leq 2.05 \cdot 10^{-246}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+22}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-37}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+129}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.5e+22)
   (+ x t)
   (if (<= z 9.2e-37)
     (+ x (* y (/ t a)))
     (if (<= z 9e+129) (- x (* y (/ t z))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+22) {
		tmp = x + t;
	} else if (z <= 9.2e-37) {
		tmp = x + (y * (t / a));
	} else if (z <= 9e+129) {
		tmp = x - (y * (t / 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 <= (-7.5d+22)) then
        tmp = x + t
    else if (z <= 9.2d-37) then
        tmp = x + (y * (t / a))
    else if (z <= 9d+129) then
        tmp = x - (y * (t / 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 <= -7.5e+22) {
		tmp = x + t;
	} else if (z <= 9.2e-37) {
		tmp = x + (y * (t / a));
	} else if (z <= 9e+129) {
		tmp = x - (y * (t / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.5e+22:
		tmp = x + t
	elif z <= 9.2e-37:
		tmp = x + (y * (t / a))
	elif z <= 9e+129:
		tmp = x - (y * (t / z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.5e+22)
		tmp = Float64(x + t);
	elseif (z <= 9.2e-37)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 9e+129)
		tmp = Float64(x - Float64(y * Float64(t / 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 <= -7.5e+22)
		tmp = x + t;
	elseif (z <= 9.2e-37)
		tmp = x + (y * (t / a));
	elseif (z <= 9e+129)
		tmp = x - (y * (t / z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.5e+22], N[(x + t), $MachinePrecision], If[LessEqual[z, 9.2e-37], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+129], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5000000000000002e22 or 9.0000000000000003e129 < z

   1. Initial program 71.0%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in z around inf 84.5%

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

   if -7.5000000000000002e22 < z < 9.1999999999999999e-37

   1. Initial program 92.3%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around 0 76.3%

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

      1. *-commutative 76.3%

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

      2. associate-/l* 83.0%

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

   7. Simplified 83.0%

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

   if 9.1999999999999999e-37 < z < 9.0000000000000003e129

   1. Initial program 89.3%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in a around 0 78.6%

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

      1. associate-*r/ 78.6%

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

      2. neg-mul-1 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in y around inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. associate-*l/ 71.4%

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

      3. *-commutative 71.4%

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

      4. distribute-rgt-neg-in 71.4%

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

      5. distribute-frac-neg2 71.4%

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

   10. Simplified 71.4%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+22}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-37}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+129}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+22}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-37}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+127}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.4e+22)
   (+ x t)
   (if (<= z 5e-37)
     (+ x (* y (/ t a)))
     (if (<= z 5.8e+127) (- x (/ y (/ z t))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.4e+22) {
		tmp = x + t;
	} else if (z <= 5e-37) {
		tmp = x + (y * (t / a));
	} else if (z <= 5.8e+127) {
		tmp = x - (y / (z / t));
	} 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 <= (-6.4d+22)) then
        tmp = x + t
    else if (z <= 5d-37) then
        tmp = x + (y * (t / a))
    else if (z <= 5.8d+127) then
        tmp = x - (y / (z / t))
    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 <= -6.4e+22) {
		tmp = x + t;
	} else if (z <= 5e-37) {
		tmp = x + (y * (t / a));
	} else if (z <= 5.8e+127) {
		tmp = x - (y / (z / t));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.4e+22:
		tmp = x + t
	elif z <= 5e-37:
		tmp = x + (y * (t / a))
	elif z <= 5.8e+127:
		tmp = x - (y / (z / t))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.4e+22)
		tmp = Float64(x + t);
	elseif (z <= 5e-37)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 5.8e+127)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.4e+22)
		tmp = x + t;
	elseif (z <= 5e-37)
		tmp = x + (y * (t / a));
	elseif (z <= 5.8e+127)
		tmp = x - (y / (z / t));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.4e+22], N[(x + t), $MachinePrecision], If[LessEqual[z, 5e-37], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+127], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.4e22 or 5.8000000000000004e127 < z

   1. Initial program 71.0%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in z around inf 84.5%

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

   if -6.4e22 < z < 4.9999999999999997e-37

   1. Initial program 92.3%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around 0 76.3%

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

      1. *-commutative 76.3%

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

      2. associate-/l* 83.0%

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

   7. Simplified 83.0%

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

   if 4.9999999999999997e-37 < z < 5.8000000000000004e127

   1. Initial program 89.3%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in a around 0 78.6%

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

      1. associate-*r/ 78.6%

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

      2. neg-mul-1 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in y around inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. associate-*l/ 71.4%

