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

Percentage Accurate: 85.7% → 98.1%

Time: 9.2s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.8%

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

   1. *-commutative 90.8%

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

   2. associate-*l/ 98.8%

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

3. Applied egg-rr 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 80.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -210000000 \lor \neg \left(z \leq 8.5 \cdot 10^{-10}\right):\\ \;\;\;\;x - \frac{t - z}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -210000000.0) (not (<= z 8.5e-10)))
   (- x (/ (- t z) (/ z y)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -210000000.0) || !(z <= 8.5e-10)) {
		tmp = x - ((t - z) / (z / y));
	} 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 <= (-210000000.0d0)) .or. (.not. (z <= 8.5d-10))) then
        tmp = x - ((t - z) / (z / y))
    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 <= -210000000.0) || !(z <= 8.5e-10)) {
		tmp = x - ((t - z) / (z / y));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -210000000.0) or not (z <= 8.5e-10):
		tmp = x - ((t - z) / (z / y))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -210000000.0) || !(z <= 8.5e-10))
		tmp = Float64(x - Float64(Float64(t - z) / Float64(z / y)));
	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 <= -210000000.0) || ~((z <= 8.5e-10)))
		tmp = x - ((t - z) / (z / y));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -210000000.0], N[Not[LessEqual[z, 8.5e-10]], $MachinePrecision]], N[(x - N[(N[(t - z), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1e8 or 8.4999999999999996e-10 < z

   1. Initial program 84.7%

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

      1. *-commutative 84.7%

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

      2. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around inf 80.4%

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

   if -2.1e8 < z < 8.4999999999999996e-10

   1. Initial program 96.0%

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

   2. Taylor expanded in z around 0 82.2%

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

      1. +-commutative 82.2%

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

      2. associate-/l* 85.2%

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

   4. Simplified 85.2%

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

      1. clear-num 85.2%

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

      2. associate-/r/ 85.2%

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

      3. clear-num 85.3%

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

   6. Applied egg-rr 85.3%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -210000000 \lor \neg \left(z \leq 8.5 \cdot 10^{-10}\right):\\ \;\;\;\;x - \frac{t - z}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 3: 80.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-69} \lor \neg \left(z \leq 6.5 \cdot 10^{-10}\right):\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6e-69) (not (<= z 6.5e-10)))
   (+ x (* z (/ y (- z a))))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6e-69) || !(z <= 6.5e-10)) {
		tmp = x + (z * (y / (z - a)));
	} 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 <= (-6d-69)) .or. (.not. (z <= 6.5d-10))) then
        tmp = x + (z * (y / (z - a)))
    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 <= -6e-69) || !(z <= 6.5e-10)) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6e-69) or not (z <= 6.5e-10):
		tmp = x + (z * (y / (z - a)))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6e-69) || !(z <= 6.5e-10))
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	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 <= -6e-69) || ~((z <= 6.5e-10)))
		tmp = x + (z * (y / (z - a)));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6e-69], N[Not[LessEqual[z, 6.5e-10]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.99999999999999978e-69 or 6.5000000000000003e-10 < z

   1. Initial program 85.7%

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

   2. Taylor expanded in t around 0 70.0%

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

      1. +-commutative 70.0%

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

      2. associate-*l/ 78.4%

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

      3. *-commutative 78.4%

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

   4. Simplified 78.4%

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

   if -5.99999999999999978e-69 < z < 6.5000000000000003e-10

   1. Initial program 97.0%

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

   2. Taylor expanded in z around 0 88.9%

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

      1. +-commutative 88.9%

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

      2. associate-/l* 90.9%

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

   4. Simplified 90.9%

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

      1. clear-num 90.9%

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

      2. associate-/r/ 91.0%

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

      3. clear-num 91.0%

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

   6. Applied egg-rr 91.0%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-69} \lor \neg \left(z \leq 6.5 \cdot 10^{-10}\right):\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 4: 79.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-35} \lor \neg \left(a \leq 6.6 \cdot 10^{-122}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2e-35) (not (<= a 6.6e-122)))
   (+ x (* y (/ (- t z) a)))
   (+ x (/ y (/ z (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2e-35) || !(a <= 6.6e-122)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2d-35)) .or. (.not. (a <= 6.6d-122))) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x + (y / (z / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2e-35) || !(a <= 6.6e-122)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2e-35) or not (a <= 6.6e-122):
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + (y / (z / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2e-35) || !(a <= 6.6e-122))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2e-35) || ~((a <= 6.6e-122)))
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + (y / (z / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2e-35], N[Not[LessEqual[a, 6.6e-122]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.00000000000000002e-35 or 6.59999999999999999e-122 < a

