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

Percentage Accurate: 98.1% → 98.6%

Time: 13.0s

Alternatives: 16

Speedup: 0.6×

Specification

Math

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

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

Initial Program: 98.1% accurate, 1.0× speedup

Math

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

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

Alternative 1: 98.6% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 (- INFINITY)) (* t (/ (- y) (- z a))) (fma y t_1 x))))

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t * N[((-y) / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -inf.0

   1. Initial program 6.7%

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

   2. Taylor expanded in t around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. associate-*r* 100.0%

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

      3. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-*r/ 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. cancel-sign-sub-inv 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. associate-*r/ 100.0%

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

   10. Simplified 100.0%

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

   if -inf.0 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 98.8%

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

      1. +-commutative 98.8%

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

      2. fma-def 98.8%

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

   3. Simplified 98.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -\infty:\\ \;\;\;\;t \cdot \frac{-y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)\\ \end{array} \]

Alternative 2: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t \cdot \frac{-y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t_1 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 (- INFINITY)) (* t (/ (- y) (- z a))) (+ x (* t_1 y)))))

C

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

Java

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

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t * (-y / (z - a))
	else:
		tmp = x + (t_1 * y)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t * N[((-y) / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -inf.0

   1. Initial program 6.7%

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

   2. Taylor expanded in t around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. associate-*r* 100.0%

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

      3. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-*r/ 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. cancel-sign-sub-inv 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. associate-*r/ 100.0%

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

   10. Simplified 100.0%

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

   if -inf.0 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 98.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -\infty:\\ \;\;\;\;t \cdot \frac{-y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{z - a} \cdot y\\ \end{array} \]

Alternative 3: 76.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+19}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-137}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+205}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e+19)
   (+ y x)
   (if (<= z 2.6e-137)
     (+ x (/ y (/ a t)))
     (if (<= z 1.45e+205) (+ x (/ (* (- z t) y) z)) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+19) {
		tmp = y + x;
	} else if (z <= 2.6e-137) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.45e+205) {
		tmp = x + (((z - t) * y) / z);
	} 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 <= (-2.8d+19)) then
        tmp = y + x
    else if (z <= 2.6d-137) then
        tmp = x + (y / (a / t))
    else if (z <= 1.45d+205) then
        tmp = x + (((z - t) * y) / z)
    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 <= -2.8e+19) {
		tmp = y + x;
	} else if (z <= 2.6e-137) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.45e+205) {
		tmp = x + (((z - t) * y) / z);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8e+19:
		tmp = y + x
	elif z <= 2.6e-137:
		tmp = x + (y / (a / t))
	elif z <= 1.45e+205:
		tmp = x + (((z - t) * y) / z)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e+19)
		tmp = Float64(y + x);
	elseif (z <= 2.6e-137)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 1.45e+205)
		tmp = Float64(x + Float64(Float64(Float64(z - t) * y) / z));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.8e+19)
		tmp = y + x;
	elseif (z <= 2.6e-137)
		tmp = x + (y / (a / t));
	elseif (z <= 1.45e+205)
		tmp = x + (((z - t) * y) / z);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e+19], N[(y + x), $MachinePrecision], If[LessEqual[z, 2.6e-137], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+205], N[(x + N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e19 or 1.4500000000000001e205 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 84.3%