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

      3. *-commutative 71.4%

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

      4. distribute-rgt-neg-in 71.4%

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

      5. distribute-frac-neg2 71.4%

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

   10. Simplified 71.4%

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

   11. Taylor expanded in x around 0 67.8%

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

       1. mul-1-neg 67.8%

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

       2. associate-*r/ 71.4%

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

       3. sub-neg 71.4%

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

       4. *-commutative 71.4%

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

       5. associate-/r/ 71.4%

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

   13. Simplified 71.4%

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

Alternative 5: 75.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+22}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+38}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+22)
   (+ x t)
   (if (<= z 4.6e+38)
     (+ x (* y (/ t a)))
     (if (<= z 2.4e+88) (* t (- 1.0 (/ y z))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+22) {
		tmp = x + t;
	} else if (z <= 4.6e+38) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.4e+88) {
		tmp = t * (1.0 - (y / 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 <= (-6.5d+22)) then
        tmp = x + t
    else if (z <= 4.6d+38) then
        tmp = x + (y * (t / a))
    else if (z <= 2.4d+88) then
        tmp = t * (1.0d0 - (y / 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 <= -6.5e+22) {
		tmp = x + t;
	} else if (z <= 4.6e+38) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.4e+88) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+22:
		tmp = x + t
	elif z <= 4.6e+38:
		tmp = x + (y * (t / a))
	elif z <= 2.4e+88:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+22)
		tmp = Float64(x + t);
	elseif (z <= 4.6e+38)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 2.4e+88)
		tmp = Float64(t * Float64(1.0 - Float64(y / 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 <= -6.5e+22)
		tmp = x + t;
	elseif (z <= 4.6e+38)
		tmp = x + (y * (t / a));
	elseif (z <= 2.4e+88)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+22], N[(x + t), $MachinePrecision], If[LessEqual[z, 4.6e+38], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+88], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.49999999999999979e22 or 2.3999999999999999e88 < z

   1. Initial program 70.6%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around inf 82.7%

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

   if -6.49999999999999979e22 < z < 4.6000000000000002e38

   1. Initial program 92.2%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in z around 0 74.6%

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

      1. *-commutative 74.6%

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

      2. associate-/l* 81.5%

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

   7. Simplified 81.5%

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

   if 4.6000000000000002e38 < z < 2.3999999999999999e88

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 82.8%

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

      1. associate-*r/ 82.8%

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

      2. neg-mul-1 82.8%

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

   7. Simplified 82.8%

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

   8. Taylor expanded in y around 0 82.8%

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

      1. associate-+r+ 82.8%

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

      2. mul-1-neg 82.8%

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

      3. unsub-neg 82.8%

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

      4. associate-/l* 82.9%

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

   10. Simplified 82.9%

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

   11. Taylor expanded in t around inf 74.2%

       \[\leadsto \color{blue}{t \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 85.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+55} \lor \neg \left(y \leq 1.7 \cdot 10^{+33}\right):\\ \;\;\;\;y \cdot \left(\frac{t}{a - z} + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.1e+55) (not (<= y 1.7e+33)))
   (* y (+ (/ t (- a z)) (/ x y)))
   (+ x (* z (/ t (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.1e+55) || !(y <= 1.7e+33)) {
		tmp = y * ((t / (a - z)) + (x / y));
	} else {
		tmp = x + (z * (t / (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 ((y <= (-4.1d+55)) .or. (.not. (y <= 1.7d+33))) then
        tmp = y * ((t / (a - z)) + (x / y))
    else
        tmp = x + (z * (t / (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 ((y <= -4.1e+55) || !(y <= 1.7e+33)) {
		tmp = y * ((t / (a - z)) + (x / y));
	} else {
		tmp = x + (z * (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.1e+55) or not (y <= 1.7e+33):
		tmp = y * ((t / (a - z)) + (x / y))
	else:
		tmp = x + (z * (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.1e+55) || !(y <= 1.7e+33))
		tmp = Float64(y * Float64(Float64(t / Float64(a - z)) + Float64(x / y)));
	else
		tmp = Float64(x + Float64(z * Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.1e+55) || ~((y <= 1.7e+33)))
		tmp = y * ((t / (a - z)) + (x / y));
	else
		tmp = x + (z * (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.1e+55], N[Not[LessEqual[y, 1.7e+33]], $MachinePrecision]], N[(y * N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.09999999999999981e55 or 1.7e33 < y