   1. Initial program 89.7%

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

   2. Taylor expanded in a around inf 79.9%

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

      1. mul-1-neg 79.9%

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

      2. unsub-neg 79.9%

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

      3. associate-/l* 86.7%

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

   4. Simplified 86.7%

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

      1. clear-num 86.6%

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

      2. associate-/r/ 86.7%

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

      3. clear-num 86.7%

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

   6. Applied egg-rr 86.7%

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

   if -2.00000000000000002e-35 < a < 6.59999999999999999e-122

   1. Initial program 92.8%

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

   2. Taylor expanded in a around 0 81.9%

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

      1. +-commutative 81.9%

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

      2. associate-/l* 88.0%

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

   4. Simplified 88.0%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-35} \lor \neg \left(a \leq 6.6 \cdot 10^{-122}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 5: 78.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-12}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-122}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.25e-12)
   (+ x (* z (/ y (- z a))))
   (if (<= a 6.6e-122) (+ x (/ y (/ z (- z t)))) (+ x (/ y (/ a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.25e-12) {
		tmp = x + (z * (y / (z - a)));
	} else if (a <= 6.6e-122) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + (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 (a <= (-1.25d-12)) then
        tmp = x + (z * (y / (z - a)))
    else if (a <= 6.6d-122) then
        tmp = x + (y / (z / (z - t)))
    else
        tmp = x + (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 (a <= -1.25e-12) {
		tmp = x + (z * (y / (z - a)));
	} else if (a <= 6.6e-122) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.25e-12:
		tmp = x + (z * (y / (z - a)))
	elif a <= 6.6e-122:
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.25e-12)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	elseif (a <= 6.6e-122)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.25e-12)
		tmp = x + (z * (y / (z - a)));
	elseif (a <= 6.6e-122)
		tmp = x + (y / (z / (z - t)));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.25e-12], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.6e-122], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.24999999999999992e-12

   1. Initial program 89.4%

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

   2. Taylor expanded in t around 0 78.9%

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

      1. +-commutative 78.9%

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

      2. associate-*l/ 84.3%

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

      3. *-commutative 84.3%

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

   4. Simplified 84.3%

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

   if -1.24999999999999992e-12 < a < 6.59999999999999999e-122

   1. Initial program 93.1%

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

   2. Taylor expanded in a around 0 80.8%

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

      1. +-commutative 80.8%

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

      2. associate-/l* 86.6%

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

   4. Simplified 86.6%

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

   if 6.59999999999999999e-122 < a

   1. Initial program 89.3%

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

   2. Taylor expanded in z around 0 78.5%

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

      1. +-commutative 78.5%

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

      2. associate-/l* 82.8%

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

   4. Simplified 82.8%

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

      1. clear-num 82.9%

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

      2. associate-/r/ 82.8%

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

      3. clear-num 83.1%

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

   6. Applied egg-rr 83.1%

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

      1. associate-*l/ 78.5%

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

      2. associate-/l* 84.4%

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

   8. Applied egg-rr 84.4%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-12}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-122}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 6: 79.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-36}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-122}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.5e-36)
   (+ x (* y (/ (- t z) a)))
   (if (<= a 6.6e-122) (+ x (/ y (/ z (- z t)))) (- x (/ y (/ a (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e-36) {
		tmp = x + (y * ((t - z) / a));
	} else if (a <= 6.6e-122) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x - (y / (a / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.5d-36)) then
        tmp = x + (y * ((t - z) / a))
    else if (a <= 6.6d-122) then
        tmp = x + (y / (z / (z - t)))
    else
        tmp = x - (y / (a / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e-36) {
		tmp = x + (y * ((t - z) / a));
	} else if (a <= 6.6e-122) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x - (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.5e-36:
		tmp = x + (y * ((t - z) / a))
	elif a <= 6.6e-122:
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = x - (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.5e-36)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	elseif (a <= 6.6e-122)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	else
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.5e-36)
		tmp = x + (y * ((t - z) / a));
	elseif (a <= 6.6e-122)
		tmp = x + (y / (z / (z - t)));
	else
		tmp = x - (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.5e-36], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.6e-122], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5000000000000001e-36