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

      1. +-commutative 84.3%

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

   4. Simplified 84.3%

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

   if -2.8e19 < z < 2.6e-137

   1. Initial program 94.3%

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

   2. Taylor expanded in z around 0 82.7%

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

      1. +-commutative 82.7%

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

      2. associate-/l* 81.8%

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

      3. associate-/r/ 84.4%

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

   4. Simplified 84.4%

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

      1. *-commutative 84.4%

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

      2. clear-num 84.4%

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

      3. un-div-inv 84.7%

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

   6. Applied egg-rr 84.7%

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

   if 2.6e-137 < z < 1.4500000000000001e205

   1. Initial program 97.3%

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

   2. Taylor expanded in a around 0 72.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+19}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-137}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+205}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 4: 78.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+18}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+205}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+18)
   (+ x (* z (/ y (- z a))))
   (if (<= z 3.05e-133)
     (+ x (/ y (/ a t)))
     (if (<= z 1.45e+205) (+ x (/ (* (- z t) y) z)) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+18) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 3.05e-133) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.45e+205) {
		tmp = x + (((z - t) * y) / z);
	} 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 <= (-1.2d+18)) then
        tmp = x + (z * (y / (z - a)))
    else if (z <= 3.05d-133) then
        tmp = x + (y / (a / t))
    else if (z <= 1.45d+205) then
        tmp = x + (((z - t) * y) / z)
    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 <= -1.2e+18) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 3.05e-133) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.45e+205) {
		tmp = x + (((z - t) * y) / z);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e+18:
		tmp = x + (z * (y / (z - a)))
	elif z <= 3.05e-133:
		tmp = x + (y / (a / t))
	elif z <= 1.45e+205:
		tmp = x + (((z - t) * y) / z)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+18)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	elseif (z <= 3.05e-133)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 1.45e+205)
		tmp = Float64(x + Float64(Float64(Float64(z - t) * y) / z));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e+18)
		tmp = x + (z * (y / (z - a)));
	elseif (z <= 3.05e-133)
		tmp = x + (y / (a / t));
	elseif (z <= 1.45e+205)
		tmp = x + (((z - t) * y) / z);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+18], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.05e-133], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+205], N[(x + N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.2e18

   1. Initial program 99.9%

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

      1. associate-*r/ 70.8%

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

   3. Simplified 70.8%

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

      1. clear-num 70.7%

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

      2. associate-/r/ 70.8%

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

   5. Applied egg-rr 70.8%

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

   6. Taylor expanded in t around 0 63.4%

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

      1. +-commutative 63.4%

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

      2. associate-*l/ 84.1%

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

      3. *-commutative 84.1%

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

   8. Simplified 84.1%

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

   if -1.2e18 < z < 3.0500000000000002e-133

   1. Initial program 94.3%

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

   2. Taylor expanded in z around 0 82.7%

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

      1. +-commutative 82.7%

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

      2. associate-/l* 81.8%

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

      3. associate-/r/ 84.4%

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

   4. Simplified 84.4%

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

      1. *-commutative 84.4%

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

      2. clear-num 84.4%

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

      3. un-div-inv 84.7%

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

   6. Applied egg-rr 84.7%

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

   if 3.0500000000000002e-133 < z < 1.4500000000000001e205

   1. Initial program 97.3%

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

   2. Taylor expanded in a around 0 72.1%

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

   if 1.4500000000000001e205 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 93.7%

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

      1. +-commutative 93.7%

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

   4. Simplified 93.7%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+18}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+205}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5: 79.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-134}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+215}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ y z)))))
   (if (<= z -7e+20)
     t_1
     (if (<= z 5.6e-134)
       (+ x (/ y (/ a t)))
       (if (<= z 5.5e+215) t_1 (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * (y / z));
	double tmp;
	if (z <= -7e+20) {
		tmp = t_1;
	} else if (z <= 5.6e-134) {
		tmp = x + (y / (a / t));
	} else if (z <= 5.5e+215) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - t) * (y / z))
    if (z <= (-7d+20)) then
        tmp = t_1
    else if (z <= 5.6d-134) then
        tmp = x + (y / (a / t))
    else if (z <= 5.5d+215) then
        tmp = t_1
    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 t_1 = x + ((z - t) * (y / z));
	double tmp;
	if (z <= -7e+20) {
		tmp = t_1;
	} else if (z <= 5.6e-134) {
		tmp = x + (y / (a / t));
	} else if (z <= 5.5e+215) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * (y / z))
	tmp = 0
	if z <= -7e+20:
		tmp = t_1
	elif z <= 5.6e-134:
		tmp = x + (y / (a / t))
	elif z <= 5.5e+215:
		tmp = t_1
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(y / z)))
	tmp = 0.0
	if (z <= -7e+20)
		tmp = t_1;
	elseif (z <= 5.6e-134)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 5.5e+215)
		tmp = t_1;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * (y / z));
	tmp = 0.0;
	if (z <= -7e+20)
		tmp = t_1;
	elseif (z <= 5.6e-134)
		tmp = x + (y / (a / t));
	elseif (z <= 5.5e+215)
		tmp = t_1;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+20], t$95$1, If[LessEqual[z, 5.6e-134], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+215], t$95$1, N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7e20 or 5.5999999999999997e-134 < z < 5.5e215