   1. Initial program 81.8%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in y around inf 74.9%

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

   6. Taylor expanded in y around inf 86.3%

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

      1. +-commutative 86.3%

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

   8. Simplified 86.3%

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

   if -4.09999999999999981e55 < y < 1.7e33

   1. Initial program 84.5%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in y around 0 78.4%

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

      1. mul-1-neg 78.4%

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

      2. unsub-neg 78.4%

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

      3. *-commutative 78.4%

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

      4. associate-*r/ 91.1%

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

   7. Simplified 91.1%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+55} \lor \neg \left(y \leq 1.7 \cdot 10^{+33}\right):\\ \;\;\;\;y \cdot \left(\frac{t}{a - z} + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.14 \lor \neg \left(z \leq 8.5 \cdot 10^{-37}\right):\\ \;\;\;\;x - t \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -0.14) (not (<= z 8.5e-37)))
   (- x (* t (/ (- y z) z)))
   (- x (/ (- z y) (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.14) || !(z <= 8.5e-37)) {
		tmp = x - (t * ((y - z) / z));
	} else {
		tmp = x - ((z - y) / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-0.14d0)) .or. (.not. (z <= 8.5d-37))) then
        tmp = x - (t * ((y - z) / z))
    else
        tmp = x - ((z - y) / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.14) || !(z <= 8.5e-37)) {
		tmp = x - (t * ((y - z) / z));
	} else {
		tmp = x - ((z - y) / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -0.14) or not (z <= 8.5e-37):
		tmp = x - (t * ((y - z) / z))
	else:
		tmp = x - ((z - y) / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -0.14) || !(z <= 8.5e-37))
		tmp = Float64(x - Float64(t * Float64(Float64(y - z) / z)));
	else
		tmp = Float64(x - Float64(Float64(z - y) / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -0.14) || ~((z <= 8.5e-37)))
		tmp = x - (t * ((y - z) / z));
	else
		tmp = x - ((z - y) / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -0.14], N[Not[LessEqual[z, 8.5e-37]], $MachinePrecision]], N[(x - N[(t * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z - y), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.14000000000000001 or 8.5000000000000007e-37 < z

   1. Initial program 75.2%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in a around 0 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

      3. associate-/l* 87.3%

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

   7. Simplified 87.3%

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

   if -0.14000000000000001 < z < 8.5000000000000007e-37

   1. Initial program 92.7%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

      1. clear-num 96.7%

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

      2. un-div-inv 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in a around inf 87.9%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.14 \lor \neg \left(z \leq 8.5 \cdot 10^{-37}\right):\\ \;\;\;\;x - t \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+22} \lor \neg \left(z \leq 4 \cdot 10^{+112}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.7e+22) (not (<= z 4e+112)))
   (+ x t)
   (+ x (/ (* y t) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e+22) || !(z <= 4e+112)) {
		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 <= (-1.7d+22)) .or. (.not. (z <= 4d+112))) 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 <= -1.7e+22) || !(z <= 4e+112)) {
		tmp = x + t;
	} else {
		tmp = x + ((y * t) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.7e+22) or not (z <= 4e+112):
		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 <= -1.7e+22) || !(z <= 4e+112))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.7e+22) || ~((z <= 4e+112)))
		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, -1.7e+22], N[Not[LessEqual[z, 4e+112]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e22 or 3.9999999999999997e112 < z

   1. Initial program 69.2%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around inf 82.4%

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

   if -1.7e22 < z < 3.9999999999999997e112

   1. Initial program 93.5%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in y around inf 85.5%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+22} \lor \neg \left(z \leq 4 \cdot 10^{+112}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+168} \lor \neg \left(y \leq 9.6 \cdot 10^{+93}\right):\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.7e+168) (not (<= y 9.6e+93))) (* y (/ t (- a z))) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.7e+168) || !(y <= 9.6e+93)) {
		tmp = 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 ((y <= (-1.7d+168)) .or. (.not. (y <= 9.6d+93))) then
        tmp = 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 ((y <= -1.7e+168) || !(y <= 9.6e+93)) {
		tmp = y * (t / (a - z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.7e+168) or not (y <= 9.6e+93):
		tmp = y * (t / (a - z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.7e+168) || !(y <= 9.6e+93))
		tmp = 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 ((y <= -1.7e+168) || ~((y <= 9.6e+93)))
		tmp = y * (t / (a - z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.7e+168], N[Not[LessEqual[y, 9.6e+93]], $MachinePrecision]], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.70000000000000001e168 or 9.60000000000000042e93 < y