   1. Initial program 90.0%

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

   2. Taylor expanded in a around inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. unsub-neg 78.3%

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

      3. associate-/l* 84.8%

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

   4. Simplified 84.8%

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

      1. clear-num 84.8%

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

      2. associate-/r/ 84.8%

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

      3. clear-num 84.9%

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

   6. Applied egg-rr 84.9%

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

   if -1.5000000000000001e-36 < a < 6.59999999999999999e-122

   1. Initial program 92.8%

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

   2. Taylor expanded in a around 0 81.9%

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

      1. +-commutative 81.9%

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

      2. associate-/l* 88.0%

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

   4. Simplified 88.0%

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

   if 6.59999999999999999e-122 < a

   1. Initial program 89.3%

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

   2. Taylor expanded in a around inf 81.6%

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

      1. mul-1-neg 81.6%

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

      2. unsub-neg 81.6%

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

      3. associate-/l* 88.6%

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

   4. Simplified 88.6%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-36}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-122}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 7: 62.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+42} \lor \neg \left(z \leq 105000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.4e+42) (not (<= z 105000.0))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e+42) || !(z <= 105000.0)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.4d+42)) .or. (.not. (z <= 105000.0d0))) then
        tmp = x + y
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e+42) || !(z <= 105000.0)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.4e+42) or not (z <= 105000.0):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.4e+42) || !(z <= 105000.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.4e+42) || ~((z <= 105000.0)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.4e+42], N[Not[LessEqual[z, 105000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3999999999999999e42 or 105000 < z

   1. Initial program 83.7%

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

   2. Taylor expanded in z around inf 77.4%

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

      1. +-commutative 77.4%

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

   4. Simplified 77.4%

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

   if -2.3999999999999999e42 < z < 105000

   1. Initial program 96.2%

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

   2. Taylor expanded in a around inf 83.1%

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

      1. mul-1-neg 83.1%

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

      2. unsub-neg 83.1%

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

      3. associate-/l* 86.0%

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

   4. Simplified 86.0%

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

   5. Taylor expanded in z around inf 56.7%

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

      1. associate-/l* 56.7%

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

      2. associate-/r/ 58.5%

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

   7. Applied egg-rr 58.5%

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

      1. sub-neg 58.5%

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

      2. associate-*l/ 56.7%

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

      3. associate-*r/ 56.7%

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

      4. distribute-rgt-neg-out 56.7%

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

      5. add-sqr-sqrt 34.7%

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

      6. sqrt-unprod 52.9%

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

      7. sqr-neg 52.9%

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

      8. sqrt-unprod 34.9%

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

      9. add-sqr-sqrt 52.8%

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

      10. associate-*r/ 52.8%

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

      11. associate-*l/ 58.0%

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

      12. *-commutative 58.0%

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

   9. Applied egg-rr 58.0%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+42} \lor \neg \left(z \leq 105000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 75.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+43} \lor \neg \left(z \leq 1.25 \cdot 10^{-9}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.8e+43) (not (<= z 1.25e-9))) (+ x y) (+ x (/ (* t y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e+43) || !(z <= 1.25e-9)) {
		tmp = x + y;
	} 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 <= (-4.8d+43)) .or. (.not. (z <= 1.25d-9))) then
        tmp = x + y
    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 <= -4.8e+43) || !(z <= 1.25e-9)) {
		tmp = x + y;
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.8e+43) or not (z <= 1.25e-9):
		tmp = x + y
	else:
		tmp = x + ((t * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.8e+43) || !(z <= 1.25e-9))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(t * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.8e+43) || ~((z <= 1.25e-9)))
		tmp = x + y;
	else
		tmp = x + ((t * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.8e+43], N[Not[LessEqual[z, 1.25e-9]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.80000000000000046e43 or 1.25e-9 < z

   1. Initial program 84.0%

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

   2. Taylor expanded in z around inf 76.1%

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

      1. +-commutative 76.1%

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

   4. Simplified 76.1%

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

   if -4.80000000000000046e43 < z < 1.25e-9

   1. Initial program 96.2%

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

   2. Taylor expanded in z around 0 80.9%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+43} \lor \neg \left(z \leq 1.25 \cdot 10^{-9}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \]