   1. Initial program 98.5%

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

   2. Taylor expanded in a around 0 68.6%

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

      1. +-commutative 68.6%

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

      2. associate-/l* 81.8%

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

      3. associate-/r/ 80.3%

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

   4. Simplified 80.3%

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

   if -7e20 < z < 5.5999999999999997e-134

   1. Initial program 94.3%

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

   2. Taylor expanded in z around 0 82.7%

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

      1. +-commutative 82.7%

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

      2. associate-/l* 81.8%

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

      3. associate-/r/ 84.4%

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

   4. Simplified 84.4%

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

      1. *-commutative 84.4%

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

      2. clear-num 84.4%

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

      3. un-div-inv 84.7%

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

   6. Applied egg-rr 84.7%

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

   if 5.5e215 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 96.7%

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

      1. +-commutative 96.7%

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

   4. Simplified 96.7%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+20}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-134}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+215}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+21}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-132}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6000:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e+21)
   (+ y x)
   (if (<= z 1.65e-132)
     (+ x (/ y (/ a t)))
     (if (<= z 6000.0) (- x (* t (/ y z))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+21) {
		tmp = y + x;
	} else if (z <= 1.65e-132) {
		tmp = x + (y / (a / t));
	} else if (z <= 6000.0) {
		tmp = x - (t * (y / z));
	} 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 <= (-1.25d+21)) then
        tmp = y + x
    else if (z <= 1.65d-132) then
        tmp = x + (y / (a / t))
    else if (z <= 6000.0d0) then
        tmp = x - (t * (y / z))
    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 <= -1.25e+21) {
		tmp = y + x;
	} else if (z <= 1.65e-132) {
		tmp = x + (y / (a / t));
	} else if (z <= 6000.0) {
		tmp = x - (t * (y / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.25e+21:
		tmp = y + x
	elif z <= 1.65e-132:
		tmp = x + (y / (a / t))
	elif z <= 6000.0:
		tmp = x - (t * (y / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.25e+21)
		tmp = Float64(y + x);
	elseif (z <= 1.65e-132)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 6000.0)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.25e+21)
		tmp = y + x;
	elseif (z <= 1.65e-132)
		tmp = x + (y / (a / t));
	elseif (z <= 6000.0)
		tmp = x - (t * (y / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e+21], N[(y + x), $MachinePrecision], If[LessEqual[z, 1.65e-132], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6000.0], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25e21 or 6e3 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 76.3%

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

      1. +-commutative 76.3%

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

   4. Simplified 76.3%

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

   if -1.25e21 < z < 1.6499999999999999e-132

   1. Initial program 94.3%

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

   2. Taylor expanded in z around 0 82.7%

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

      1. +-commutative 82.7%

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

      2. associate-/l* 81.8%

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

      3. associate-/r/ 84.4%

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

   4. Simplified 84.4%

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

      1. *-commutative 84.4%

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

      2. clear-num 84.4%

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

      3. un-div-inv 84.7%

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

   6. Applied egg-rr 84.7%

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

   if 1.6499999999999999e-132 < z < 6e3

   1. Initial program 93.9%

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

   2. Taylor expanded in t around inf 81.6%

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

      1. associate-*r/ 81.6%

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

      2. associate-*r* 81.6%

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

      3. mul-1-neg 81.6%

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

   4. Simplified 81.6%

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

   5. Taylor expanded in z around inf 75.2%

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

      1. mul-1-neg 75.2%

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

      2. unsub-neg 75.2%

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

      3. associate-*r/ 75.3%

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

   7. Simplified 75.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+21}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-132}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6000:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7: 80.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+15} \lor \neg \left(z \leq 1.65 \cdot 10^{-132}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.2e+15) (not (<= z 1.65e-132)))
   (+ 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 ((z <= -8.2e+15) || !(z <= 1.65e-132)) {
		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 ((z <= (-8.2d+15)) .or. (.not. (z <= 1.65d-132))) 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 ((z <= -8.2e+15) || !(z <= 1.65e-132)) {
		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 (z <= -8.2e+15) or not (z <= 1.65e-132):
		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 ((z <= -8.2e+15) || !(z <= 1.65e-132))
		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 ((z <= -8.2e+15) || ~((z <= 1.65e-132)))
		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[Or[LessEqual[z, -8.2e+15], N[Not[LessEqual[z, 1.65e-132]], $MachinePrecision]], 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 2 regimes

