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

Percentage Accurate: 85.8% → 99.6%

Time: 9.2s

Alternatives: 12

Speedup: 0.3×

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: 85.8% 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: 99.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+285}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+285)))
     (fma (/ y (- z a)) (- z t) x)
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+285)) {
		tmp = fma((y / (z - a)), (z - t), x);
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+285))
		tmp = fma(Float64(y / Float64(z - a)), Float64(z - t), x);
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+285]], $MachinePrecision]], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision] + x), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 5.00000000000000016e285 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 39.6%

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

      1. +-commutative 39.6%

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

      2. associate-*l/ 100.0%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 5.00000000000000016e285

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 5 \cdot 10^{+285}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+288}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+288)))
     (+ x (/ y (/ z (- z t))))
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+288)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+288)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+288):
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+288))
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+288)))
		tmp = x + (y / (z / (z - t)));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+288]], $MachinePrecision]], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 1e288 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 38.6%

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

   3. Taylor expanded in a around 0 33.3%

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

      1. +-commutative 33.3%

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

      2. associate-/l* 82.1%

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

   5. Simplified 82.1%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 1e288

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 10^{+288}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+285}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+285)))
     (+ x (/ (- z t) (/ (- z a) y)))
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+285)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+285)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+285):
		tmp = x + ((z - t) / ((z - a) / y))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+285))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+285)))
		tmp = x + ((z - t) / ((z - a) / y));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+285]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 5.00000000000000016e285 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 39.6%

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

      1. *-commutative 39.6%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 5.00000000000000016e285

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 5 \cdot 10^{+285}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{z - a}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-84}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-245}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-76}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y (- z a))))))
   (if (<= z -1.35e+56)
     t_1
     (if (<= z -1.3e-84)
       (- x (/ y (/ z t)))
       (if (<= z -2.4e-245)
         (+ x (/ (* y t) a))
         (if (<= z 2.1e-76) (+ x (* y (/ t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / (z - a)));
	double tmp;
	if (z <= -1.35e+56) {
		tmp = t_1;
	} else if (z <= -1.3e-84) {
		tmp = x - (y / (z / t));
	} else if (z <= -2.4e-245) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.1e-76) {
		tmp = x + (y * (t / a));
	} 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 + (z * (y / (z - a)))
    if (z <= (-1.35d+56)) then
        tmp = t_1
    else if (z <= (-1.3d-84)) then
        tmp = x - (y / (z / t))
    else if (z <= (-2.4d-245)) then
        tmp = x + ((y * t) / a)
    else if (z <= 2.1d-76) then
        tmp = x + (y * (t / a))
    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 + (z * (y / (z - a)));
	double tmp;
	if (z <= -1.35e+56) {
		tmp = t_1;
	} else if (z <= -1.3e-84) {
		tmp = x - (y / (z / t));
	} else if (z <= -2.4e-245) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.1e-76) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / (z - a)))
	tmp = 0
	if z <= -1.35e+56:
		tmp = t_1
	elif z <= -1.3e-84:
		tmp = x - (y / (z / t))
	elif z <= -2.4e-245:
		tmp = x + ((y * t) / a)
	elif z <= 2.1e-76:
		tmp = x + (y * (t / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / Float64(z - a))))
	tmp = 0.0
	if (z <= -1.35e+56)
		tmp = t_1;
	elseif (z <= -1.3e-84)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	elseif (z <= -2.4e-245)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 2.1e-76)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / (z - a)));
	tmp = 0.0;
	if (z <= -1.35e+56)
		tmp = t_1;
	elseif (z <= -1.3e-84)
		tmp = x - (y / (z / t));
	elseif (z <= -2.4e-245)
		tmp = x + ((y * t) / a);
	elseif (z <= 2.1e-76)
		tmp = x + (y * (t / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+56], t$95$1, If[LessEqual[z, -1.3e-84], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-245], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-76], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.35000000000000005e56 or 2.09999999999999992e-76 < z