Alternative 9: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+42} \lor \neg \left(z \leq 5.2 \cdot 10^{-10}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.06e+42) (not (<= z 5.2e-10))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.06e+42) || !(z <= 5.2e-10)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.06d+42)) .or. (.not. (z <= 5.2d-10))) then
        tmp = x + y
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.06e+42) || !(z <= 5.2e-10)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.06e+42) or not (z <= 5.2e-10):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.06e+42) || !(z <= 5.2e-10))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.06e+42) || ~((z <= 5.2e-10)))
		tmp = x + y;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.06e+42], N[Not[LessEqual[z, 5.2e-10]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0599999999999999e42 or 5.19999999999999962e-10 < z

   1. Initial program 84.0%

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

   2. Taylor expanded in z around inf 76.1%

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

      1. +-commutative 76.1%

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

   4. Simplified 76.1%

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

   if -1.0599999999999999e42 < z < 5.19999999999999962e-10

   1. Initial program 96.2%

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

   2. Taylor expanded in z around 0 80.9%

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

      1. +-commutative 80.9%

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

      2. associate-/l* 83.8%

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

   4. Simplified 83.8%

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

      1. associate-/r/ 83.2%

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

   6. Applied egg-rr 83.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+42} \lor \neg \left(z \leq 5.2 \cdot 10^{-10}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 10: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+42} \lor \neg \left(z \leq 9.5 \cdot 10^{-10}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e+42) (not (<= z 9.5e-10))) (+ x y) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e+42) || !(z <= 9.5e-10)) {
		tmp = x + y;
	} 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 <= (-3.5d+42)) .or. (.not. (z <= 9.5d-10))) then
        tmp = x + y
    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 <= -3.5e+42) || !(z <= 9.5e-10)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.5e+42) or not (z <= 9.5e-10):
		tmp = x + y
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.5e+42) || !(z <= 9.5e-10))
		tmp = Float64(x + y);
	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 <= -3.5e+42) || ~((z <= 9.5e-10)))
		tmp = x + y;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.5e+42], N[Not[LessEqual[z, 9.5e-10]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.50000000000000023e42 or 9.50000000000000028e-10 < z

   1. Initial program 84.0%

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

   2. Taylor expanded in z around inf 76.1%

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

      1. +-commutative 76.1%

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

   4. Simplified 76.1%

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

   if -3.50000000000000023e42 < z < 9.50000000000000028e-10

   1. Initial program 96.2%

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

   2. Taylor expanded in z around 0 80.9%

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

      1. +-commutative 80.9%

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

      2. associate-/l* 83.8%

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

   4. Simplified 83.8%

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

      1. clear-num 83.8%

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

      2. associate-/r/ 83.8%

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

      3. clear-num 83.8%

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

   6. Applied egg-rr 83.8%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+42} \lor \neg \left(z \leq 9.5 \cdot 10^{-10}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 11: 62.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+41} \lor \neg \left(z \leq 0.0009\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.7e+41) (not (<= z 0.0009))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e+41) || !(z <= 0.0009)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.7d+41)) .or. (.not. (z <= 0.0009d0))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e+41) || !(z <= 0.0009)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.7e+41) or not (z <= 0.0009):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.7e+41) || !(z <= 0.0009))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.7e+41) || ~((z <= 0.0009)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.7e+41], N[Not[LessEqual[z, 0.0009]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.69999999999999999e41 or 8.9999999999999998e-4 < z

   1. Initial program 83.8%

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

   2. Taylor expanded in z around inf 76.7%

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

      1. +-commutative 76.7%

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

   4. Simplified 76.7%

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

   if -1.69999999999999999e41 < z < 8.9999999999999998e-4

   1. Initial program 96.2%

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

   2. Taylor expanded in x around inf 52.1%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+41} \lor \neg \left(z \leq 0.0009\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 50.9% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.8%

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

2. Taylor expanded in x around inf 52.9%

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

3. Final simplification 52.9%

   \[\leadsto x \]

Developer target: 98.2% accurate, 1.0× speedup

Math

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

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(y / Float64(Float64(z - a) / Float64(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[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023322 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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