2. if z < -8.2e15 or 1.6499999999999999e-132 < z

   1. Initial program 98.7%

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

   2. Taylor expanded in a around 0 63.8%

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

      1. +-commutative 63.8%

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

      2. associate-/l* 84.3%

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

   4. Simplified 84.3%

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

   if -8.2e15 < z < 1.6499999999999999e-132

   1. Initial program 94.3%

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

   2. Taylor expanded in z around 0 82.7%

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

      1. +-commutative 82.7%

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

      2. associate-/l* 81.8%

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

      3. associate-/r/ 84.4%

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

   4. Simplified 84.4%

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

      1. *-commutative 84.4%

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

      2. clear-num 84.4%

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

      3. un-div-inv 84.7%

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

   6. Applied egg-rr 84.7%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+15} \lor \neg \left(z \leq 1.65 \cdot 10^{-132}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 8: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+59} \lor \neg \left(t \leq 4.8 \cdot 10^{-31}\right):\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4e+59) (not (<= t 4.8e-31)))
   (- x (* t (/ y (- z a))))
   (+ x (/ y (/ (- z a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e+59) || !(t <= 4.8e-31)) {
		tmp = x - (t * (y / (z - a)));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4d+59)) .or. (.not. (t <= 4.8d-31))) then
        tmp = x - (t * (y / (z - a)))
    else
        tmp = x + (y / ((z - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e+59) || !(t <= 4.8e-31)) {
		tmp = x - (t * (y / (z - a)));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4e+59) or not (t <= 4.8e-31):
		tmp = x - (t * (y / (z - a)))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4e+59) || !(t <= 4.8e-31))
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4e+59) || ~((t <= 4.8e-31)))
		tmp = x - (t * (y / (z - a)));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4e+59], N[Not[LessEqual[t, 4.8e-31]], $MachinePrecision]], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.99999999999999989e59 or 4.8e-31 < t

   1. Initial program 94.1%

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

   2. Taylor expanded in t around inf 76.9%

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

      1. associate-*r/ 76.9%

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

      2. associate-*r* 76.9%

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

      3. mul-1-neg 76.9%

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

   4. Simplified 76.9%

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

   5. Taylor expanded in x around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. associate-*r/ 87.9%

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

      3. distribute-lft-neg-in 87.9%

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

      4. cancel-sign-sub-inv 87.9%

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

   7. Simplified 87.9%

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

   if -3.99999999999999989e59 < t < 4.8e-31

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 74.7%

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

      1. +-commutative 74.7%

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

      2. associate-/l* 91.7%

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

   4. Simplified 91.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+59} \lor \neg \left(t \leq 4.8 \cdot 10^{-31}\right):\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 9: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+17} \lor \neg \left(z \leq 2.2 \cdot 10^{-25}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.5e+17) (not (<= z 2.2e-25))) (+ y x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e+17) || !(z <= 2.2e-25)) {
		tmp = y + x;
	} 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 <= (-2.5d+17)) .or. (.not. (z <= 2.2d-25))) then
        tmp = y + x
    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 <= -2.5e+17) || !(z <= 2.2e-25)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.5e+17) or not (z <= 2.2e-25):
		tmp = y + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.5e+17) || !(z <= 2.2e-25))
		tmp = Float64(y + x);
	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 <= -2.5e+17) || ~((z <= 2.2e-25)))
		tmp = y + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.5e+17], N[Not[LessEqual[z, 2.2e-25]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5e17 or 2.2000000000000002e-25 < z

   1. Initial program 99.9%

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

   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 -2.5e17 < z < 2.2000000000000002e-25

   1. Initial program 93.8%

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

      1. associate-*r/ 93.7%

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

   3. Simplified 93.7%

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

      1. clear-num 93.7%

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

      2. associate-/r/ 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in z around 0 75.9%