   1. Initial program 80.2%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around inf 77.3%

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

   6. Taylor expanded in x around 0 51.5%

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

      1. *-commutative 51.5%

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

      2. associate-*r/ 61.7%

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

   8. Simplified 61.7%

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

   if -1.70000000000000001e168 < y < 9.60000000000000042e93

   1. Initial program 84.5%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in z around inf 74.4%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+168} \lor \neg \left(y \leq 9.6 \cdot 10^{+93}\right):\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+22} \lor \neg \left(z \leq 1.5 \cdot 10^{-104}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.4e+22) (not (<= z 1.5e-104))) (+ x t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.4e+22) || !(z <= 1.5e-104)) {
		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 <= (-6.4d+22)) .or. (.not. (z <= 1.5d-104))) 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 <= -6.4e+22) || !(z <= 1.5e-104)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.4e+22) or not (z <= 1.5e-104):
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.4e+22) || !(z <= 1.5e-104))
		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 <= -6.4e+22) || ~((z <= 1.5e-104)))
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.4e+22], N[Not[LessEqual[z, 1.5e-104]], $MachinePrecision]], N[(x + t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.4e22 or 1.5000000000000001e-104 < z

   1. Initial program 76.4%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around inf 75.4%

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

   if -6.4e22 < z < 1.5000000000000001e-104

   1. Initial program 92.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 58.4%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+22} \lor \neg \left(z \leq 1.5 \cdot 10^{-104}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+120}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+237}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.55e+120) t (if (<= t 1.7e+237) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.55e+120) {
		tmp = t;
	} else if (t <= 1.7e+237) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.55d+120)) then
        tmp = t
    else if (t <= 1.7d+237) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.55e+120) {
		tmp = t;
	} else if (t <= 1.7e+237) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.55e+120:
		tmp = t
	elif t <= 1.7e+237:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.55e+120)
		tmp = t;
	elseif (t <= 1.7e+237)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.55e+120)
		tmp = t;
	elseif (t <= 1.7e+237)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.55e+120], t, If[LessEqual[t, 1.7e+237], x, t]]

Derivation

1. Split input into 2 regimes

2. if t < -2.55000000000000014e120 or 1.7000000000000002e237 < t

   1. Initial program 49.6%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in a around 0 62.8%

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

      1. associate-*r/ 62.8%

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

      2. neg-mul-1 62.8%

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

   7. Simplified 62.8%

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

   8. Taylor expanded in y around 0 57.3%

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

      1. associate-+r+ 57.3%

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

      2. mul-1-neg 57.3%

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

      3. unsub-neg 57.3%

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

      4. associate-/l* 68.3%

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

   10. Simplified 68.3%

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

   11. Taylor expanded in t around inf 64.6%

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

   12. Taylor expanded in y around 0 39.6%

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

   if -2.55000000000000014e120 < t < 1.7000000000000002e237

   1. Initial program 91.9%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf 62.8%

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

Alternative 12: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.3%

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

   1. associate-/l* 97.2%

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

3. Simplified 97.2%

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

5. Final simplification 97.2%

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

Alternative 13: 19.0% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.3%

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

   1. associate-/l* 97.2%

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

3. Simplified 97.2%

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

5. Taylor expanded in a around 0 67.6%

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

   1. associate-*r/ 67.6%

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

   2. neg-mul-1 67.6%

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

7. Simplified 67.6%

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

8. Taylor expanded in y around 0 67.8%

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

   1. associate-+r+ 67.8%

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

   2. mul-1-neg 67.8%

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

   3. unsub-neg 67.8%

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

   4. associate-/l* 67.8%

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

10. Simplified 67.8%

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

11. Taylor expanded in t around inf 31.0%

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

12. Taylor expanded in y around 0 19.0%

    \[\leadsto \color{blue}{t} \]
13. Add Preprocessing

Developer target: 99.3% 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 2024086 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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