   1. Initial program 74.4%

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

   3. Taylor expanded in t around 0 69.1%

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

      1. +-commutative 69.1%

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

      2. associate-*l/ 85.1%

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

      3. *-commutative 85.1%

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

   5. Simplified 85.1%

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

   if -1.35000000000000005e56 < z < -1.3e-84

   1. Initial program 92.6%

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

   3. Taylor expanded in a around 0 78.2%

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

   4. Taylor expanded in z around 0 84.9%

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

      1. associate-*r/ 84.9%

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

      2. *-commutative 84.9%

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

      3. neg-mul-1 84.9%

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

      4. distribute-lft-neg-in 84.9%

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

      5. associate-/l* 84.9%

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

   6. Simplified 84.9%

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

   if -1.3e-84 < z < -2.4e-245

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 83.7%

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

   if -2.4e-245 < z < 2.09999999999999992e-76

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0 84.3%

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

      1. +-commutative 84.3%

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

      2. associate-/l* 83.6%

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

      3. associate-/r/ 85.7%

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

   5. Simplified 85.7%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+56}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-84}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-245}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-76}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+100}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-84}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-76}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e+100)
   (+ y x)
   (if (<= z -1.3e-84)
     (- x (* y (/ t z)))
     (if (<= z 6.8e-76) (+ x (* y (/ t a))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+100) {
		tmp = y + x;
	} else if (z <= -1.3e-84) {
		tmp = x - (y * (t / z));
	} else if (z <= 6.8e-76) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + 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 <= (-6.8d+100)) then
        tmp = y + x
    else if (z <= (-1.3d-84)) then
        tmp = x - (y * (t / z))
    else if (z <= 6.8d-76) then
        tmp = x + (y * (t / a))
    else
        tmp = y + 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 <= -6.8e+100) {
		tmp = y + x;
	} else if (z <= -1.3e-84) {
		tmp = x - (y * (t / z));
	} else if (z <= 6.8e-76) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e+100:
		tmp = y + x
	elif z <= -1.3e-84:
		tmp = x - (y * (t / z))
	elif z <= 6.8e-76:
		tmp = x + (y * (t / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e+100)
		tmp = Float64(y + x);
	elseif (z <= -1.3e-84)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (z <= 6.8e-76)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.8e+100)
		tmp = y + x;
	elseif (z <= -1.3e-84)
		tmp = x - (y * (t / z));
	elseif (z <= 6.8e-76)
		tmp = x + (y * (t / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e+100], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.3e-84], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-76], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999988e100 or 6.7999999999999998e-76 < z