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

      1. associate-*r/ 75.8%

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

   8. Simplified 75.8%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+17} \lor \neg \left(z \leq 2.2 \cdot 10^{-25}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10: 75.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+17} \lor \neg \left(z \leq 1.2 \cdot 10^{-41}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.1e+17) (not (<= z 1.2e-41))) (+ y x) (+ x (/ (* t y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e+17) || !(z <= 1.2e-41)) {
		tmp = y + x;
	} 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 <= (-2.1d+17)) .or. (.not. (z <= 1.2d-41))) then
        tmp = y + x
    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 <= -2.1e+17) || !(z <= 1.2e-41)) {
		tmp = y + x;
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.1e+17) or not (z <= 1.2e-41):
		tmp = y + x
	else:
		tmp = x + ((t * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.1e+17) || !(z <= 1.2e-41))
		tmp = Float64(y + x);
	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 <= -2.1e+17) || ~((z <= 1.2e-41)))
		tmp = y + x;
	else
		tmp = x + ((t * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.1e+17], N[Not[LessEqual[z, 1.2e-41]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1e17 or 1.20000000000000011e-41 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 75.8%

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

      1. +-commutative 75.8%

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

   4. Simplified 75.8%

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

   if -2.1e17 < z < 1.20000000000000011e-41

   1. Initial program 93.7%

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

   2. Taylor expanded in z around 0 76.8%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+17} \lor \neg \left(z \leq 1.2 \cdot 10^{-41}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \]

Alternative 11: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+16} \lor \neg \left(z \leq 8.2 \cdot 10^{-26}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7e+16) (not (<= z 8.2e-26))) (+ y x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7e+16) || !(z <= 8.2e-26)) {
		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 <= (-7d+16)) .or. (.not. (z <= 8.2d-26))) 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 <= -7e+16) || !(z <= 8.2e-26)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7e+16) or not (z <= 8.2e-26):
		tmp = y + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7e+16) || !(z <= 8.2e-26))
		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 <= -7e+16) || ~((z <= 8.2e-26)))
		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, -7e+16], N[Not[LessEqual[z, 8.2e-26]], $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 < -7e16 or 8.1999999999999997e-26 < z

   1. Initial program 99.9%

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

   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 -7e16 < z < 8.1999999999999997e-26

   1. Initial program 93.8%

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

   2. Taylor expanded in z around 0 75.9%

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

      1. +-commutative 75.9%

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

      2. associate-/l* 75.9%

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

      3. associate-/r/ 78.0%

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

   4. Simplified 78.0%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+16} \lor \neg \left(z \leq 8.2 \cdot 10^{-26}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 12: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+16} \lor \neg \left(z \leq 3.9 \cdot 10^{-25}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.1e+16) (not (<= z 3.9e-25))) (+ y x) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e+16) || !(z <= 3.9e-25)) {
		tmp = y + x;
	} 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 ((z <= (-1.1d+16)) .or. (.not. (z <= 3.9d-25))) then
        tmp = y + x
    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 ((z <= -1.1e+16) || !(z <= 3.9e-25)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.1e+16) or not (z <= 3.9e-25):
		tmp = y + x
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.1e+16) || !(z <= 3.9e-25))
		tmp = Float64(y + x);
	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 ((z <= -1.1e+16) || ~((z <= 3.9e-25)))
		tmp = y + x;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.1e+16], N[Not[LessEqual[z, 3.9e-25]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e16 or 3.9e-25 < z

   1. Initial program 99.9%

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

   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 -1.1e16 < z < 3.9e-25

   1. Initial program 93.8%

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

   2. Taylor expanded in z around 0 75.9%

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

      1. +-commutative 75.9%

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

      2. associate-/l* 75.9%

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

      3. associate-/r/ 78.0%

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

   4. Simplified 78.0%

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

      1. *-commutative 78.0%

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

      2. clear-num 78.0%

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

      3. un-div-inv 78.2%

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

   6. Applied egg-rr 78.2%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+16} \lor \neg \left(z \leq 3.9 \cdot 10^{-25}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 13: 61.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+252}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.5e+150)
   (* y (/ t a))
   (if (<= t 2.3e+252) (+ y x) (* y (- (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.5e+150) {
		tmp = y * (t / a);
	} else if (t <= 2.3e+252) {
		tmp = y + x;
	} else {
		tmp = y * -(t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-8.5d+150)) then
        tmp = y * (t / a)
    else if (t <= 2.3d+252) then
        tmp = y + x
    else
        tmp = y * -(t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.5e+150) {
		tmp = y * (t / a);
	} else if (t <= 2.3e+252) {
		tmp = y + x;
	} else {
		tmp = y * -(t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.5e+150:
		tmp = y * (t / a)
	elif t <= 2.3e+252:
		tmp = y + x
	else:
		tmp = y * -(t / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.5e+150)
		tmp = Float64(y * Float64(t / a));
	elseif (t <= 2.3e+252)
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(-Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8.5e+150)
		tmp = y * (t / a);
	elseif (t <= 2.3e+252)
		tmp = y + x;
	else
		tmp = y * -(t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.5e+150], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+252], N[(y + x), $MachinePrecision], N[(y * (-N[(t / z), $MachinePrecision])), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.4999999999999999e150