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf 84.4%

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

      1. +-commutative 84.4%

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

   5. Simplified 84.4%

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

   if -6.79999999999999988e100 < z < -1.3e-84

   1. Initial program 88.5%

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

   3. Taylor expanded in a around 0 74.3%

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

   4. Taylor expanded in z around 0 76.3%

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

      1. associate-*r/ 76.3%

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

      2. *-commutative 76.3%

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

      3. neg-mul-1 76.3%

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

      4. distribute-lft-neg-in 76.3%

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

      5. associate-/l* 78.6%

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

   6. Simplified 78.6%

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

   7. Taylor expanded in x around 0 76.3%

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

      1. mul-1-neg 76.3%

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

      2. associate-*l/ 78.6%

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

      3. distribute-lft-neg-out 78.6%

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

      4. *-commutative 78.6%

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

      5. distribute-rgt-neg-in 78.6%

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

      6. sub-neg 78.6%

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

   9. Simplified 78.6%

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

   if -1.3e-84 < z < 6.7999999999999998e-76

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 84.1%

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

      1. +-commutative 84.1%

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

      2. associate-/l* 81.5%

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

      3. associate-/r/ 84.4%

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

   5. Simplified 84.4%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+100}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-84}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-76}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+100}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-73}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e+100)
   (+ y x)
   (if (<= z -1.85e-82)
     (- x (/ y (/ z t)))
     (if (<= z 1.9e-73) (+ x (* y (/ t a))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+100) {
		tmp = y + x;
	} else if (z <= -1.85e-82) {
		tmp = x - (y / (z / t));
	} else if (z <= 1.9e-73) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + 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 <= (-5.2d+100)) then
        tmp = y + x
    else if (z <= (-1.85d-82)) then
        tmp = x - (y / (z / t))
    else if (z <= 1.9d-73) then
        tmp = x + (y * (t / a))
    else
        tmp = y + 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 <= -5.2e+100) {
		tmp = y + x;
	} else if (z <= -1.85e-82) {
		tmp = x - (y / (z / t));
	} else if (z <= 1.9e-73) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e+100:
		tmp = y + x
	elif z <= -1.85e-82:
		tmp = x - (y / (z / t))
	elif z <= 1.9e-73:
		tmp = x + (y * (t / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e+100)
		tmp = Float64(y + x);
	elseif (z <= -1.85e-82)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	elseif (z <= 1.9e-73)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.2e+100)
		tmp = y + x;
	elseif (z <= -1.85e-82)
		tmp = x - (y / (z / t));
	elseif (z <= 1.9e-73)
		tmp = x + (y * (t / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e+100], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.85e-82], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-73], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2000000000000003e100 or 1.9000000000000001e-73 < z

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf 84.4%

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

      1. +-commutative 84.4%

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

   5. Simplified 84.4%

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

   if -5.2000000000000003e100 < z < -1.85e-82

   1. Initial program 88.5%

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

   3. Taylor expanded in a around 0 74.3%

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

   4. Taylor expanded in z around 0 76.3%

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

      1. associate-*r/ 76.3%

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

      2. *-commutative 76.3%

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

      3. neg-mul-1 76.3%

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

      4. distribute-lft-neg-in 76.3%

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

      5. associate-/l* 78.6%

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

   6. Simplified 78.6%

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

   if -1.85e-82 < z < 1.9000000000000001e-73

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 84.1%

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

      1. +-commutative 84.1%

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

      2. associate-/l* 81.5%

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

      3. associate-/r/ 84.4%

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

   5. Simplified 84.4%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+100}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-73}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-82} \lor \neg \left(z \leq 0.032\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.85e-82) (not (<= z 0.032)))
   (+ x (/ y (/ z (- z t))))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e-82) || !(z <= 0.032)) {
		tmp = x + (y / (z / (z - t)));
	} 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 <= (-1.85d-82)) .or. (.not. (z <= 0.032d0))) then
        tmp = x + (y / (z / (z - t)))
    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 <= -1.85e-82) || !(z <= 0.032)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.85e-82) or not (z <= 0.032):
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.85e-82) || !(z <= 0.032))
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	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 <= -1.85e-82) || ~((z <= 0.032)))
		tmp = x + (y / (z / (z - t)));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.85e-82], N[Not[LessEqual[z, 0.032]], $MachinePrecision]], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85e-82 or 0.032000000000000001 < z

   1. Initial program 75.7%

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

   3. Taylor expanded in a around 0 67.6%

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

      1. +-commutative 67.6%

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

      2. associate-/l* 87.9%

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

   5. Simplified 87.9%

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

   if -1.85e-82 < z < 0.032000000000000001

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0 84.4%

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

      1. +-commutative 84.4%

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

      2. associate-/l* 82.3%

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

      3. associate-/r/ 84.7%

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

   5. Simplified 84.7%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-82} \lor \neg \left(z \leq 0.032\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-52} \lor \neg \left(z \leq 4.2 \cdot 10^{-73}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.8e-52) (not (<= z 4.2e-73))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.8e-52) || !(z <= 4.2e-73)) {
		tmp = y + x;
	} 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 <= (-6.8d-52)) .or. (.not. (z <= 4.2d-73))) then
        tmp = y + x
    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 <= -6.8e-52) || !(z <= 4.2e-73)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.8e-52) or not (z <= 4.2e-73):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.8e-52) || !(z <= 4.2e-73))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.8e-52) || ~((z <= 4.2e-73)))
		tmp = y + x;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.8e-52], N[Not[LessEqual[z, 4.2e-73]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.80000000000000035e-52 or 4.1999999999999997e-73 < z

   1. Initial program 76.9%

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

   3. Taylor expanded in z around inf 77.0%

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

      1. +-commutative 77.0%

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

   5. Simplified 77.0%

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

   if -6.80000000000000035e-52 < z < 4.1999999999999997e-73

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 83.6%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-52} \lor \neg \left(z \leq 4.2 \cdot 10^{-73}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-19} \lor \neg \left(z \leq 4 \cdot 10^{-73}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.85e-19) (not (<= z 4e-73))) (+ y x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e-19) || !(z <= 4e-73)) {
		tmp = y + x;
	} 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 <= (-1.85d-19)) .or. (.not. (z <= 4d-73))) then
        tmp = y + x
    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 <= -1.85e-19) || !(z <= 4e-73)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.85e-19) or not (z <= 4e-73):
		tmp = y + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.85e-19) || !(z <= 4e-73))
		tmp = Float64(y + x);
	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 <= -1.85e-19) || ~((z <= 4e-73)))
		tmp = y + x;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.85e-19], N[Not[LessEqual[z, 4e-73]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85000000000000003e-19 or 3.99999999999999999e-73 < z

   1. Initial program 77.3%

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

   3. Taylor expanded in z around inf 78.6%

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

      1. +-commutative 78.6%

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

   5. Simplified 78.6%

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

   if -1.85000000000000003e-19 < z < 3.99999999999999999e-73

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-/l* 79.3%

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

      3. associate-/r/ 82.0%

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

   5. Simplified 82.0%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-19} \lor \neg \left(z \leq 4 \cdot 10^{-73}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+55} \lor \neg \left(z \leq 4.7 \cdot 10^{-74}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.02e+55) (not (<= z 4.7e-74))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.02e+55) || !(z <= 4.7e-74)) {
		tmp = y + x;
	} 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 <= (-1.02d+55)) .or. (.not. (z <= 4.7d-74))) then
        tmp = y + x
    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 <= -1.02e+55) || !(z <= 4.7e-74)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.02e+55) or not (z <= 4.7e-74):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.02e+55) || !(z <= 4.7e-74))
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.02e+55) || ~((z <= 4.7e-74)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.02e+55], N[Not[LessEqual[z, 4.7e-74]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.02000000000000002e55 or 4.7000000000000001e-74 < z

   1. Initial program 74.4%

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

   3. Taylor expanded in z around inf 81.6%

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

      1. +-commutative 81.6%

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

   5. Simplified 81.6%

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

   if -1.02000000000000002e55 < z < 4.7000000000000001e-74

   1. Initial program 97.6%

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

   3. Taylor expanded in x around inf 59.7%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+55} \lor \neg \left(z \leq 4.7 \cdot 10^{-74}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+239}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+188}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.6e+239) y (if (<= y 5.1e+188) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.6e+239) {
		tmp = y;
	} else if (y <= 5.1e+188) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.6d+239)) then
        tmp = y
    else if (y <= 5.1d+188) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.6e+239) {
		tmp = y;
	} else if (y <= 5.1e+188) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.6e+239:
		tmp = y
	elif y <= 5.1e+188:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.6e+239)
		tmp = y;
	elseif (y <= 5.1e+188)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.6e+239)
		tmp = y;
	elseif (y <= 5.1e+188)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.6e+239], y, If[LessEqual[y, 5.1e+188], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6000000000000002e239 or 5.1000000000000002e188 < y

   1. Initial program 60.4%

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

   3. Taylor expanded in x around 0 50.7%

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

   4. Taylor expanded in z around inf 47.4%

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

   if -2.6000000000000002e239 < y < 5.1000000000000002e188

   1. Initial program 90.5%

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

   3. Taylor expanded in x around inf 66.0%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+239}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+188}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.6% 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 85.6%

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

3. Taylor expanded in x around inf 57.5%

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

4. Final simplification 57.5%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.5% 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 2024018 
(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))))