   1. Initial program 89.8%

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

   2. Taylor expanded in t around inf 77.1%

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

      1. associate-*r/ 77.1%

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

      2. associate-*r* 77.1%

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

      3. mul-1-neg 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in x around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. associate-*r/ 92.3%

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

      3. distribute-lft-neg-in 92.3%

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

      4. cancel-sign-sub-inv 92.3%

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

   7. Simplified 92.3%

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

   8. Taylor expanded in x around 0 55.8%

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

      1. neg-mul-1 55.8%

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

      2. associate-/l* 66.5%

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

      3. distribute-frac-neg 66.5%

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

      4. associate-/r/ 60.8%

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

   10. Simplified 60.8%

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

   11. Taylor expanded in z around 0 45.2%

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

   if -8.4999999999999999e150 < t < 2.3e252

   1. Initial program 99.0%

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

   2. Taylor expanded in z around inf 69.7%

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

      1. +-commutative 69.7%

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

   4. Simplified 69.7%

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

   if 2.3e252 < t

   1. Initial program 85.6%

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

   2. Taylor expanded in t around inf 77.5%

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

      1. associate-*r/ 77.5%

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

      2. associate-*r* 77.5%

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

      3. mul-1-neg 77.5%

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

   4. Simplified 77.5%

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

   5. Taylor expanded in x around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. associate-*r/ 84.8%

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

      3. distribute-lft-neg-in 84.8%

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

      4. cancel-sign-sub-inv 84.8%

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

   7. Simplified 84.8%

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

   8. Taylor expanded in x around 0 63.1%

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

      1. neg-mul-1 63.1%

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

      2. associate-/l* 70.5%

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

      3. distribute-frac-neg 70.5%

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

      4. associate-/r/ 63.6%

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

   10. Simplified 63.6%

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

   11. Taylor expanded in z around inf 62.7%

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

       1. associate-*r/ 62.7%

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

       2. neg-mul-1 62.7%

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

   13. Simplified 62.7%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+252}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \end{array} \]

Alternative 14: 60.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+153}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.7e+153) (* y (/ t a)) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+153) {
		tmp = 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 (t <= (-1.7d+153)) then
        tmp = 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 (t <= -1.7e+153) {
		tmp = y * (t / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.7e+153:
		tmp = y * (t / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.7e+153)
		tmp = 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 (t <= -1.7e+153)
		tmp = y * (t / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.7e+153], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6999999999999999e153

   1. Initial program 89.8%

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

   2. Taylor expanded in t around inf 77.1%

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

      1. associate-*r/ 77.1%

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

      2. associate-*r* 77.1%

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

      3. mul-1-neg 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in x around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. associate-*r/ 92.3%

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

      3. distribute-lft-neg-in 92.3%

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

      4. cancel-sign-sub-inv 92.3%

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

   7. Simplified 92.3%

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

   8. Taylor expanded in x around 0 55.8%

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

      1. neg-mul-1 55.8%

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

      2. associate-/l* 66.5%

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

      3. distribute-frac-neg 66.5%

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

      4. associate-/r/ 60.8%

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

   10. Simplified 60.8%

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

   11. Taylor expanded in z around 0 45.2%

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

   if -1.6999999999999999e153 < t

   1. Initial program 98.2%

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

   2. Taylor expanded in z around inf 67.1%

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

      1. +-commutative 67.1%

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

   4. Simplified 67.1%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+153}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 15: 60.8% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(y + x), $MachinePrecision]

Derivation

1. Initial program 97.0%

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

2. Taylor expanded in z around inf 61.1%

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

   1. +-commutative 61.1%

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

4. Simplified 61.1%

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

5. Final simplification 61.1%

   \[\leadsto y + x \]

Alternative 16: 51.3% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

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

2. Taylor expanded in x around inf 46.6%

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

3. Final simplification 46.6%

   \[\leadsto x \]

Developer target: 98.3% 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 2023310 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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